Thermodynamics

Question 1

What is a thermodynamic system?

Answer 1

It is a body that is engaged in mass and/or energy exchange with its surroundings.

The classic example of a thermodynamic system is a piston filled with gas.

Question 2

Define:

an open thermodynamic system

Answer 2

It can exchange both mass and energy with the environment.

For example, a bottle of gas with no lid is an open thermodynamic system.

Question 3

Define:

a closed thermodynamic system

Answer 3

It cannot exchange mass with the environment, but can exchange energy.

For example, a bottle of gas with the lid securely on is a closed thermodynamic system.

Question 4

Define:

an isolated thermodynamic system

Answer 4

It cannot exchange energy or mass with the environment.

For example, a closed, insulated container with a temperature that is independent of its environment is an isolated system.

Question 5

With regard to a thermodynamic system, what are the surroundings?

Answer 5

Also known as the environment, they are everything capable of exchanging mass and/or energy with the system.

Question 6

Define:

a state function

Answer 6

It is any property of a thermodynamic system that depends only on the characteristics of the system at that moment.

Since state functions are calculated based on current vs past properties only, their values do not depend on the path by which the current state was achieved; they are path-independent.

Question 7

If X is a state function, what is the change in X when a system moves from a value of X₁ to X₂?

Answer 7

ΔX = X₂ - X₁

Since X is a state function, the path by which it gets from state 1 to state 2 is irrelevant; the change in X depends only on the initial and final states.

Question 8

Define:

enthalpy

(H)

Answer 8

It is a measure of the heat contained in a system.

Enthalpy’s absolute value cannot be directly measured, so the change in enthalpy, ΔH, is calculated instead.

Question 9

What are the properties of an exothermic reaction?

Answer 9

It is any reaction whose products have a lower enthalpy than the reactants. In such reactions, ΔH < 0, and heat is lost from the system to the environment.

Remember that “exo” is like “exit”; heat exits the system in an exothermic reaction.

Question 10

What are the properties of an endothermic reaction?

Answer 10

It is any reaction whose products have a higher enthalpy than the reactants. In such reactions, ΔH > 0, and heat is absorbed by the system from the environment.

Remember that “endo” is like “into”; heat flows into the system in an endothermic reaction.

Question 11

Define:

standard enthalpy of formation

(ΔH^o_f)

Answer 11

It is the enthalpy change for a material’s formation from its fundamental elements under standard conditions.

For example, the enthalpy of formation for NaCl is -411.12 kJ mol⁻¹ and follows from the general equation:

Question 12

What is the standard enthalpy of formation (ΔH^o_f), of oxygen gas, O₂?

Answer 12

0

By definition, the enthalpy of formation for any material in its standard state is zero.

Question 13

What are the requirements for a reaction to take place under standard conditions?

Answer 13

• Pressure = 1 atm
• Temperature = 25º C = 298 K
• Concentration = 1 M for all products and reactants

Question 14

If the chemical reaction

(1) 2A ⇒ C ΔH₁

can be broken down into two steps:

(2) 2A ⇒ B ΔH₂
(3) B ⇒ C ΔH₃

what does Hess’s Law tell you about the overall enthalpy change ΔH₁?

Answer 14

ΔH₁ = ΔH₂ + ΔH₃

Hess’s Law simply states that the enthalpy of a reaction can be calculated by adding together the enthalpies of a chain of component steps which add up to the overall reaction.

Although most commonly applied to enthalpy, Hess’s Law applies to all state functions.

Question 15

What is the enthalpy change when 2 moles of CH₄ are formed according to the following reactions?

2H₂(g) ⇒ 4H(g)
ΔH₁= -870 kJ/mol

C(s) + 4H(g) ⇒ CH₄(g)
ΔH₂= +794 kJ/mol

Answer 15

-152 kJ

1) Adding the reactions together yields the formation reaction of CH₄:

C(s) + 4H(g) + 2H₂(g) ⇒ CH₄(g) + 4H(g)
Canceling common terms leaves:
C(s) + 2H₂(g) ⇒CH₄(g)

2) To complete the calculation, combine the reactions’ enthalpies in the same way the reactions themselves were combined.

ΔH_rxn = ΔH₁ + ΔH₂
-870 + 794 = -76kJ/mol

3) Finally, multiply by the number of moles produced (2) to get the final answer.

