AAMC 1 - Chem/Phys Flashcards
How does the concentration of solute affect the migration rate in paper chromatography?
Migration rate is not affected by concentration.
The solute concentration will affect the size of spots on a paper chromatogram, not the average migration rate.
How can one increase the size of spots that appear in paper chromatography or TLC?
They can increase the concentration of solute
The solute concentration will affect the size of spots on a paper chromatogram, but not the average migration rate.
Is it possible to adjust the concentration of the stationary phase in a chromatography set-up?
No.
The stationary phase does not have a concentration as it is an immobilized surface, not a solution.
What does the thickness of filter paper affect in a paper-chromatography setup?
The thickness of the paper will affect the amount of each component that can be fully separated, but not the relative migration rates of the components.
True or False:
Tertiary alcohols readily dehydrate
True.
If a reaction leads to a mixture of cis- and trans-alkenes, is the reaction stereospecific?
No, this is enough evidence to conclude that the reaction is NOT stereospecific.
The functional group that represents a peptide bond is called an _______ group.
The functional group that represents a peptide bond is called an amide group.
In gas-liquid chromatography, what are the properties of the compound that makes the first peak observed in the GC trace?
In gas-liquid chromatography, the first peak to emerge will be from the least polar, most volatile compound.
Least polar, lowest boiling point
Which compound is stronger, an alkyl halide or an alkene?
Alkyl halide is stronger.
Alkyl halides are polar, so they can interact with themselves through dipole-dipole forces as well as london dispersion forces.
Alkenes are non-polar, therefore they can only interact with themselves through london dispersion forces.
For this reason, alkenes will have a lower boiling point.
What is deuterium, and where would it fall when ranking priority to assign absolute configuration?
Deuterium is an isotope of Hydrogen that contains one proton as well as a neutron. Standard H does not contain a neutron. When assigning priority, we can not use atomic number as they are identical, so the tie is broken my atomic mass. Deuterium has atomic mass of 2, so it is higher priority than Hydrogen but lower than everything else.
What kind of substitution reaction results in an inversion of stereochemistry 100% of the time?
SN2 reactions invert stereochemistry 100% of the time.
What kind of substitution reaction creates a racemic mixture of products, and why?
SN1 reactions produce racemic mixtures of products. This is because a leaving group will leave first, creating a carbocation. At this point, the substituting molecule can attack the carbocation from either side, creating a racemic mixture.
What is the stereochemistry of this molecule?
R
O is the highest priority, followed by the carbon chain, followed by Deuterium (Hydrogen + neutron), and lastly H
What would be the stereochemistry of this molecule after an SN2 reaction?
Before the reaction, the molecule is R. Oxygen is the highest priority, followed by the carbon chain, followed by Deuterium (Hydrogen + neutron), and lastly H.
SN2 reactions result in the inversion of stereochemistry 100% of the time. Therefore this would be an S absolute configuration.
Which reactions between the carboxylic acid or the primary alcohol loses the -OH group in an esterification?
The -OH from the carboxylic acid will be lost, while the O from the alcohol will be the oxygen in the ester linkage.
A person, whose eye has a lens-to-retina distance of 2.0 cm, can only clearly see objects that are closer than 1.0 m away. What is the strength S of the person’s eye lens? (Note: Use the thin lens formula .)
A. –50 D
B. –10 D
C. 51 D
D. 55 D
Solution: The correct answer is C.
- The negative sign of the lens strength is indicative of a diverging lens, whereas the eye lens is a converging lens.
- The negative sign of the lens strength is indicative of a diverging lens, whereas the eye lens is a converging lens.
- According to the thin lens formula, the strength of the eye lens is equal to the inverse of the focal length of the eye lens. Its numerical value is given by (1 m)−1 + (0.02 m)−1 = 1 D + 50 D = 51
- This answer implies the person can only clearly see objects that are closer than 20 cm away.
What does a enzyme stabilize in order to affect reactions?
An enzyme stabilizes the transition state, thus lowering the activation energy of a reaction.
An enzyme stabilizes the _________, thus lowering the activation energy of a reaction.
An enzyme stabilizes the transition state, thus lowering the activation energy of a reaction.
Which of the following will decrease the percentage ionization of 1.0 M acetic acid, CH3CO2H(aq)?
A. Chlorinating the CH3 group
B. Diluting the solution
C. Adding concentrated HCl(aq)
D. Adding a drop of basic indicator
C. Adding concentrated HCl(aq)
- Replacing H with Cl will stabilize the formation of negative charge on the nearby carboxylic acid group. This is because chlorine is an electronegative atom. This change will therefore increase the percentage ionization of the acid.
- Diluting the solution will increase the percentage ionization by Le Châtelier’s Principle.
- HCl is a strong acid that will increase the amount of H+ in solution and thus decrease the percentage of CH3CO2H that ionizes.
