Phases

Question 1

What are some basic differences between solids, liquids, and gases?

Answer 1

Solids have greater intermolecular forces or attraction and much less space in between molecules
- Solids favored at high pressures and compression
Gases have lower intermolecular forces and much more space
- Higher kinetic energies of molecules (and T) are likely to break free of intermolecular bonds and exist in liquid or gas phase

Question 2

Real gas

Answer 2

Typical real gas is a loose collection of weakly attracted atoms or molecules moving rapidly in random directions
Volume of molecules is ~0.1% of total volume occupied by gas
Fairly spread out at STP
Attractive forces between molecules decreases as distance increases (attractive forces can almost be ignored)
Average speed of O2 is ~481 m/s, mean free path is 10^-4 mm, 2.5 billion collisions / s

Question 3

Why is a mixture of compounds in gas phase homogeneous regardless of polarity differences?

Answer 3

Molecules are so far apart that they exert negligible attractive or repulsive force on each other
However, density at lower temperatures can cause denser gases to settle beneath less dense gases
Hot air rises because it is less dense than cold air

Question 4

Kinetic Molecular Theory

Answer 4

An ideal gas lacks certain real gas characteristics:
1. Gas molecules have no size, (0 molecular volume)
2. Gas molecules do not exert attractive or repulsive forces on one another
3. Gas molecules have completely elastic collisions
4. Avg KE of gas molecule is directly proportional to temperature of gas
Ideal gas molecules use all of energy to collide with sides of container and exert pressure

Question 5

Ideal Gas Law

Answer 5

PV = nRT

R is universal gas constant = 0.08206 L atm /K mol = 8.314 J /K mol

Question 6

Simple Mercury Barometer

Answer 6

Measures atmospheric pressure
Tube of mercury that is closed at one end is inverted and placed in an uncovered mercury bath open to the atmosphere
Some mercury will fall down into bath, remainder suspended above in the tube
Amount of mercury left in the tube is related to atmospheric pressure pushing down on the mercury bath by:
P_atm = /rho g h
/rho is density of mercury in kg /m^3, g is gravitational constant 9.8 m/s^2, P_atm is measured in Pascals
Historically, height of mercury so important that it became own units, mm Hg which are equivalent to torr
760 torr = 760 mm Hg = 1 atm

Question 7

What is the density of water?

Answer 7

/rho_H2O = 1000 kg/m^3 = 1 g/mL

Question 8

Boyles Law

Answer 8

PV = constant

Pressure and volume are inversely proportional

Question 9

Charle’s Law

Answer 9

V / T = constant
Volume of gas directly proportional to temperature
Think of a constant pressure situation, such as in a balloon
The atmospheric pressure will always necessarily equal the pressure exerted by the balloon on the atmosphere
If not, the balloon would be expanding or contracting

Question 10

Avogadro’s Law

Answer 10

V / n = constant
Volume is directly proportional to moles of gas
Balloon would expand if more air added to the balloon

Question 11

Isovolumetric Process

Answer 11

Change in volume of a process is zero
Therefore the work done is zero
Delta E = w + q = 0 + q
Delta E = q

Question 12

Adiabatic Process

Answer 12

A process that occurs without the transfer of heat, such as with a heavily insulated system
No heat transfer:
Delta E = q + w = w
If gas expanding, w < 0
Gas does work on environment and loses kinetic energy by expansion, decreasing temperature, and pressure also decreases with decreased T and increased V

Question 13

Isothermal Process

Answer 13

Gas remains in thermal equilibrium with surroundings, heat can be exchanged between gas and surroundings
No change in internal energy
Delta E = q + w = 0
If surroundings heated, both temperature and volume of gas will increase in accordance with gas law
Work is done by the gas during expansion, but compensated for by transfer of heat
For an ideal gas, work is equal to internal energy

Question 14

Standard molar volume

Answer 14

AT STP, one mole of any ideal gas will occupy that standard molar volume of 22.4 L
P = 1 atm, T = 273K (STP)

Question 15

Partial Pressure

Answer 15

(Of a particular gas) is total pressure of gaseous mixture multiplied by the mole fraction of the particular gas
P_a = \Chi_a P_total
P_a is partial pressure for gas a, \Chi_a is mole fraction of gas a
In a mixture of gases, each gas contributes to pressure in same proportion as it contributes to number of molecules of gas
Mole fraction: number of moles of gas a divided by total number of moles of gas in sample

Question 16

Dalton’s Law

Answer 16

Total pressure exerted by a gaseous mixture is sun of partial pressures of each of its gases
P_total = P_1 + P_2 + P_3 + …

Question 17

Partial Pressure Equilibrium Constant

Answer 17

Equilibrium constant can be written in terms of partial pressures for reactions involving gases
K_p = P_C^c P_D^d / P_A^a P_B^b = products^coeff / reactants^coeff
To convert between K_p and K_c:
K_p = K_c (RT)^\delta n
\delta n: sum of coefficients of products minus the sum of the coefficients of reactants
Partial pressure equilibrium constants ONLY vary with temperature as with K_c

Question 18

When do real gases deviate from ideal gas behavior?

