Eta Flashcards
Polarizability
Polarizability is the extent to which an electron cloud of an atom can be distorted by an external charge or by an applied electric field to produce a dipole.
Electronegativity
It is the tendency of an atom to attract electrons within a bond.
Electron Affinity
It assesses the tendency of an atom to accept an additional electron by measuring the energy change when an electron is added to an atom.
Ionization energy
It is the opposite of electron affinity and measures the energy required to remove an electron from an atom. The smaller the ionization energy, the higher the reactivity.
Important note about Telomeres and Centromeres
Telomeres are regions at chromosomal ends that are repeatedly truncated with each round of cell division. Centromeres join two sister chromatids and are required for proper chromosome division during mitosis. Despite their different chromosomal locations, both telomeres and centromeres are composed of heterochromatin, a tightly condensed complex of DNA wrapped around histones. Because of its structurally restrictive form, heterochromatin is transcriptionally inactive, meaning that proteins responsible for regulating gene expression cannot access the tightly packed DNA. As a result, hetechromatic regions are often gene-poor and contain repetitive DNA.
(Choice A) Telomeres contain repeats of only TTAGGG, a single DNA sequence of six nucleotides that is added by the enzyme telomerase. Multiple repeats of differing DNA sequences are not present in telomeres.
(Choice C) Telomeres are shortened with each round of cell division. However, only embryonic stem cells (not somatic cells) express telomerase and therefore have very long telomeres; this allows them to proliferate indefinitely in a controlled manner.
(Choice D) DNA polymerase, which is responsible for carrying out DNA synthesis, cannot replicate chromosomal ends.
Origin of replication
Prokaryotes typically have circular DNA with a single origin of replication in the cytoplasm whereas eukaryotes have linear DNA with multiple origins of replication in the nucleus. An origin of replication expands to form a replication bubble, which contains two replication forks that move apart in opposite directions during DNA synthesis.
Projection area
Projection areas are areas in the four lobes (frontal, parietal, temporal, occipital) of the brain where sensory processing occurs.
Allport’s Three basic types of Traits
Cardinal
Central
Secondary
Eysenck’s Three Major Traits
Psychoticism
Extraversion
Neuroticism
Big Five Trait Theorists
Openness Conscientiousness Extraversion Agreeableness Neuroticisim
Gas Chromatography
Think the total number of molecular weight and the polarity, in addition to intermolecular attractions
Ionic Radii, Neutral radii, and Isoelectronic species
Ionic radii tend to decrease in size across a period (row) of the periodic table (left to right) and increase moving down a group (column). This trend occurs for metal cations, and then resets and repeats for anions beginning near the division between metals and nonmetals, past which anions tend to preferentially form.
Compared to the neutral atom of a given element, its cation will be smaller but its anion will be larger. Losing electrons to form a cation causes the remaining electrons to experience a greater effective nuclear charge (Zeff), pulling the electrons closer to the nucleus. Conversely, gaining electrons to form an anion produces greater electronic repulsion and nuclear shielding (lesser Zeff), which pushes electrons farther from the nucleus.
Na+, F−, Mg2+, and O2− ions are isoelectronic (have the same number of electrons), but because the number of protons is different in each ion, the electrons in each ion experience a different Zeff. Therefore, in an isoelectronic series, ionic radii decrease with increasing atomic number. Because magnesium has the highest atomic number (greatest number of protons) in the isoelectronic series, Zeff is greatest in this ion, making it the smallest within the given series.
Atomic Mass Unit and Molecular Weight
An atomic mass unit (amu) is defined as one-twelfth of the mass contained in a carbon-12 atom (the average mass of 6 protons and 6 neutrons). On this basis, the amu provides a useful measure for assessing the masses of different atoms relative to the carbon-12 standard.
Mass measurements on the macroscale (grams) must account for a large quantity of amu. For this purpose, a mole is defined as the number of carbon-12 atoms required to yield exactly 12 grams. This number of atoms is called Avogadro’s number (NA) and is equal to 6.022 × 1023 atoms. Because each carbon-12 atom contains 12 amu, the mole can also be viewed as the number of amu required to yield 1 gram of mass.
6.022 × 1023 amu = 1 mol amu = 1 g
The molecular weight of a compound is simply the sum of the amu contributions from each atom in a formula unit. For example, the molecular weight of a single (NH4)2CO3 molecule is 96.11 amu. On the macroscale, 6.022 × 1023 formula units (1 mole) result in the molar mass. Because 1 mole of amu contains 1 gram of mass, the molar mass numerically correlates to the molecular weight but indicates the amount of mass (in grams) contained in 1 mole of the formula unit (grams/mole).
96.11 amu × (1 g / 1 mol amu) = 96.11 g/mol
For (NH4)2CO3, a molecular weight of 96.11 amu means that 1.00 mole of (NH4)2CO3 molecules has a mass of 96.11 g (Number I). Likewise, a 96.11 g sample of (NH4)2CO3 will contain 1 mole (6.022 × 1023 units) of (NH4)2CO3 molecules (Number II). Conversely, 96.11 amu of (NH4)2CO3 refers only to a single molecule of (NH4)2CO3, which does not contain the same mass as a mole of (NH4)2CO3 molecules (Number III).
Electronic Configuration - Interesting Concept
An electron configuration sequentially lists the placement of all electrons within the shells and subshells of an atom or ion in order of increasing energy, according to the Aufbau principle. Subshells are labeled by type (s, p, d, f), which indicates the kind of orbitals present within the subshell. Accordingly, an s subshell contains one s orbital, a p subshell contains three p orbitals, a d subshell contains five d orbitals, and an f subshell contains seven f orbitals.