- Adding a drop of basic indicator will slightly increase the amount of dissociated (ionized) acid due to the acid−base reaction that occurs between the two.
Knowing that the speed of light in the vitreous humor is 2.1 × 108 m/s, what is the index of refraction of the vitreous humor? (Note: The speed of light in a vacuum is 3.0 × 108 m/s.)
A. 0.7
B. 1.4
C. 2.1
D. 3.0
The correct answer is B
- This option implies light travels faster through the vitreous humor than through vacuum, which is a scientific impossibility.
- The index of refraction of a medium is equal to the ratio of the speed of light in vacuum to the speed of light in the medium, thus in this case is equal to (3.0 × 108 m/s)/(2.1 × 108 m/s) = 1.4.
- This is 50% larger than the index of refraction of the vitreous humor, which is equal to (3.0 × 108 m/s)/(2.1 × 108 m/s) = 1.4.
- The index of refraction of the vitreous humor is equal to (3.0 × 108 m/s)/(2.1 × 108 m/s) = 1.4; however, this (3.0) number is 114% larger.
What is the energy of the photons emitted by the LED at a frequency of 610 THz? (Note: h = 6.6 × 10–34 J·s)
A. 9.2 × 10–12 J
B. 1.6 × 10–16 J
C. 1.1 × 10–18 J
D. 4.0 × 10–19 J
D. 4.0 × 10–19 J
The energy of a photon of frequency 610 THz is equal to 6.6 × 10−34 J•s × 610 x 1012 Hz = 4 × 10−19 J.
note: Tera = x 1012
What is the work generated by a healthy adult who circulates 9 L of blood through the brachial artery in 10 min? (at 900 ml/min there is 200 W of work done)
We’re given blood in liters in our question stem, so we can use dimensional analysis to convert to mL. 1000 mL in 1 L tells us the adult circulates 9000 mL of blood / 10 minutes. Simplifying here gives us 900 mL/min.
We are told at 900 ml/min there are 200 W of work done.
Work is power x time, so we can multiply the power generated (200 W) by time (600s) to get 120,000 J or 120 kJ.
Why is the velocity of blood flow slower in capillaries than in arteries?
A. Capillary walls are more elastic than arterial walls.
B. Capillaries have less resistance to blood flow than arteries.
C. The total cross-sectional area of capillaries exceeds that of arteries.
D. Blood pressure is higher in the capillaries than in arteries.
C. The total cross-sectional area of capillaries exceeds that of arteries.
The high number of capillaries in the body means that the total cross-sectional area of these vessels is larger than any other vessel type in the circulatory system. This causes the velocity of the blood to decrease.
Which of the following types of orbitals of the central atom are involved in bonding in octahedral compounds?
A. sp
B. sp3
C. p
D. d2 sp3
D. d2sp3
Octahedral compounds have six σ bonds and no stereochemically active lone pairs. According to valence bond theory, the central atom requires the hybridization of six atomic orbitals, d2sp3.
True or False:
The molar volume of an ideal gas at 25°C is 22.4 L
FALSE
The molar volume of an ideal gas at 25°C is 24.4 L
Each of the following equations shows the dissociation of an acid in water. Which of the reactions occurs to the LEAST extent?
A. HCl + H2O → H3O+ + Cl−
B. HPO42− + H2O → H3O+ + PO43−
C. H2SO4 + H2O → H3O+ + HSO4−
D. H3PO4 + H2O → H3O+ + H2PO4−
B. HPO42− + H2O → H3O+ + PO43−
- Hydrochloric acid is a strong acid. This reaction will occur to completion.
- HPO42– has a high negative charge and so dissociation of it will occur to the least extent.
- Sulfuric acid is a strong acid. This means that the dissociation shown will go to completion as water is a stronger base than the hydrogen sulfate anion.
- Phosphoric acid is a much stronger Brønsted acid than the hydrogen phosphate anion. This is readily seen due to the increased charge on the anion which will make it much harder to lose another proton.
When a 0.1 M H2SO4 solution is added to pulverized blackboard chalk, the following reaction takes place.
CaCO3(s) + H2SO4(aq) CaSO4(s) + CO2(g) + H2O(l)
At 25°C, the reaction is spontaneous and has:
A. negative ΔG° and positive ΔS°.
B. negative ΔG° and negative ΔS°.
C. positive ΔG° and negative ΔS°.
D. positive ΔG° and positive ΔS°.
A. negative ΔG° and positive ΔS°
At 25°C, the reaction is spontaneous and has:
First thing we want to note is the state of each of our reactants and products. We have solids and liquids in our reactants, but solids, liquids, and gases in our products. Entropy is the measure of the disorder of a system. The concept of disorder can best be described in terms of the states of matter. Solids, liquids, and gasses all have different degrees of disorder. We can think of the degrees of the number of different states the molecules in each can occupy. Because molecules in gases are able to change both volume and shape, they can be considered the most disordered. Liquids can be considered the second most disordered, and solids can be considered the least disordered. That means we’re looking for an answer with a positive ΔS°.