Question 16

How can the enthalpy change of a reaction be calculated from the enthalpies of formation of the reactants and products?

Answer 16

∆Hº_rxn= Σ∆Hº_f(products) - Σ∆Hº_f(reactants)

To calculate the enthalpy change of a reaction, sum the enthalpies of formation of the products. Then subtract the sum of the enthalpies of formation of the reactants.

Question 17

Is this reaction endothermic or exothermic?

CH₄ + 2O₂ ⇒ CO₂ + 2H₂O

• ΔH^o_f (CH₄) = -75 kJ/mol
• ΔH^o_f (CO₂) = -394 kJ/mol
• ΔH^o_f (H₂O) = -286 kJ/mol

Answer 17

exothermic

∆H°_rxn= Σ∆H^o_f(products) - Σ∆H^o_f(reactants)
[CO₂ + 2*H₂O] - [CH₄ + O₂]

[-394 kJ/mol + 2(-286 kJ/mol)] - [-75 kJ/mol + 2(0)]

-891 kJ/mol

Remember, on the MCAT, you won’t have a calculator. Approximate to get close to the final answer.

Question 18

Define:

bond enthalpy

Answer 18

It is the energy absorbed or released when a particular chemical bond is broken.

Most chemical bonds are stabilizing, so most bond-breaking reactions are endothermic, and most bond enthalpies are therefore positive.

Question 19

How can the enthalpy of a reaction be calculated from the bond enthalpies of the reactants and products?

Answer 19

∆H_rxn = Σ∆H(bonds broken) - Σ∆H(bonds formed)

The reaction’s enthalpy change is identical to the energy needed to break all the bonds in the reactants, minus the energy released when the bonds in the products form.

Question 20

What is the overall enthalpy change of this reaction?

CH₄ + 2O₂ ⇒ CO₂ + 2H₂0

• ΔH (C-H) = 411 kJ/mol
• ΔH (O=O) = 494 kJ/mol
• ΔH (C=O) = 799 kJ/mol
• ΔH (O-H) = 463 kJ/mol

Answer 20

-818 kJ/mol

∆H_rxn = Σ∆H(bonds broken) - Σ∆H(bonds formed)
[4*(C-H) + 2*(O=O)] - [2*(C=O) + 2*2*(H-O)]

[(4 * 411) + (2 * 494)] - [(2 * 799) + (4 * 463)] kJ/mol

-818 kJ/mol

Remember, you won’t have a calculator on the MCAT, so approximate to get close to the correct answer.

Question 21

Define:

specific heat

(c)

Answer 21

It is a characteristic property of a material, and is the amount of heat which must be added to raise 1 g of the substance by 1 ºC.

The higher the specific heat, the more energy input required to raise the substance’s temperature.

Question 22

What formula can be used to calculate the necessary quantity of heat to raise the temperature of a material?

Answer 22

q = mcΔT

Where:

q = heat required (J)
m = mass of substance present (g)
c = substance’s specific heat (J/g*ºC)
ΔT = temperature change (ºC)

Question 23

What is the specific heat of water?

Answer 23

4.18 J/g*K

This is a value that you should have memorized. According to this measurement, it requires 4.18 J to raise 1 g of water by 1 K (or ºC).

This value is equal to 1 cal/g*K.

Question 24

8 J of heat is applied to 1 g of both iron and water at 25 ºC. Which material changes its temperature more?

The specific heat of water is 4.184 J/g*K.
The specific heat of iron is 0.46 J/g*K.

Answer 24

The temperature of the iron changes more.

Applying the equation q = mcΔT to both cases and solving for ΔT reveals that the iron will change temperature by about 20 degrees (final T = 45 ºC), while the water will only increase by 2 degrees (final T = 27 ºC).

The higher a material’s specific heat, the less responsive its temperature is to heat flow.

Question 25

What does a calorimeter measure?

Answer 25

It measures the amount of heat given off by a particular chemical reaction or process.

There are many different styles of calorimeter, but for the MCAT, you should focus on the fact that they all measure heat generated when a system’s temperature changes, using the equation q = mcΔT.

Question 26

Why doesn’t the specific heat equation q = mcΔT apply during a phase change?

Answer 26

Temperature stays constant as heat is added. The added heat causes the material to change in phase by breaking intermolecular forces, rather than increasing its temperature.

The amount of heat needed to make a material change its phase is known as the latent heat of that phase change.