The Pauli exclusion principle states that each orbital within a subshell can hold a maximum of two electrons, but two electrons in the same orbital must have opposite spins. Therefore, s, p, d, and f subshells can hold a maximum of 2, 6, 10, and 14 electrons, respectively. In schematic diagrams, orbitals are often represented by blanks or boxes, and electrons are represented by arrows. The spin of each electron is indicated by the orientation of the arrow (up or down).
Accordingly, a subshell represented as 3s ↑↑
(Number I) cannot exist because the electrons in the s orbital have the same spin. Likewise, a subshell indicated by 2p7 (Number II) also cannot exist because a p subshell holds a maximum of 6 electrons (two electrons in each of the three p orbitals).
(Number III) 6d ↑↓ ↑ ↑↓ ↑ ↑
is a valid subshell configuration. A d subshell contains five d orbitals of equal energy that together can accommodate up to 10 electrons. Because the d orbitals are equivalent in energy, paired electrons of opposite spin can be placed in any of the five orbitals without distinction.
(Number IV) 4f14 is a correct subshell configuration. An f subshell contains seven f orbitals of equal energy that together can accommodate up to 14 electrons in total.
Bohr’s Model Assumption
In the Bohr model of the atom, several assumptions are made regarding electrons and their locations around the nucleus. The Bohr model asserts that:
- Electrons move around the nucleus in fixed circular orbits, which are only allowed at particular intervals from the nucleus.
- Electrons in orbits farther from the nucleus have higher energy than electrons in orbits closer to the nucleus.
- Energy is absorbed by an electron moving from a lower orbit to a higher orbit, but energy is emitted by an electron returning from a higher orbit back to a lower orbit.
- The energy that is absorbed or emitted by an electron equals the energy difference between two orbits.
Nature of Coordination of d-orbitals
When placed within a coordination sphere, the atomic d orbitals of a metal are no longer degenerate, so they will have different energies. This occurs because some orbitals are pointing toward the ligands, which are electron donors, and other d orbitals are pointing away from or between the ligands. The orbitals that point toward the ligands are higher in energy than the orbitals pointing away from or between them because electrons repel each other. The energy of the orbitals determines which wavelengths of light can be absorbed. Some ligands cause greater differences in the energy of the d orbitals than other ligands, resulting in the absorption of different wavelengths of light. These wavelengths are usually in the visible spectrum.
When heme binds O2, the nature of the O2 ligand changes the energy of iron’s d orbitals. This energy change causes heme to absorb blue-green light and reflect red light.
Further information on Coordination Bonds
Coordinate covalent bonds are a special type of bond between a central atom, such as a metal, and a ligand. Both electrons in the bond come from the ligand. Coordination bonds are neither covalent nor ionic but have some properties of both bond types. The metal ion maintains its oxidation state, as in the case of an ionic bond, and the ligands are not charged but are usually electronegative, as in covalent bonds. The metal and its ligands together form a complex, and the number of coordinate bonds to the metal is known as the coordination number.
The metal ion Fe2+ is positively charged whereas the donor atoms (nitrogen) are neutral, resulting in a net charge of +2 for the complex. Unlike ionic bonds, the donor atoms do not give electrons to the positively charged metal. Instead counterions often surround the complex in solution to balance the metal’s positive charge.
(Choice A) The nitrogen ligands each have a lone pair of electrons that provide the bonding electrons in the coordinate covalent bond.
(Choice C) The lone pairs of nitrogen’s electrons interact with iron’s d orbitals to form the coordinate bond. In a coordination bond, the d orbitals are no longer degenerate and have distinct shapes, some of which point directly at the negatively charged ligands.
(Choice D) The strength of the coordination bond depends on which d orbitals have electrons in them.
Acid-Base Neutralization Reaction
In a titration, a measured amount of a solution with a known concentration (titrant) is added to another solution containing an unknown concentration of the compound to be measured (analyte). In acid-base titrations, an acid is titrated with a base (or vice versa). The resulting acid-base neutralization reaction produces a change in pH, which is monitored by a pH indicator that signals the equivalence point of the neutralization.
The analyte must be fully dissolved before it can be measured. Sebacic acid has low solubility in water due to a high nonpolar hydrocarbon character. A base will convert the carboxylic acid groups into highly polar ionic salts with much higher aqueous solubility.
Once dissolved, the carboxylate ions can then be titrated with an acid. Subtracting the number of moles of base (such as KOH) in the initial solution from the number of moles of acid (such as HCl) required to reach the equivalence point during the titration will give the number of moles of carboxylate groups from sebacic acid in the sample.
(Choices A and B) Sebacic acid is a ten-carbon organic acid and will not significantly dissolve in dilute aqueous acids. Only a base will ionize the carboxylic acid groups and allow the compound to dissolve. Once dissolved, titration of the basic solution should then be performed using an acid.
(Choice C) A dilute base will dissolve the sebacic acid sample, but basic solutions must be titrated with acids rather than with bases.
Educational objective:
Acid-base neutralization reactions can be used in titrations with an indicator to determine the concentration of an acidic (or basic) analyte. By assessing the equivalence point of the neutralization, the volume of titrant required can be correlated to the amount of an analyte present in solution. Acids or bases may also aid the solubility of nonpolar analytes by forming more soluble ionic salts.
Equivalence Point
In an acid-base titration, a measured amount of an acid (or a base) solution (titrant) with a known concentration is slowly added to another solution containing an unknown concentration of a base (or an acid) to be measured. As the titration proceeds, an acid-base neutralization reaction occurs, producing a change in the pH of the solution being titrated.
When the acid (or base) being titrated is fully neutralized, the number of equivalents of acid exactly equals the number of equivalents of base (equivalence point). When passing through this point, the pH changes rapidly. On the titration curve, this is seen as a nearly vertical line, and at its midpoint lies the equivalence point.