The test-maker also mentions the reaction is spontaneous so we’re looking for an answer with negative ΔG°.
Using an electrical wire with a smaller diameter will ________ the resistance of the wire. According to Ohm’s law, this will decrease the current in the circuit.
Using an electrical wire with a smaller diameter will increase the resistance of the wire. According to Ohm’s law, this will decrease the current in the circuit.
Increasing the temperature of the electrical wire will ________ the resistance of the wire. According to Ohm’s law, this will decrease the current in the circuit.
Increasing the temperature of the electrical wire will increase the resistance of the wire. According to Ohm’s law, this will decrease the current in the circuit.
The equilibrium
BaCrO4(s) Ba2+(aq) + CrO42–(aq)
exists in a saturated aqueous solution of BaCrO4. Dissolution of Na2CrO4 in a saturated aqueous BaCrO4 solution would:
A. have no effect on the position of this equilibrium.
B. shift this equilibrium left.
C. shift this equilibrium right.
D. shift this equilibrium first right and then left.
B. shift this equilibrium left.
Dissolution of Na2CrO4 would introduce the common ion, CrO42–, which would reduce the solubility of BaCrO4 due to the common ion effect.
What volume of a 0.120 M CaI2 solution would contain 0.078 mol of the solute?
A. 35.0 mL
B. 65.0 mL
C. 350 mL
D. 650 mL
D. 650 mL
Solution: The correct answer is D.
- A volume of 35 mL corresponds to only 0.035 L × 0.120 mol/L = 0.0042 mol of solute.
- A volume of 65 mL corresponds to only 0.065 L × 0.120 mol/L = 0.0078 mol of solute.
- A volume of 350 mL corresponds to only 0.35 L × 0.120 mol/L = 0.042 mol of solute.
- In order to obtain the volume of solution necessary to provide a given amount of solute in moles, one needs to take the number of moles and divide by the solution concentration in molarity: 0.078 mol × 1 L/0.120 mol = 0.65 L = 650 mL.
Which measurement unit CANNOT be used to express power?
A. kg•m2 •s2
B. J•s-1
C. ft•lb •s-1
D. W
A. kg•m2 •s2
Solution: The correct answer is A.
This answer is correct because the measurement unit of power is watt, defined as
J/s = ft (lb/s) = kg(m2/s3)
List the units of power
W = J/s = ft (lb/s) = kg(m2/s3)
True or false:
Water (H2O) is both a nucleophile and electrophile
This statement is true.
The oxygen in a water molecule has two lone pairs, making this a nucleophilic site. The hydrogen atoms of a water molecule however are electrophilic sites. Whether water forms predominantly hydroxide anion or hydronium ion depends to a large degree on the chemical environment present.
In Fischer esterification, the oxygen of the alcohol performs a nucleophilic attack on the carbonyl carbon of the carboxylic acid. Therefore, the 18O isotope initially present in ethanol should consistently appear only in position 1.
Arrange the following nucleophiles from strongest to weakest:
water, hydroxide, hydronium
hydroxide > water > hydronium
An unknown ion has the electron configuration 1s2 and you have observed that it has 3 protons.
Do you predict this element to be electrophilic or nucleophilic?
Electrophilic
The ion in question is the lithium cation. Even without consulting a periodic table, we can notice that this ion should be positively charged. A positively charged species can safely be said to be electrophilic.
True or False:
All Lewis bases are also nucleophiles
True
Both are lone pair donors
True or false:
Histidine has a lone pair that can act as a base.
This statement is true.
Histidine has a lone pair on nitrogen #2 and is therefore a likely nucleophile by the rules we have learned. Nucleophiles are Lewis bases.
What is the rate-limiting step of an SN1 reaction?
Carbocation formation by the departure of the leaving group is the rate-limiting step.
Carbocations are highly reactive, unstable species that do not form readily. They are formed slowly.
True or false:
An SN1 reaction proceeds in at least two steps, while an SN2 reaction proceeds in just one step.
This statement is true.
An SN1 reaction proceeds through the formation of a carbocation first, then a nucleophilic attack. It is for this reason categorized as stepwise reaction mechanism.
SN2 reactions, by contrast, happen in a single step that is driven by a nucleophile attacking the electrophilic site of the substrate, and these reactions are therefore categorized as concerted reactions.
Sodium bromide and tert-butanol are reacted in an SN1 reaction to form an alkyl halide. This reaction can be sped up by which of the following steps?