Question 27

The curve below represents a sample’s temperature versus the heat added. What phases (solid, liquid, and/or gas) are present at each labeled point on the plot?

Answer 27

a. solid
b. both solid and liquid
c. liquid
d. both liquid and gas
e. gas

Question 28

The curve below represents a sample’s temperature versus the heat added. Which heat (q) formula must be applied to calculate heat added to the system at each labeled point on the plot?

Answer 28

a. q=mcΔT
b. q=mΔH_fusion
c. q=mcΔT
d. q=mΔH_vap
e. q=mcΔT

Question 29

Define:

entropy

Answer 29

It is a macroscopic property of a system, representing the number of possible ways the atoms or molecules of the system can arrange themselves.

Colloquially, entropy is said to represent the possibility for “disorder” of a system. This definition is effective for most entropy questions on the MCAT.

Question 30

What does increasing entropy say about a system’s properties?

Answer 30

As a system’s entropy increases, it becomes more disordered.

Systems spontaneously tend towards arrangements with higher entropy.

Question 31

Arrange the relative entropy levels of the 3 phases of matter:

S_solid, S_gas, S_liquid

Answer 31

S_solid < S_liquid < S_gas

Since entropy is a measure of disorder, the more ordered a system, the lower its entropy. Solid matter, with its regularly-repeating units and fairly well-defined locations for the atoms, is therefore low in entropy, while gases, with their continuous, random motion, have the highest entropy values.

Question 32

What is the sign of the entropy change for this chemical reaction?

2H₂(g) + O₂(g) ⇒ 2H₂O(l)

Answer 32

ΔS < 0; in other words, the change in entropy is negative.

Gases have more entropy than liquids; hence, in any chemical reaction, the side with more moles of gas will have higher entropy.

In general, reactions with fewer moles of products than reactants will have a lower final entropy value.

Question 33

What are the signs of the enthalpy and entropy changes for this reaction?

H₂O (l) ⇒ H₂O (g)

Answer 33

ΔH_rxn > 0
ΔS_rxn > 0

The reaction is endothermic, since heat must be added to vaporize the water. Since the reaction creates gas, it represents an increase in entropy.

Question 34

What are the enthalpy and entropy changes for this reaction?

CO₂ (g) ⇒ CO₂ (s)

Answer 34

ΔH_rxn < 0
ΔS_rxn < 0

The reaction is exothermic, since heat must be removed to deposit the CO₂. Since the reaction results in a net decrease of gas, it represents an decrease in entropy.

Question 35

Define:

Gibbs free energy

(ΔG)

Answer 35

It is a measure of the work which can be extracted from a thermodynamic system. ΔG can be calculated as such:

ΔG = ΔH - TΔS

A handy mnemonic for remembering the formula for ΔG is “Get Higher Test Scores.”

Question 36

What does a negative value for ΔG imply about a chemical reaction?

Answer 36

The forward reaction is spontaneous, favoring the creation of more products.

Question 37

What does a positive value for ΔG imply about a chemical reaction?

Answer 37

The forward reaction is nonspontaneous and the reverse reaction is spontaneous. This favors the creation of more reactants.

Question 38

Define:

an exergonic reaction

Answer 38

It is any reaction for which ΔG < 0; because of this, all exergonic reactions are spontaneous.

This is very similar to the definition of “exothermic,” for which ΔH < 0. “Thermic” refers to enthalpy, “gonic” to Gibbs free energy.

Question 39

Define:

an endergonic reaction

Answer 39

It is any reaction for which ΔG > 0; because of this, all endergonic reactions are non-spontaneous.

This is very similar to the definition of endothermic, for which ΔH > 0. “Thermic” refers to enthalpy, “gonic” to Gibbs’ free energy.

Question 40

Describe the spontaneity of a reaction where:

ΔH_rxn > 0
ΔS_rxn < 0

Answer 40

It will always be nonspontaneous.

Remember that ΔG = ΔH - TΔS. Since T is in Kelvin and will always be positive, then both ΔH and -TΔS are positive. The quantity ΔG must always be positive, then, so the reaction is endergonic at all temperatures.

Question 41

Describe the spontaneity of a reaction where:

ΔH_rxn < 0
ΔS_rxn < 0

Answer 41

It will be spontaneous at low temperatures, and nonspontaneous at sufficiently high temperatures.