To visually detect when a titration is complete, an indicator that has an endpoint (color change) near the pH of the equivalence point can be added to the solution. Different indicators change color across a particular pH range (endpoint range). The best indicator for a given titration is one that has a pH range that corresponds most closely to the pH of the equivalence point.
In the titration of aqueous ammonia, the equivalence point occurs at pH 5.3. Among the four indicators listed, methyl red has an endpoint range that overlaps closest to the equivalence point. Therefore, methyl red is the best indicator for the titration.
Buffers
Buffers are solutions that resist changes in pH when small amounts of acid or base are added. Buffers consist of a mixture of either a weak acid and a salt of its conjugate base, or a weak base and a salt of its conjugate acid. The acidic component of a buffer mixture can neutralize any added base, and the basic component of a buffer mixture can neutralize any added acid. As a result, large changes in pH are impeded.
For example, acetic acid (CH3COOH) is a weak acid, and its conjugate base is the acetate anion (CH3COO−). As such, a buffer could be made by mixing equal concentrations of each into solution. A salt such as sodium acetate (CH3COONa) could function as the source of acetate ions. Once formed, the buffer would establish the following equilibrium:
CH3COOH+H2O⇌CH3COO−+H3O+
Any strong base (OH−) added to the solution would be neutralized by the CH3COOH to form more acetate ions:
CH3COOH+OH−⇌CH3COO−+H2O
Similarly, any strong acid (H3O+) added to the solution would be neutralized by the CH3COO− to form more CH3COOH:
CH3COO−+H3O+⇌CH3COOH+H2O
Therefore, an aqueous mixture of CH3COOH and CH3COONa will function as a buffer.
(Choice A) NaNO3 is the salt of the conjugate base of HNO3, but HNO3 is a strong acid and strong acids are not suitable for making buffers.
(Choice C) NaBr with NaCN is a mixture of two salts. A buffer requires a weak acid (or a weak base) to be present with the salt of its corresponding conjugate base (or conjugate acid).
(Choice D) NaOH is a strong base, and strong bases are not suitable for making buffers. Moreover, NaCl is not the salt of the conjugate acid of NaOH.
Four characteristics of an ideal gas
- An ideal gas has no attractive or repulsive forces between the gas molecules
- The size (molecular volume) of the individual gas molecules of an ideal gas is negligible (taken to be zero) compared to the volume (space) of the container the gas occupies.
- Collisions between the molecules of an ideal gas are completely elastic (no energy is lost by interactions or friction)
- Ideal gas molecules have an average kinetic energy (energy of motion) that is directly proportional to the gas temperature.
Equilibrium from Graphs
Equilibrium is achieved in a reversible reaction when the forward reaction and the reverse reaction occur simultaneously at the same rate. Once equilibrium is achieved, the forward reaction generates products as fast as the reverse reaction converts those products back into the original reactants, and this causes the concentrations of the reactants and the products to become constant. Although constant, the equilibrium concentrations are not necessarily equal because equilibrium refers to a state of equal reaction rates (changes in concentration over time) but not to a state of equal concentrations.
In the graph of concentration vs. time for the reaction between H2(g) and I2(g), the constant (horizontal) regions of the curves (after approximately 5 hours) indicate a state of equilibrium in which the concentrations of the chemical species no longer change. From this region of the graph, the equilibrium concentration of HI(g) is seen to be 6.0 M. Therefore, if a 750 mL sample of the reaction mixture were analyzed at equilibrium, the number of moles of HI(g) present in the sample would be determined as follows:
750 mL×1 L1000 mL×6.0 mol1 L=4.5 mol
(Choice A) At equilibrium, a 750 mL sample of the reaction mixture contains 0.8 mol each of H2(g) and I2(g), but the question asks for the moles of HI(g).
(Choice B) A 750 mL sample measured at the intersection point of the lines on the graph (after approximately 1 hour) contains 1.9 moles of HI(g), but this point does not indicate the equilibrium of the reaction.
(Choice D) At equilibrium, the HI(g) has a molar concentration of 6.0 mol/L. This is the number of moles of HI(g) per liter rather than the number of moles in a 750 mL sample of the reaction mixture.
Educational objective:
Equilibrium is achieved when two opposing chemical reactions occur simultaneously at the same rate such that the concentrations of the chemical species become constant. Equilibrium reaction rates are equal, but the equilibrium concentrations of chemical species may be unequal.
Measurement of Pressuree
1 atm=760 mmHg=760 torr=101,325 Pa=101.325 kPa
Reaction Activation
Most chemical reactions can only occur when two or more molecules collide with enough energy to break bonds, allowing new bonds to form. This required energy is called the activation energy. Temperature is a measure of the average kinetic energy of the molecules in a system. At higher temperatures, the molecules move more quickly and collide more often and with more energy. Therefore, an increase in temperature will increase the rate of a reaction by providing more molecules with the required activation energy.
The reaction between hydrogen and oxygen is thermodynamically favorable, meaning that it occurs spontaneously. However, the reaction has a high activation energy. At room temperature, most of the molecules lack the energy necessary to initiate the reaction, and the reaction proceeds so slowly that it effectively does not occur at all. A spark releases heat into the system, raising the temperature and therefore the kinetic energy of nearby molecules. These molecules are then able to react exothermically, releasing more heat into the system and providing more molecules with sufficient energy to react.
(Choice A) The equilibrium position of a reaction is not appreciably altered by the presence of a spark. Instead, the rate at which equilibrium is achieved changes.
(Choice B) The spark consumes a negligible amount of oxygen. Because oxygen is a reactant, its consumption would drive the reaction toward reactant formation based on Le Châtelier principle.
(Choice D) Oxidizers such as oxygen gain electrons in combustion reactions. They do not lose electrons.