A. Addition of NaOH
B. Addition of H2O
C. Addition of NaBr
D. Addition of tert-butanol
D. Addition of tert-butanol
The carbocation intermediate must be formed, and this is the rate-limiting step of SN1 reactions. Of the options given, only the addition of more substrate can accelerate this reaction.
An SN2 reaction must be of at least which order?
Second order
Second order reactions depend on the concentration of two species to the first power. This is the minimal reaction order for any SN2 reaction, as the reaction rate must depend on at least the concentration of the nucleophile and the concentration of the substrate.
What type of solvent is preferred in an SN1 reaction?
Polar protic solvents
These help to stabilize the carbocation and prevent the leaving group from rejoining the original substrate.
What characteristics are required of the nucleophile in an SN2 reaction?
The nucleophile must be strong and small.
This allows is to attack strongly without steric hinderance being a factor.
What solvents are ideal for an SN2 reaction?
Polar aprotic solvents
Solvents like acetone and DMSO are ideal. This is because they are polar aprotic and do not affect the nucleophilicity.
If the substrate in a nucleophilic attack reaction is secondary, how can you determine whether it is SN1 or SN2?
A strong, small nucleophile and a polar aprotic solvent would signify SN2
A weak nucleophile and a polar protic solvent would signify SN1
What does a negative charge on a molecule tell you about its nucleophilicity?
A negative charge indicates a strong nucleophile
True or false:
Ethanol, ethanoic acid, and propanol are all solvents which are conducive to SN1 reactions.
This statement is true.
All the named structures are polar protic solvents. Polar protic solvents are most conducive to SN1 reactions.
True or False:
The stability of carbanions is opposite that of carbocations.
True.
Among carbanions, a primary carbanion is more stable than a secondary carbanion, which is in turn far more stable than a tertiary carbanion. This is the opposite of carbocations, in which a tertiarty carbocation is the most stable, followed by a secondary carbocation, and lastly a primary carbocation.
True or false:
According to Beer’s Law, UV absorbance is inversely proportional to solution concentration.
This statement is false.
Beer’s Law states that UV absorbance is directly proportional to concentration. Therefore, the absorption that occurs at the maximum wavelength of absorption can be used to calculate the molarity of a sample.
IR spectroscopy can detect functional groups present on a compound by recording the vibration of polar covalent bonds in response to different wavelengths of infrared radiation.
Mass spectrometry can provide information about the mass of a compound by ionizing it and detecting fragments of different sizes.
UV-Vis spectroscopy is best for determining the concentration of a compound because it can be used to measure the amount of light absorbed by a sample.
Lastly, NMR spectroscopy can be used to determine fine structural details, such as how different atoms are connected within a molecule, based on how nuclei interact with an external magnetic field.
Electrons in a hydrogen atom have a velocity of 2.2 x 106 m/s. Given an electronic mass of 9.0 x 10-31 kg, what is the wavelength of the electrons? (Note: Planck’s constant, h = 6.62 x 10-34 J*s).
The de Broglie equation gives the wavelength of a piece of matter as λ = h/mv.
Plugging the given values into this equation, the wavelength calculation would be:
λ = (6.62 x 10-34 Js) / (9.0 x 10-31 kg)(2.2 x 106 m/s) =
3.67 x 10-10m
An electron’s kinetic energy was calculated to be 2.0 x 10-20 J, just after being ejected from an aluminum atom after exposure to high energy photons. Given this information, what was the incident photon’s kinetic energy? (Aluminum’s work function is 8.0 x 10-20 J).
The energy of an ejected electron due to the photoelectric effect is equal to the energy of the incident photon minus the work function of the metal (in this case aluminum). Since we’re asked to find the energy of the photon, the equation arranges to
Ephoton = KEelectron + Work function
E = (2.0 x 10-20 J) + (8.0 x 10-20 J)
Ephoton= 1 x 10-19 J
What is the difference between light frequency and light intensity?
Though the terms may appear similar, light frequency describes the energy per photon,
while light intensity describes the number of photons in the incident light.
What are two variations of the equation used to find the energy of a photon?
E = hf
and
E = hc/λ
If mendelevium-258 has a half-life of one hour, how much of the sample would have undergone beta-minus decay after 240 minutes?
94%
Since radioactive decay is exponential, it can be analyzed in terms of half-lives such that 1/2n = fraction remaining after n half-lives have passed.
240 minutes is equivalent to 4 hours, thus the sample undergoes 4 rounds of beta-minus decay, or n = 4. Plugging this into the equation 1/24 = 1/16 = 6.25% remains. It is important to note here that the question asks about how much of the sample has decayed, NOT the amount of sample remaining.
Therefore, if 6.25% remains, 93.75% of the sample must have decayed.
After 1 half-life, how much of a substance is remaining in both a fraction and percent?
½ or 50%
After 2 half-lives, how much of a substance is remaining in both a fraction and percent?