Answer 18

When their molecules are close together either due to low temperatures or high pressures
Generally deviate above 10 atm

Question 19

Van der Waals’ equation

Answer 19

[P + (n^2 a / V^2)] (V - nb) = nRT
Approximates real pressure and real volume of a gas, where a and b are constants for specific gases
Variable b: accounts for actual volume occupied by a mole of gas
Variable a: reflects strength of intermolecular attractions
Generally both increase with molecular mass and molecular complexity of a gas, so complex gases deviate significantly from ideal behavior

Question 20

Explain the deviations from ideal gases that Van der Waals’ expresses

Answer 20

Molecules of real gas do have volume, so volume must be added to ideal volume:
V_real > V_ideal, where V_ideal is calculated from PV = nRT
Molecules in a real gas do exhibit forces on each other (mostly attractive):
Gas molecules are pulled inward toward center of gas and slow before colliding with container walls (strike the container wall with less force than predicted by kinetic molecular theory, and thus exert less pressure):
P_real < P_ideal, where P_ideal is calculated from PV=nRT

Question 21

If PV/RT is greater than 1 for one mole of a real gas, what does this mean? If PV/RT is less than 1 for one mole of real gas, what does this mean?

Answer 21

For greater than 1, this means the contribution of the volume of the gas itself is contributing more to deviations from ideal gases (increased volume in ratio)
For less than 1, this means that the deviation due to intermolecular forces must be greater than the deviation due to molecular volume

Question 22

What are some general rules of thumb for what molecules are gas at room temperature, and which tend to be liquids or solids?

Answer 22

The more polar a molecule, the greater the dipole moments, and consequently the stronger the intermolecular forces, and so the more likely it is to be liquid or solid at room temperature (e.g. H2O)
The larger a molecule, the more likely it is to have strong intermolecular forces, independent of polarity
Simplest alkane, methane (CH4) is a gas at STP, C6H14 is a liquid, and eicosane (C20H42) is a solid

Question 23

Heat Capacity

Answer 23

Added energy required to increase the temperature of a given substance by one Kelvin (or equivalently, one degree Celsius)
Different substances can absorb different amounts of energy before their temperature increases a certain amount
C = q / delta T
Remember that heat is a process of energy transfer, not something that can be stored so ‘Internal energy capacity’ would be a better name

Question 24

Two types of heat capacities for a substance

Answer 24

Constant volume heat capacity (Cv) = q / delta T_{constant volume}
If volume constant, no PV work and all energy change must be in form of heat
None of energy going into system can escape as work done by system
Constant pressure heat capacity (Cp) = q / delta T_{constant pressure}
When pressure is held constant, and substance is allowed to expand, some energy can leave system as PV work done on surroundings as volume changes
Cp > Cv because delta T is greater for Cv than for Cp, difference only significant for molecules in gas phase

Question 25

When energy is transferred into a system, what are the possible ways the energy can have an effect on the system?

Answer 25

\Delta E = q + w
Some of the work in the system goes into performing PV work, some of it goes into change in temperature
Compound can also absorb energy as atoms in a molecule increase their motion and stretch their intramolecular bonds (kind of potential energy)
The more bonds a molecule has, the more energy it can channel into bond stretching rather than raising temperature
Intermolecular bonds must also be broken to raise KE and therefore temperature

Question 26

What does heat capacity vary with?

Answer 26

Heat capacity changes as temperature changes

However, for MCAT assume heat capacity of a substance is constant and does not change with temperature

Question 27

What is a common unit for heat capacity?

Answer 27

1 Calorie = 1000 calories = 4184 Joules
1 cal is ~= to amount of energy required to raise one gram of water by 1 degree Celsius
Overall heat capacity for a system may use units J / K or cal / deg C

Question 28

Specific heat capacity

Answer 28

Intrinsic property that represents the heat capacity per unit mass
Units: J / kg K or cal / g deg C
(Heat capacity is an extrinsic property that depends on size of sample)
Use equation for heat transfer with specific heat capacity:
q = mc delta T
Where m is mass

Question 29

calorimeter

Answer 29

Device that measures heat change
Container that holds a liquid, often water, with a thermometer placed inside to measure any changes in temperature
Useful because they are highly insulated from surroundings, so well-suited to track the energy changes associated with a reaction

Question 30

Consider an endothermic reaction in a water-filled calorimeter, describe how to calculate the heat transfer.