Educational objective:
Molecules must collide with sufficient energy, known as the activation energy, for a reaction to occur. Increased temperature increases the kinetic energy of the molecules in a system, and therefore increases the rate of a reaction.
Transition and Intermediate steps
The transition state of a reaction is the state of the molecules where new bonds are forming and old bonds are being broken. It is an unstable state and normally requires a large amount of energy to form, which is called the activation energy. The activation energy provides an energy barrier to a reaction’s progress.
A catalyst is a substance that increases the rate of a reaction without being consumed by the reaction. It increases the rate by stabilizing the transition state and thereby lowering the activation energy of the reaction. The passage states that platinum increases the reaction rate of hydrogen combustion without being consumed; therefore, platinum must be acting as a catalyst, stabilizing the transition state of the combustion reaction.
(Choices A and B) Stabilization of reactants or products would not help a reaction proceed more quickly because the energy barrier between them (the transition state) would still be present.
(Choice C) An intermediate step is a relatively stable step in a reaction that exists between two transition states. Its stabilization would not help increase the rate of a reaction.
Educational objective:
The transition state of a reaction is unstable and presents an energy barrier to the reaction’s progress. A catalyst stabilizes the transition state, and therefore increases the reaction rate without being consumed.
Rates and Products
The amount of product formed in a reaction depends on the equilibrium constant of the reaction. This constant is not changed by the presence or absence of a catalyst, which affects only the rate of the reaction.
The passage states that the combustion of hydrogen is thermodynamically favorable, with the equilibrium position being such that essentially all available reactants are consumed. Platinum acts as a catalyst and affects the rate but not the equilibrium of the reaction. Therefore, both engines would produce the same amount of water in one cycle.
(Choices A and B) Figure 1 indicates that the platinum engine produces more power than the spark engine, suggesting that it consumes the reactants at a higher rate. However, this difference indicates only that the platinum engine completes each cycle more quickly. It does not indicate a change in the equilibrium or in the amount of water produced once the reaction is complete.
(Choice D) As long as the temperature and initial concentrations of two reactions are identical, they will reach the same equilibrium regardless of whether a catalyst is present or not. The question states that temperature and injection conditions are identical, so sufficient information is provided to draw this conclusion.
Educational objective:
The amount of product formed in a reaction is dependent on the equilibrium constant of the reaction. This constant is not changed by a catalyst, which only changes the rate at which equilibrium is achieved.
Law of Mass Action
The law of mass action states that the rate of a reaction is proportional to the molar amount (concentration or partial pressure) of each reactant raised to the power of its reaction order. An elementary reaction is a reaction that proceeds in a single step, and in these reactions, the reaction order of each species is equal to its stoichiometric coefficient. For non-elementary reactions, the order must be determined empirically.
Many non-elementary reactions behave as if they were elementary with respect to reaction rate. Assuming the combustion of hydrogen is one such non-elementary reaction, it is second order with respect to H2 but only first order with respect to O2. Therefore, the rate of the reaction depends on the partial pressure of oxygen and on the square of the partial pressure of hydrogen. As long as enough oxygen is provided for the reaction to proceed, removing some oxygen and replacing it with the same number of moles of hydrogen will result in a rate increase because hydrogen makes a greater contribution to the rate than oxygen does.
(Choice A) The Pauli exclusion principle states that no two electrons in an atom can have the same set of quantum numbers. It is not related to the reaction rate.
(Choice C) Boyle’s law says that the pressure of a gas is inversely proportional to the volume it occupies. It does not directly predict the rate of any reaction.
(Choice D) Henry’s law states that the amount of a gas that dissolves in a liquid is proportional to the partial pressure of that gas. It is not predictive of the reaction rate.
Educational objective:
The law of mass action states that the rate of a reaction is proportional to the molar amount of each reaction component raised to the power of its reaction order. For elementary reactions, the reaction order of each species is equal to its stoichiometric coefficient.
Catalyst Impact
Catalysts increase reaction rates by stabilizing transition states. They do so by providing a surface on which more stable transition states can form. Increased catalyst surface area provides more surfaces on which transition states may be stabilized, and therefore increases the reaction rate.
The passage states that the power output of an engine is directly related to its rate of combustion. An increased rate is facilitated by a greater surface area of platinum, which acts as a catalyst. Breaking a given mass of platinum into smaller particles creates more surfaces, and therefore more surface area. A fine platinum powder provides more catalytic surfaces, and increases the speed of the reaction and the resulting power output.
(Choice B) Larger platinum particles provide less catalytic surface area, and therefore a slower reaction rate.
(Choice C) Smooth surfaces have less surface area than rough surfaces, so a polished platinum wall would yield a slower reaction rate.
(Choice D) The small amount of platinum in the chamber has no appreciable effect on the amount of reactant that can enter the chamber. Decreasing the amount of platinum would decrease catalytic surface area and yield a slower reaction.
Educational objective:
Catalysts provide a surface on which stable transition states can form. A greater catalytic surface area corresponds to a greater reaction rate.
Kinetic vs. Thermodynamic Products
Thermodynamic:
- Lower in energy
- More stable
- Major Product
Kinetic product:
- Higher in energy
- Less stable
- Minor product
Isomers
Isomers are compounds that have the same molecular formula but a different arrangement of atoms. Conformational isomers are structures that have the same connectivity and can be interconverted by the rotation of σ bonds. Because conformational isomers are identical except for bond rotations, they are the same compound.
Six-membered rings can be depicted in two different ways: as a wedge-dash projection or a chair conformation. In wedge-dash projections, wedges indicate the substituent is up and above the ring, and dashes indicate the substituent is down and below the ring. Substituents can be either axial or equatorial in a chair conformation. However, axial and equatorial do not dictate whether the substituent is up and above the ring or down and below the ring.