¼ or 25%
After 3 half-lives, how much of a substance is remaining in both a fraction and percent?
1/8 or 12.5%
After 4 half-lives, how much of a substance is remaining in both a fraction and percent?
1/16 or 6.25%
After 5 half-lives, how much of a substance is remaining in both a fraction and percent?
1/32 or 3.125%
Students are trying to determine by which elimination reaction mechanism two different reactions are proceeding. The rate of reaction A seems to depend only on the concentration of the substrate, while reaction B seems to depend on both the concentration of base and concentration of substrate. Can a determination be made from this information, and if so, what is it?
Reaction A is likely E1
Reaction B is likely E2
E1 reactions obey a unimolecular rate law (rate = k[A]) while E2 reactions obey a bimolecular rate law (rate = k[A][B]). Given that it is already known that elimination reactions are occurring, we can rather confidently assume that reaction A is proceeding through an E1 mechanism while reaction B is proceeding through an E2 mechanism
True or false: The pictured reaction is a nucleophilic substitution.
This statement is true.
The formation of an acetal from a hemiacetal - as is pictured here in this glycosidic bond formation mechanism between two molecules of glucose to form trehalose - is a nucleophilic substitution reaction, as one -OH substituent is replaced in the process.
Predict the major product of the reaction below, assuming it follows Zaitsev’s rule and no substitution reaction takes place.
Zaitsev’s rule states that the most substituted and most stable product (the Zaitsev product) will be formed during an elimination reaction. You will not be required to be familiar with all the possible cases for Zaitsev’s rule for the MCAT, but you are expected to be able to apply it or similar rules when presented with them.
True or False:
Cyclization of an aldohexose (or ketohexose, through an intermediate tautomerization step) is an example of an intramolecular nucleophilic addition mechanism.
True
True or false:
Blood is more likely to have turbulence if the person’s hematocrit (number of blood cells) rises.
This statement is true.
A higher hematocrit causes an increase in density and introduces “chunks” to the blood that do not behave like a normal fluid, causing some chaotic (or turbulent) flow.
The pressure at the front end of a pipe is 40 kPa, and the pressure at the other end is 60 kPa. What will happen to the flow rate if the pressure at the front end of the pipe is lowered to 20 kPa while the pressure at the other end remains the same?
It will double the original flow rate
Poiseuille’s law tells us that the flow rate in a pipe is directly related to the change in pressure:
Where Q is the flow rate, ΔP is the change in pressure, r is the radius of the pipe, n is the fluid viscosity, and l is the length of the pipe.
The pressure starts at a difference of 20 kPa between the two ends of the pipe. When the pressure at one end is lowered, this pressure difference increases to 40 kPa. Since the pressure change doubled, the flow rate will also double.
What happens to the flow in a pipe if the radius and length of the pipe are both doubled, but all other variables remain the same?
The flow will increase by a factor of 8
Poiseuille’s law is as follows:
Q=(π ΔPr4)/8ηL
This means that doubling the length will cut the flow in half, and doubling the radius will increase the flow by a factor of 16, since radius is raised to the fourth power. Together, these changes result in a flow that is 8 times larger in the new pipe.
If the velocity remains constant in a pipe that changes elevation, which part of the pipe will have the highest pressure?
The part of the pipe that is the lowest
Beginning with Bernoulli’s equation:
(P1 + ρgh + ½ ρv2 = P2 + ρgh + ½ ρv2), we can cancel out the terms that include velocity because the velocity is constant in all regions of the pipe. This yields:
P1 + ρgh = P2 + ρgh
For both sides to be equal, whichever side has the highest pressure must have the lowest height.
A large pipe with a cross sectional area of 6 m2 branches into 3 smaller pipes, each with a cross sectional area of 4 m2. At what speed does water travel in the smaller pipes if its velocity is 6 m/s in the large pipe?
3 m/s
The continuity equation tells us that the total flow must remain constant. Because there are three smaller pipes that are each 4 m2, the total cross sectional area is 12 m2. Using the continuity equation, we get:
A1v1 = A2v2
(6 m2)(6 m/s) = (12 m2) (v2)
36 m3/s = 12 m2 (v2)
v2 = 3 m/s
Water is flowing through a funnel. Considering only the Venturi effect, which end would you expect to have the highest pressure?
The larger end would have the highest pressure
The Venturi effect says that when a tube narrows, the velocity increases and the pressure decreases. Thus, the narrow end of the tube has the lowest pressure and the larger end has the highest pressure.
Using a pitot tube for a fluid with a density of 2 kg/m3, you discover that the static pressure is 80 kPa and the stagnation pressure is 120 kPa. How fast is the fluid traveling?