Answer 30

Calorimeter is insulated from environment, so all heat will come from water in calorimeter and temperature of water will decrease
Heat transfer can be calculated using q = mc \delta T
Thermodynamic properties of the reaction can be determined by calculating the change in energy of the calorimeter
This means q_water < 0 since water transferred heat away, and q_reactants > 0
Also means: q_water = -q_reactants

Question 31

Coffee cup calorimeter

Answer 31

Constant pressure calorimeter, measures the energy change at atmospheric pressure
Insulated container to prevent heat exchange with surroundings
Thermometer used to measure changes in temperature
Used to measure heats of reaction, \delta H
At constant pressure, we know that q = \delta H, so can calculate with q = mc \delta T

Question 32

Bomb calorimeter

Answer 32

Measures energy changes at constant volume and indicates the internal energy change in a reaction (q = \delta U)
Reaction takes place inside a rigid container inside a thermally insulated container
When reaction occurs, heat is transferred to surrounding liquid and inner container
Cannot just use specific heat capacity, so use heat capacity of calorimeter, q = C \delta T

Question 33

Describe the phase change of water as heat is added

Answer 33

Heat is uniformly added to ice at a constant rate
Energy going into ice increases vibration of molecules, increasing KE and raising temperature, then as ice reaches 0 deg C, temperature stops increasing
Energy now goes into breaking and weakening H bonds, resulting in phase change from ice to liquid
After all is converted to liquid water, temperature begins to rise again as heat goes into increased movement of molecules
When water reaches 100 deg C, temperatures stops rising again and energy goes into breaking H bonds, resulting in second phase change from liquid to steam
Once all H bonds are broken and water is steam, heat increases the speed of molecules and temperatures rise again

Question 34

What is the heat capacity during a phase change?

Answer 34

Technically infinite: energy is being transferred in as heat, but temperature remains constant (\delta T = 0)

Question 35

Normal melting point and normal boiling point for water

Answer 35

At constant pressure of 1 atm, normal melting point of water is 0 deg C and normal boiling point is 100 deg C

Question 36

Heat of fusion

Answer 36

Enthalpy change associated with melting
Amount of heat absorbed during melting is exactly the same as the amount released during freezing
Usually less than the heat of vaporization for a compound
Based on the intermolecular forces holding a compound in its solid form
Heat of fusion of ice to water: 0.33 kJ/g

Question 37

Heat of vaporization

Answer 37

Enthalpy change associated with boiling and the conversion from liquid to gas
Based on intermolecular forces holding molecule in liquid form
Same forward as reverse process
Heat of vaporization for water to steam: 2.26 kJ/g

Question 38

What does a heating curve show? What is the slope?

Answer 38

Shows the heat transfer to temperature of a molecule over different phase changes T vs. q
Will see a flat line during the change from solid to liquid (heat of fusion is length of line) and a flat line during the change from liquid to gas (heat of vaporization is length)
In between these phase changes, temperature increases linearly as defined by q = mc \delta T, where the c is different depending on the phase of the molecule
Slope of increasing lines is 1/mc
Equation of lines in increasing areas: \delta T = q / mc

Question 39

How does the specific heat of a gas compare to a liquid?

Answer 39

Gas molecules are usually so dispersed that their intermolecular forces are virtually nonexistent, so gases tend to have much lower specific heats than their respective solids and liquids (this means on heat curve we see the slope after gas heat change is steeper)

Question 40

What is the name for the phase change from a solid to a gas? A gas to a solid?

Answer 40

Sublimation: solid to a gas
Deposition: gas to a solid

Question 41

What impact do melting, boiling, and sublimation usually have on volume, molecular motion, and entropy?

Answer 41

Usually increase volume and molecular motion which results in an increase in entropy
For most phase changes, entropy and enthalpy have the same sign ( all three of these phase changes are endothermic and require the addition of heat, therefore \delta H > 0)
With phase changes, the temperature dictates whether the forward or reverse reaction will be spontaneous
\delta G = \delta H - T \delta S (when H and S are positive, temperature controls sign of G)

Question 42

Phase Diagram

Answer 42

Indicates the phase of a substance at different pressures and temperatures
Lines marking the boundaries of each section represent temperatures and pressures where the corresponding phases are in equilibrium with one another
Equilibrium is dynamic (forward and reverse reactions occurring)
Triple point: only point where a substance can exist in equilibrium between the solid, liquid, and gas phases
Critical temperature: temperature above which a substance cannot be liquefied, regardless of pressure
Critical pressure: Pressure required to produce the liquid phase when the substance is exactly at the critical temperature
Together, define the critical point: fluid beyond the critical point has characteristics of both gas and liquid, called supercritical fluid

Question 43

What are ideal conditions for sublimation?

Answer 43

Low temperature and low pressure
Low temperature: molecules that tend to enter liquid phase under normal conditions will tend to favor solid
Low pressures: favor gas phase where molecules are not very restricted

Question 44

What does the negative slope of the line between the solid and liquid phase for a phase diagram of water mean?

Answer 44

That liquid is actually more dense than solids

For higher temperatures, need less pressure to push a solid to a liquid

Question 45

Why are melting or boiling points really a curve?

Answer 45

At fixed pressure, the mp or bp is a point, however mp and bp vary with pressure, so really a function of pressure or a curve
Temperature at which a substance melts or vaporizes lies along a melting or boiling curve