The wedge-dash projection of Compound 1 shows the –OH and the –CH3 both on a dash (down). Likewise, the chair conformation of Compound 2 shows the –OH and –CH3 as equatorial down. To represent this wedge-dash projection as a chair conformation, both substituents can be shown as axial down. A chair flip puts the substituents in an equatorial down position (still on the same side of the ring), yielding an identical structure to Compound 2. Because these compounds have the same connectivity and can be interconverted from one to the other through bond rotations (via chair flip), they are conformational isomers.
(Choice A) Enantiomers are nonsuperimposable mirror images in which all stereocenters are inverted. The stereocenter configurations in Compounds 1 and 2 are identical, and therefore cannot be enantiomers.
(Choice B) Diastereomers are stereoisomers in which at least one, but not all, stereocenters are inverted. Because none of the stereocenters in Compounds 1 and 2 are inverted, they cannot be diastereomers.
(Choice D) Compounds 1 and 2 have the same molecular formula and the same connectivity, so they are not constitutional isomers.
Educational objective:
Conformational isomers are structures that have the same formula and connectivity, and can be interconverted by the rotation of σ bonds. Because conformational isomers are identical except for structural bond rotations, they are the same compound.
Stereocenters and Stereoisomers
Stereoisomers are compounds that contain the same molecular formula and same connectivity but differ in spatial arrangement. The number of stereoisomers for a molecule is related to the number of stereocenters in the compound. The maximum number of stereoisomers possible for a compound is determined by the expression 2n, where n is the number of stereocenters.
The actual number of stereoisomers for a particular compound could be less than 2n if two of the stereoisomers have an internal mirror plane of symmetry (a meso compound), such that the symmetry causes the stereoisomers to be conformations of the same compound.
This compound has two stereocenters (on carbons 1 and 3) because each carbon has four different substituents. Using the expression 2n, the maximum number of stereoisomers is 22 = 4. The (1S, 3S) and (1R, 3R) stereoisomers are nonsuperimposable mirror images, as are the (1S, 3R) and (1R, 3S) stereoisomers, indicating that each of these compound pairs are enantiomers. None of the four stereoisomers has an internal plane of symmetry. Therefore, the compound in this question has four different stereoisomers.
(Choice A) The number of stereocenters in this compound is two, but this value does not provide the number of different stereoisomers.
(Choice B) The maximum possible number of stereoisomers is four, but the actual number of stereoisomers could be three only if one of the stereocenter configuration combinations for this compound were a meso compound (with an internal plane of symmetry). In such a case, two of the possible four stereochemical configurations would be the same compound, which would decrease the number of different stereoisomers by one.
(Choice D) There would be eight maximum possible stereoisomers if this compound had three stereocenters (23 = 8). However, the central carbon is not chiral, so there are only two stereocenters.
Educational objective:
The maximum number of stereoisomers possible for a compound is determined by the expression 2n, where n is the number of stereocenters. However, the actual number of stereoisomers for a particular compound could be less than 2n if two of the possible stereochemical configurations have an internal mirror plane of symmetry (meso compound), making them conformations of the same compound.
Intermolecular and Intramolecular bonding
Distillation is a purification technique used to separate molecules based on boiling point. A liquid mixture is heated to a temperature that overcomes the intermolecular forces keeping the compound in the liquid phase. The vapors then condense in the collection flask as a liquid. A molecule that participates in strong intermolecular forces will have a higher boiling point than molecules with weak intermolecular forces. Hydrogen bonding can be intermolecular (between two molecules) or intramolecular (within the same molecule), and therefore can have a significant impact on a molecule’s boiling point.
The difference in connectivity of the constitutional isomers 2-nitrophenol and 4-nitrophenol causes the molecules to experience different intermolecular forces, which contributes to the difference in their boiling points. Because the hydroxyl and nitro groups in 2-nitrophenol are ortho and therefore close in proximity to each other, the hydrogen from the hydroxyl group can hydrogen bond intramolecularly with the lone pair of electrons on the nitro group. This intramolecular bonding decreases the number of intermolecular bonds that can form, thereby decreasing the boiling point of the compound.
Because the hydroxyl and nitro groups on 4-nitrophenol are para, they are able to hydrogen bond intermolecularly but not intramolecularly. Intermolecular bonds hold the molecules of 4-nitrophenol together, thereby increasing the boiling point and causing it to stay in the flask while 2-nitrophenol distills.
(Choices A and C) 2-nitrophenol experiences less intermolecular hydrogen bonding than 4-nitrophenol, and therefore has a lower boiling point and distills more rapidly than 4-nitrophenol.
(Choice D) 4-nitrophenol experiences more intermolecular hydrogen bonding causing it to have a higher boiling point than 2-nitrophenol.
Educational objective:
Distillation separates compounds based on their boiling point. Constitutional isomers can experience different intermolecular forces, contributing to the difference in their boiling points. The isomer that experiences increased intermolecular hydrogen bonding has a higher boiling point compared to the isomer that experiences increased intramolecular hydrogen bonding.
Super heating
Superheating occurs when a liquid is heated above its boiling point but does not boil. Surface tension can cause superheating because it can inhibit the formation of bubbles. As bubbles attempt to form, surface tension causes a local increase in vapor pressure that surpasses the ambient pressure, allowing the liquid to heat beyond its boiling point. This phenomenon can cause the formation of large bubbles at the surface, which can erupt violently and eject the hot liquid from the distillation flask in a process called bumping. This effect is difficult to overcome without scratches or crevices in the container where smaller bubbles can begin to form.