The difference between the static pressure and the stagnation pressure reflects the contribution of the flowing fluid, which is known as the dynamic pressure. The dynamic pressure is expressed as ½ ρv^2. We can plug in the values given and solve for v:
40,000 Pa = ½ (2 kg/m^3) v^2
40,000 = v^2
200 m/s = v
The velocity of the fluid is 200 m/s.
Provide two ways that the units of viscosity can be expressed
Pa*s
N*s / m2
How does raising temperature affect viscosity?
Increasing temperature decreases viscosity.
What effect does an increased temperature have on the turbulence of a fluid?
A higher temperature will decrease the viscosity of a fluid, therefore increasing the Reynolds number and increasing turbulent flow. Note that this is a small effect for most fluids.
What happens to the flow through a pipe if the radius is cut in half?
The flow drops to 1/16 of the original flow
Q = (πr4ΔP) / 8ηL
Using Poiseuille’s law, we know that the flow is proportional to the radius raised to the fourth power. This means that if it the radius is cut in half, the flow is drops to (½)4, or 1/16, of the original flow.
Using Bernoulli’s equation, what is the velocity of water that is leaking through a small hole in a dam that is 20 m below the surface of the lake?
20 m/s
First, we want to compare the water at the top of the lake to the water leaving via the hole using Bernoulli’s equation:
P1 + ρg(h1) + 1/2ρ(v1)2 = P2 + ρg(h2) + 1/2ρ(v2)2
P1 and P2 are both atmospheric pressure, so they will cancel out. Additionally, the water leaving the hole can be set at a height of 0 m, making h2 = 0. Finally, the velocity of the water on the surface of the lake is so small that it is insignificant. This means v1= 0. Combining all of this information, the equation is now:
ρg(h1) = ½ ρ(v2)2
We can now cancel out density, and the equation rearranged:
(v2)2 = 2gh1 = 2(10 m/s2)(20 m)= 400 m2/s2
Therefore v2 = 20 m/s
What is the relationship between radius and area?
area = π r2
An artery has a cross sectional area of 2 cm2, and it branches into 5 arterioles that each have a cross sectional area of 1 cm2. If blood travels at 10 m/s in the artery, how fast is the average speed of the blood in the arterioles?
4 m/s
The continuity equation tells us that the total flow cannot change, so the amount of blood going in must be equal to the amount of blood going out. Since there are 5 arterioles that the blood splits into, the flow in the artery is equal to five times the flow through one of those arterioles.
(Velocity in artery) (area of artery) = 5(velocity in arteriole) (area of arteriole)
(10 m/s) (2 cm2) = 5(velocity in arteriole) (1 cm2)
20 m/s = 5 (velocity)
Velocity = 4 m/s
True or false:
The Venturi effect states that when a fluid starts moving faster, it exerts more pressure on its surroundings.
This is false.
The Venturi effect states that when a fluid starts moving faster, it exerts LESS pressure on its surroundings.
True or False:
Pa*s is a valid unit for flow
False.
Pa*s are units for viscosity, not flow
The pressure on the front end of a pipe is 60 kPa and the pressure on the other end is 80 kPa. What happens to the flow rate if the pressure on the front end of the pipe is lowered to 20 kPa while the pressure at the other end stays the same?
It will triple the original flow rate
Poiseuille’s law tells us that the flow rate in a pipe is directly related to the change in pressure:
Where Q is the flow rate, ΔP is the change in pressure, r is the radius of the pipe, n is the fluid viscosity, and l is the length of the pipe.
The pressure starts at a difference of 20 kPa between the two ends of the pipe. When the pressure is lowered at one end, the pressure difference increases to 60 kPa. Since the pressure change tripled, the flow rate will also triple.
What happens to the flow in a pipe if the radius is doubled and the length of the pipe is quadrupled, but all other variables remain the same?
The flow will increase by a factor of 4
Poiseuille’s law is as follows:
Q=(π r4ΔP)/(8ηL)
This means that quadrupling the length will decrease the flow by ¼ , while doubling the radius will increase the flow by a factor of 16, since radius is raised to the fourth power. Together, this indicates that the flow will increase by a factor of 16/4, or 4, in the new pipe.
If the velocity remains constant in a pipe that changes elevation, which part of the pipe will have the lowest pressure?
The part of the pipe that is the highest
Beginning with Bernoulli’s equation
(P1 + ρgh + ½ ρv2 = P2 + ρgh + ½ ρv2), we can cancel out the terms that include velocity because the velocity is constant in all regions of the pipe. This yields:
P1 + ρgh = P2 + ρgh
For both sides to be equal, whichever side has the lowest pressure must have the highest height.
A small pipe with a cross sectional area of 8 m2 branches into 2 larger pipes, each with a cross sectional area of 10 m2. At what speed does water travel in the larger pipes if it travels at 5 m/s in the small pipe?
2 m/s
The continuity equation tells us that the total flow must remain constant. Because there are two larger pipes each with an area of 10 m2, the total cross sectional area is 20 m2. Using the continuity equation, we get:
A1v1 = A2v2
(8m2)(5m/s) = (20m2) (v2)
40= 20 (v2)
v2 = 2 m/s
Using a pitot tube for a fluid with a density of 4 kg/m3, you discover that the static pressure is 25 Pa, and the stagnation pressure is 75 Pa. How fast is the fluid traveling?
5 m/s
Pstag - Pstatic = ½ρv2
The difference between the static pressure and the stagnation pressure reflects the contribution of the flowing fluid, which is known as the dynamic pressure. The dynamic pressure is expressed as ½ pv2. Plugging in the given values, we can solve for v:
50 Pa = ½ (4 kg/m3) v2
50 = 2 v2
25 = v2
5 m/s = velocity
What equation should you think of if you see the terms stagnation pressure and static pressure?
The dynamic pressure equation
Pstag - Pstatic = ½ρv2
This is often used to find the velocity of a fluid
A ventilator machine expands a patient’s chest approximately 5 x 10-4 m3 in an isobaric process at 1 x 105 Pa with each breathing cycle. What is the total amount of work done on the patient’s chest in one expansion?
5 x 101 J
Work can be calculated as pressure multiplied by the change in volume of a container, or the patient’s lungs in this case.
The equation for this is W = PΔV, where P is pressure and ΔV is the change in volume. This form of work is termed PV work. Using the values provided to us in the question stem,
W = (1 x 105 Pa)(5 x 10-4 m3) = 5 x 101 J.
A new ramp system is installed at a hospital that reduces the angle of incline from 28° to 21°. How will this change the amount of work that is needed to reach the top of the ramp?
The amount of work done is independent of the angle of incline.
Simple machines such as ramps do NOT change the amount of work done. Using an inclined plane, which is essentially just a ramp, means that we push an object over the larger distance of the hypotenuse while really only moving it UPWARD over the smaller distance of the height, which is one leg of the triangle. The work done is exactly the same regardless of which ramp is used, or if no ramp is used at all. This also follows from the fact that gravity is a conservative force.
For a ramp to have mechanical advantage, what must be true?
For ramps, the ideal mechanical advantage can be calculated as follows: mechanical advantage = length of incline / height of incline.
For mechanical advantage to be an “advantage” at all, it needs to be higher than 1, meaning that we get a larger output force than the input force we put in. The higher the mechanical advantage, the more dramatic this difference between output force and the smaller input force - and the easier our lives will be.
A physical therapist has designed a series of ramps offering a different degree of mechanical advantage. The ramps are included in patient treatment plans so that as patients progress through their course of physical therapy, they will be walking up ramps with less and less degrees of mechanical advantage. In what order should the following ramps be assigned in a patient’s treatment plan from the earliest stages of treatment to latest stages of treatment?
Ramp A: 5 m length of incline and 1 m height of incline
Ramp B: 0.5 m length of incline and 0.09 m height of incline
Ramp C: 3 m length of incline and 0.85 m height of incline
The correct order is Ramp B, followed by Ramp A, followed by Ramp C. The question stem specifies that the ramp offering the least mechanical advantage should be used last so we need to order the ramps from most mechanical advantage to least mechanical advantage. For ramps, the ideal mechanical advantage can be calculated as follows:
MA = length of incline / height of incline.
The mechanical advantage for Ramp A is equal to 5 m / 1 m = 5.
The mechanical advantage for Ramp B is 0.5 m/0.09 m which is approximately 0.5 m/0.1 m = 5 but because 0.09 m is a little less than 0.1m the true mechanical advantage is a little greater than 5.
The mechanical advantage for Ramp C is 3.0 m/0.85 m which is approximately 3 m/1 m = 3 because 0.85 m is a little less than 1 m then the true mechanical advantage is a little greater than 3.
What is the amount of work performed in half a minute by a system with an average power output of 180 watts?
5.4 kJ
Power is defined as work divided by time. Since the units for work are joules, the units for power must be joules over seconds, and in fact, this unit for power has a special name: the watt (W), where 1 watt equals one joule per second. In this case we are given power and asked to find work. We can plug the given values into our equation for power, power= work/ time, to give us 180 W = work/(30 s).
Manipulating the equation to solve for work gives us (180 W)(30 s) = 5400 J = 5.4 kJ. Remember to convert correctly between minutes and seconds and joules and kilojoules.
What is the work done on the endotracheal tube balloon cuff during an intubation procedure if the balloon is inflated 4 x 10-3 m3 to a pressure of 1.5 atm?
6 x 10-1 kJ
In this case, work is calculated as pressure multiplied by the change in volume of a balloon cuff. Work is measured in joules, pressure should be in units of pascals, and volume should be in meters cubed. Note that 1 atm = 1 x 105 Pa.