Boiling chips are made of nonreactive porous material and provide nucleation sites where small bubbles of vapor can form. This effect overcomes the surface tension and allows the liquid to boil evenly at its normal boiling temperature, thereby preventing superheating.
(Choice B) Increasing the rate at which the distillation flask is heated will cause the liquid to reach its boiling point faster but will not keep the liquid from superheating.
(Choice C) Cold water in the condenser promotes condensation of the vapors into the collection flask. This setup does not have any effect on heating the liquid to be distilled, and therefore does not prevent superheating.
(Choice D) Decreasing the pressure will decrease the boiling points of the mixture components; it has no effect on superheating.
Educational objective:
Superheating happens when a liquid is heated above its boiling point, but it does not boil. Surface tension causes the vapor pressure inside bubbles to increase as they form, causing them to explode at the surface. Addition of boiling chips gives the bubbles a surface to form on as the liquid is heated, and allows for even boiling.
Polarity
Thin layer chromatography (TLC) is a technique used to separate compounds based on polarity. The mobile phase (organic solvent) travels up the stationary phase, a thin absorbent plate coated with silica (SiO2), via capillary action. The components of a mixture travel up the plate at different rates based on their polarity. In normal phase TLC, nonpolar compounds have less affinity for the polar stationary phase than polar compounds, and therefore travel farther up the plate.
The Rf value is expressed by the ratio of the distance traveled by the compound of interest to the distance traveled by the mobile phase. Values can be calculated for A and B as follows:
Rf(A) = 6 cm9 cm = 2 cm3 cm = 0.67
Rf(B) = 3 cm9 cm = 1 cm3 cm = 0.33
An Rf value is always less than 1, and a smaller Rf value corresponds to a more polar, less mobile compound. Spot B has an Rf of 0.33 and has traveled a shorter distance up the plate than spot A, making it the more polar compound. To decide whether spot B is 4-aminophenol or acetaminophen, determine which compound is more polar.
The only difference between the two compounds is the change from amine in 4-aminophenol to amide in acetaminophen. An amide is a hydrogen bond donor and acceptor via two electronegative atoms (oxygen and nitrogen) whereas an amine (primary and secondary) is a hydrogen bond donor and acceptor via only one electronegative atom (nitrogen). Because an amide has more hydrogen bond acceptors, it is more polar; therefore, spot B must be acetaminophen.
(Choices A and C) Spot A has an Rf value of 0.67.
(Choices C and D) 4-aminophenol is the less polar compound, and therefore could not be the more polar spot B.
Educational objective:
Thin layer chromatography is used to separate compounds based on polarity. The Rf value of a compound is a ratio of the distance up the plate a compound travels to the distance the solvent travels. A polar compound will have a smaller Rf value than a nonpolar compound.
IR Signals
Acetaminophen contains several functional groups, including a phenol (hydroxyl group), aromatic ring, and amide that would show a strong absorption in the infrared (IR) spectrum. Each functional group shows absorption at a different frequency depending on the type of bond the functional group contains. The carbonyl (C=O) group from an amide shows an absorption from the 1690–1650 cm−1 region in the IR spectrum.
(Choices B, C, and D) In the IR spectrum, an alkyne CΞC stretch absorbs from 2150–2,100 cm−1, a nitrile CΞN stretch absorbs from 2260–2240 cm−1, and an aldehyde C–H stretch absorbs from 2850–2750 cm−1. Acetaminophen does not contain these groups; therefore, it will not have a strong absorbance at these frequencies.
Educational objective:
Functional groups show absorption in the infrared spectrum at different frequencies depending on the bond type present in the particular functional group. Characteristic functional group absorptions include 3650–3200 cm−1 (alcohol and phenol O−H stretch); 3550–3060 cm−1 (amide N–H stretch); 3100 cm−1 (sp2 C–H stretch); 3000–2875 cm−1 (sp3 C–H stretch); 2260–2,100 cm−1 (triple bonds); and 1850–1650 cm−1 (C=O stretch).
Dilution Factor
DF=(VT1/VF1)×(VT2/VF2)
Gabriel Synthesis
The Gabriel synthesis is a method that uses potassium phthalimide and diethyl bromomalonate as starting materials to synthesize amino acids. The starting reagents of the Gabriel and Strecker syntheses are all planar and lack chiral centers; therefore, the product is a mixture of L- and D-amino acids.
Strecker Synthesis
Potassium cyanide and an aldehyde
Amino acids important notes
All naturally occurring amino acids have an L configuration with the exception of glycine, which is not chiral, and therefore neither L nor D. Of the chiral amino acids, all are in the S configuration except cysteine.
Like natural amino acids, the dansylalanine shown in Reaction 1 is in the L configuration because it was incorporated into a protein. In biological systems, D-amino acids cannot be incorporated into proteins
Chromatography Notes
Chromatography methods separate molecules based on their relative affinities for a stationary phase versus a mobile phase. For compounds to separate efficiently on any column, they need sufficient time to interact with the stationary phase. Given enough time, even subtle differences in affinity for the stationary phase can be amplified, allowing separation of compounds with similar properties. Increasing the length of the stationary phase through which the compounds must travel can provide the necessary time.
Ethanol and ethyl acetate have similar, but not identical, boiling points and can be separated on a gas chromatograph by running them through a longer column.
Acidity Notes
For a compound in solution, as the pH is increased, the most acidic functional group of the compound will be deprotonated first. The acidity of a functional group is determined largely by the electronegativity of the proton-donating atom and by the ability to stabilize the negative charge in the corresponding conjugate base through charge distribution (atom size) or delocalization (resonance). Negative charge is stabilized better on more electronegative atoms, and negative charge that can participate in resonance will be stabilized further by being delocalized across more than one atom. Sites that better stabilize a negative charge are more likely to be deprotonated (more acidic).
Atoms I–IV in Compound 2 are oxygen (alcohol), sp2 carbon (alkene), sp3 carbon (alkane), and methyl ketone (α-H), respectively. Upon deprotonation, the negatively charged atom in the conjugate base of these functional groups is oxygen for alcohols and carbon for the others. Because oxygen is more electronegative than carbon, a negative charge on oxygen in the conjugate base of the alcohol is more stabilized than the charge on the carbon atoms in the three other functional groups. Therefore, the alcohol oxygen atom has the most acidic proton and will be deprotonated when reacted with NaOH.
(Choices B and C) Alkene protons (sp2 C–H) are more acidic than alkane protons (sp3 C–H), but both are less acidic than an alcohol proton because the conjugate bases of alkenes and alkanes are less stable, with the negative charge concentrated on a less electronegative carbon atom.
(Choice D) Ketones are less acidic than alcohols but more acidic than hydrocarbons. The negative charge in the conjugate base of a ketone is delocalized by resonance across the α-carbon and carbonyl oxygen atoms, which helps stabilize the charge.
Educational objective:
Acidity of a functional group is determined by the stability of the conjugate base it forms. Factors such as the size and electronegativity of the proton-donating atom as well as the ability to stabilize the negatively charged atom in the conjugate base by charge distribution or resonance contribute to acidity.
Power and Stopping the Flow of Current
Electric power is the rate of electric energy transfer, and it is dissipated as heat in resistors (devices that resist the flow of electric current).
Current only stops if there is no voltage across the resistor (V = 0) or if the resistance is infinite. Neither of these is true for this circuit.
Propagation of sound
- Velocity of the sound increases with temperature
- Velocity is slowest in gases, faster in liquids, and fastest in solids.
- Within a phase of matter, velocity increases with stiffness and decreases with density.
Intensity is the energy per area and it decreases with propagation due to reflection. Also, the change in the velocity of the sound wave is related to the wavelength. The frequency is CONSTANT
Doppler Shift
With relative motion between a source and an observer, the observed waveform differs from the original, emitted waveform in terms of both frequency and wavelength. This phenomenon is known as the Doppler effect, and the frequency shift is proportional to the relative velocity of the source.
According to the passage, blood flow velocity is determined by the magnitude of the Doppler shift (Δf) detected by the ultrasound device (ie, the observer). Because the ultrasound waves are first reflected off the blood before detection by the probe occurs, the flowing blood acts as the source of sound.
When blood is flowing toward the device, flow velocity (vB) is negative (ie, subtracted from waveform velocity) and the frequency shift is positive (ie, observed frequency > original frequency). A positive frequency shift occurs because each successive wave is reflected closer to the device.
Conversely, when blood is flowing away from the device, flow velocity is positive (ie, added to waveform velocity) and the frequency shift is negative (ie, observed frequency < original frequency). A negative frequency shift occurs because each successive wave is reflected farther from the device.
(Choice A) The graph must pass through the origin because the frequency shift changes from positive to negative as the blood approaches and passes the probe.
(Choice B and D) A positive frequency shift means that the observed frequency increased, which would only occur if the blood is flowing toward the ultrasound device (ie, negative velocity).
Educational objective:
The Doppler effect occurs when the observed frequency and wavelength of a sound are shifted from those of the original due to relative motion between the source and the observer. The frequency shift is positive when the source velocity is negative (moving closer) and negative when the source velocity is positive (moving away).
How is sound wave created?
Sound is propagated in the form of longitudinal waves of oscillating pressure. Compressions (areas of high pressure) and rarefactions (areas of low pressure) are formed through the back-and-forth vibrations of the molecules of the medium.
The passage states that piezoelectric crystals produce sound when an alternating voltage is applied to them. It is reasonable to conclude that the expansion and contraction of the crystals will cause molecules in the surrounding medium to vibrate, creating sound waves.
Doppler Effect
Given relative motion between a source and an observer, the observed wave differs from the original wave in frequency and wavelength. This phenomenon is known as the Doppler effect and can be approximated by
∆ff=vc
where Δf is the frequency shift, f is the original frequency, v is the relative velocity between the source and the observer, and c is the speed of the wave in the medium. From the above relationship, the magnitude of the Doppler shift is inversely related to the speed of the wave.
An infrared laser uses a form of electromagnetic radiation (light), which travels at the speed of light c = 3 × 108 m/s. The speed of sound in blood is given in the passage as c = 1,570 m/s. Because the speed of light is much greater than the speed of sound, the observed frequency shift will be smaller for laser Doppler flowmetry.
Educational objective:
The Doppler effect can be approximated by the relative velocity between the source and the observer and the speed of the wave in the medium (∆ff=vc)
. The magnitude of the frequency shift is inversely proportional to the wave’s speed. The Doppler effect of light will result in smaller observed frequency shifts because the speed of light is much greater than that of sound.
Heat Capacity Terminology
The amount of heat q gained or lost by an object is the product of its mass m, its specific heat c, and its change in temperature ΔT: q = mcΔT
Heat capacity = mc
Thermal expansion
The thermal expansion of the length L or volume V of a substance is linearly proportional to its change in temperature ΔT:
∆L=αL∆T
∆V=αVV∆T
where α or αV is the coefficient of thermal expansion specific to the substance. Although the liquid in the thermometer will expand volumetrically, it is confined in a column, and therefore its expansion causes its height to increase linearly with temperature. According to the question, the change in the height of the liquid ΔL is 2 mm after the first 2 min, which corresponds to a temperature change ΔT of 2°C
Heating and Freezing
At the melting (or freezing) point of a substance, the substance can exist in either its solid or liquid phase. Because the freezing/melting point of water is 0°C, the ice bath will remain as a mixture of solid ice and liquid water unless heat is added to or removed from the mixture. The latent heat of fusion (melting) is the amount of heat (energy) required to convert a solid at its melting point temperature to its liquid phase by breaking the bonds between the molecules in the solid phase.