W = (1.5 x 105 Pa)(4 x 10-3 m3)
= 6 x 102 J
= 6 x 10-1 kJ
Be careful with the change in units between joules and kilojoules.
What difference is there in the amount of work required to raise a 2 kg object 4 m using a ramp with an incline angle of 30°, versus raising a 2 kg object 4 m using a ramp with an incline angle of 60°?
There is NO difference in work required
Ramp incline does NOT change the amount of work done. Ramps only provide a mechanical advantage in that less force can be used because the smaller force will be applied over a greater distance.
True or false:
Power output can be increased by increasing the rate at which work is done.
This is true.
Power is, by definition, the rate at which work is done.
True or False:
The kinetic product is favored by reversible reactions
False.
Reversible reactions favor the thermodynamic product, not the kinetic one.
This is because the kinetic product is less stable than the thermodynamic product, even though the kinetic product forms more rapidly. If the reaction is reversible, then the reactants and products are in equilibrium. The kinetic product still forms more quickly, but it can revert to the original reactant and then form the thermodynamic product instead. The equilibrium will ultimately favor the more stable thermodynamic product.
What is the product of a Michael addition?
A Michael addition example is shown below. The product has two carbonyl groups separated by three carbons. Another way to describe this product is a “1,5-dicarbonyl” compound, since if we label one of the carbonyl carbons “1,” the other carbonyl carbon will be number 5.
In a Michael addition mechanism, a base is used to form an enolate, which attacks the β-carbon of an α,β-unsaturated carbonyl compound. This attack shifts the α,β carbon-carbon double bond to form a second enolate. The enolate is protonated to give a final 1,5-dicarbonyl product.
True or false:
The product of a Michael addition is an α,β-unsaturated ketone or aldehyde.
This statement is false.
An α,β-unsaturated ketone or aldehyde is the product of an aldol condensation, and it is also one of the reactants in a Michael reaction as shown below (the α,β-unsaturated ketone above the arrow).
The product of a Michael addition is a 1,5 dicarbonyl structure.
What is the total resistance supplied by three resistors in parallel with resistance values of 4 Ω, 20 Ω, and 5 Ω, respectively?
Rtotal = 2 Ω
Total resistance for resistors in parallel is calculated according to the equation: 1/Rtotal = 1/R1 + 1/R2 + 1/R3…+ 1/Rn. Therefore, the total resistance of the circuit in question is:
1/Rtotal = 1/4 Ω + 1/20 Ω + 1/5 Ω
1/Rtotal = 5/20 Ω + 1/20 Ω + 4/20 Ω
1/Rtotal = 10/20 Ω
1/Rtotal = 1/2 Ω
Rtotal = 2 Ω
If a circuit produces 20 watts of power and has a total resistance of 2 Ω, how much current is flowing through the circuit?
3.2 amps
The best equation to use here is P=I2R. Since all of the given values are already in the correct SI units, we can simply plug them in, yielding:
20 W = I2(2 Ω)
Dividing both sides by 2 gives:
10 = I2
Though the square root of 10 is not a value that you should have memorized, you should know that the square root of 9 is 3, so the square root of 10 should be slightly larger, or about 3.2 amperes.
Solve the following logarithm: log(10,000) = ?
4
If no base is written for a logarithm, we can assume it is base 10. This question can therefore be rewritten as log10(10,000).
This can be rearranged to: 10x = 10,000
104, or 10 x 10 x10 x 10 is equal to 10,000, so 4 must be our answer.
How many times more intense is a 90 dB sound than a 60 dB sound?
1000 times more intense
The decibel equation is dB = 10log(I/I°), where I is the intensity of the sound being measured and I° is the reference intensity. The difference between 90 dB and 60 dB is 30 dB, so we can plug this into our equation:
30 dB = dB = 10log(I/I°)
Dividing each side by 10 yields:
3 dB = log(I/I°)
Since no base is specified, this log must be base 10, so we can rearrange this equation like this:
103 = (I/I°)
103 is equal to 1000
Solve the following logarithm: log(100,000) = ?
5
If no base is written for a logarithm, we can assume it is base 10.
This question can therefore be rewritten as log10(100,000).
This can be rearranged to:10x = 100,000. 105, or 10 x 10 x 10 x 10 x 10 is equal to 100,000, so 5 must be our answer.
How many times more intense is a 25 dB sound than a 5 dB sound?
100
The decibel equation is dB = 10log(I/I°), where I is the intensity of the sound being measured and I° is the reference intensity. The difference between 25 dB and 5 dB is 20 dB, so we can plug this into our equation:
20 dB = dB = 10log(I/I°)
Dividing each side by 10 yields:
2 dB = log(I/I°)
Since no base is specified, this log must be base 10, so we can rearrange this equation like this:
102 = (I/I°)
102 is equal to 100