The heat released from the combustion reaction will first go toward the latent heat of fusion to melt the ice into liquid water. The temperature of the water will be constant at 0°C as long as ice is still present and will not start to increase until after all the ice melts. Therefore, the temperature of the water would begin to increase at a later time (compared to the original experiment) when enough heat is transferred from the combustion reaction to first melt the ice (latent heat of fusion).
(Choice A) Because some of the heat released goes toward the latent heat of fusion of the ice to melt it, less heat will be available to increase the temperature of the water. Therefore, the magnitude of the temperature increase would be less than the 10°C temperature change in the original experiment.
(Choice C) Ice absorbs heat when it melts. Conversely, liquid water releases heat equal to the latent heat of fusion when it freezes.
(Choice D) The amount of heat released from the combustion would be unchanged because it depends on the mass of the reactants (powdered sample), which is unchanged.
Educational objective:
The phase transition from a solid to a liquid requires heat (energy) to break the bonds between molecules; this energy is the latent heat of fusion. When heat is added to a mixture of ice and water at 0°C, the heat will first go toward melting the ice before raising the temperature of the water.
Closed, open, and isolated system
In thermodynamics, the “system” is the physically enclosed space being studied that is separated from the rest of the universe, known as the “surroundings.” There are three main types of thermodynamic systems, which are characterized by the type of barrier between the system and its surroundings:
An open system allows heat and matter to be exchanged with the surroundings. A closed system allows heat but not matter to be exchanged with the surroundings. An isolated system does not allow heat or matter to be exchanged.
According to the passage, the bomb cell houses the combustion reaction, and its surroundings include the water in the calorimetry device. Because the temperature of the surrounding water increased during the combustion reaction, heat can be exchanged between the bomb cell and its surroundings. Because the container is enclosed and does not allow for the exchange of matter, the bomb cell is an example of a closed system (Choices B and D).
The calorimetry device houses the bomb cell and the water it is submerged in, and its surroundings are the surface it rests on and the nearby air. Because the enclosed walls of the device are thermally insulated (poor conductors of heat), neither heat nor matter can be exchanged with its surroundings, and the device is an example of an isolated system (Choice A).
Educational objective:
An open system allows heat and matter to be exchanged with the surroundings. A closed system allows heat but not matter to be exchanged with the surroundings. An isolated system does not allow heat or matter to be exchanged with the surroundings.
Friction
Any object may be acted on by multiple translational forces of different origin, magnitude, and direction. For example, an object located in two-dimensional space will accelerate when the sum of all forces acting along one or both axes of the xy-coordinate system does not equal zero.
Because forces acting along the same axis can be either antagonistic or cooperative, free-body diagrams can be used to assess the balance of forces along each axis provided that the vector components of each force are known:
Σxforces=(+x forces)+(–x forces)
Σyforces=(+y forces)+(–y forces)
When the sum of all forces acting on a mass along each axis of the xy-coordinate system is equal to zero, the object is said to be in equilibrium such that no acceleration occurs:
Σxforces=0
Σyforces=0
In contrast to an equilibrium in which an object is moving, static equilibrium results when the balance of forces acting on an object maintains the absence of motion by that object.
In the prompt, a 5 kg mass is suspended in static equilibrium by a cable with a tension of 45 N. Isolating only the vertical (y-axis) forces, the magnitude of the gravitational force acting on the object can be determined by the simple equation for weight:
F=mg
= (5 kg)(9.8 m/s2) = ~50 N
Because this downward (−y) gravitational force acting on the mass is greater than the 45 N tension force pulling the block upward (+y), it can be concluded that the frictional force acting on the mass must act in an opposing, upward (+y) direction to maintain the static equilibrium.
Using the equation for static equilibrium, the magnitude of the frictional force (Ff) between the mass and the wall can be calculated:
Σyforces=(+y forces)+(−y forces)=0
(+45 N+Ff)+(−50 N)=0
Ff−5 N=0
Ff=+5 N
Therefore, the frictional force acting between the object and the wall must be 5 N and oriented in an upward (+y) direction (Choice A).
Educational objective:
Static equilibrium occurs when the sum of all forces acting on a motionless object is equal to zero. Free-body diagrams are used to illustrate the directional components of translational forces.
Slipping and Sliding
Static friction is the frictional force that prevents two surfaces from sliding. After the cannula is inserted, static friction between the cannula and skin prevents slipping because static friction counters the forces that promote sliding. Static friction has an upper limit, and if the forces that promote sliding exceed this value, slipping occurs. The upper limit of static friction Fs is the product of the coefficient of static friction μs and the normal force N (the perpendicular force one surface exerts on the other):
Fs = μsN
The greater the upper limit of static friction, the better the cannula is prevented from slipping (Choice B). Therefore, slipping can be better prevented by increasing the normal force. The normal force keeping the cannula in place is due to the skin pressing on the cannula. According to the question, cannulas inserted with blunt-tipped trocars experience greater stretching of the skin. Therefore, the cannula is subject to a greater normal force, producing a greater static frictional force.
(Choice A) According to the question, the cannulas are of equal size, and therefore the sizes of the contact areas are the same.
(Choice D) The coefficient of static friction depends only on the properties of the surfaces involved, and therefore it will not change.
Educational objective:
Friction is the force that resists sliding between two surfaces, and static friction prevents surfaces from sliding. The maximum value of static friction is proportional to the normal force, which is the perpendicular force one surface exerts on the other. Therefore, greater stretching of skin creates a greater normal force around a cannula and greater static friction to better prevent slipping.