Remember that ΔG = ΔH - TΔS. When T is sufficiently low, the second term can be ignored, and ΔG will be negative due to ΔH. But when T becomes large enough, the positive sign of the -TΔS term dominates, and ΔG becomes positive.

Question 42

Describe the spontaneity of a reaction where:

ΔH_rxn > 0
ΔS_rxn > 0

Answer 42

It will be spontaneous at high temperatures and nonspontaneous at sufficiently low temperatures.

Remember that ΔG = ΔH - TΔS. When T is sufficiently low, the second term can be ignored, and ΔG will be positive (corresponding to a nonspontaneous reaction) because ΔH > 0. However, when T becomes large enough, the negative sign of the -TΔS term dominates and ΔG becomes negative (corresponding to a spontaneous reaction).

Question 43

Describe the spontaneity of a reaction where:

ΔH_rxn < 0
ΔS_rxn > 0

Answer 43

It will always be spontaneous.

Remember that ΔG = ΔH - TΔS. Since T is in Kelvin and will always be positive, both ΔH and -TΔS are negative. The quantity ΔG will always be negative, so the reaction is exergonic at all temperatures.

Question 44

What is the difference between ΔG and ΔGº?

Answer 44

• ΔG describes the change in Gibbs free energy for a chemical system at a particular pressure and temperature, which must be given.
• ΔGº describes the change in Gibbs’ free energy for a chemical system at standard conditions (1 atm, 298 K, 1 M in all concentrations).

Typically, different reactions’ ΔGº values will be compared, since it allows for a common point of reference between them.

Question 45

What is the relationship between a thermodynamic system’s temperature and its internal energy?

Answer 45

They are equivalent concepts.

If a system’s absolute temperature doubles, so does the amount of energy that it contains.

This is the foundation of the zeroth law of thermodynamics, which states that if systems A and C are both in thermal equilibrium with system B, they are also in equilibrium with each other. In other words, they are at the same temperature.

Question 46

Give the relationship between a fluid’s temperature and the internal energy (average kinetic energy) of the molecules in the fluid.

Answer 46

U = KE_avg = (3/2)nkT

Where:

k = Boltzmann’s constant (1.38 x 10^-23 J/K)
T = absolute temperature (K)
n = number of moles of fluid molecules

Question 47

Define:

work

Answer 47

It is the flow of energy between a system and its surroundings in the form of changing pressure and volume of the system.

In thermodynamics, work is signified by the symbol w and measured in joules.

Question 48

Define:

heat

Answer 48

It is the flow of energy between a system and its surroundings in any form other than work.

In thermodynamics, heat is signified by the symbol q and measured in joules.

Question 49

Explain the First Law of Thermodynamics.

Answer 49

It states that heat and work are the only possible mechanisms of energy flow into and out of a system. It also states that energy is always conserved; for this reason, energy change can be calculated as:

ΔE = Δq + Δw

Question 50

Explain the direction of work being done and the sign of ΔE during the compression of a thermodynamic system.

Answer 50

Work is being done by the environment, on the system.

Since energy is flowing into the system due to the work being done, ΔE > 0.

Question 51

Explain the direction of work being done and the sign of ΔE during the expansion of a thermodynamic system.

Answer 51

Work is being done by the system, on the environment.

Since energy is flowing out of the system due to the work being done, ΔE < 0.

Question 52

What is the direction of heat flow for a thermodynamic system that is surrounded by an environment at a higher temperature? What does this mean for the sign of ΔE?

Answer 52

When the environment is at a higher temperature than the system, heat flows from the environment into the system, and Δq > 0.

This direction of heat flow leads to energy being added to the system, and ΔE > 0 as well.

Question 53

What is the direction of heat flow for a thermodynamic system that is surrounded by an environment at a lower temperature? What does this mean for the sign of ΔE?

Answer 53

When the environment is at a lower temperature than the system, heat flows from the system to the environment, and Δq < 0.

This direction of heat flow leads to energy being removed from the system, and ΔE < 0.

Question 54

What are the characteristics of an adiabatic thermodynamic process?

Answer 54

It is one in which heat cannot flow. In such a process, Δq = 0 and ΔE = Δw; all energy change is due to work being done on or by the system.

Adiabatic processes either take place in heat-insulated systems, or occur so quickly that heat cannot flow between system and environment.

Question 55

What happens to the temperature of a system during an adiabatic compression?

Answer 55

The system’s temperature must increase.

Remember, Δq = 0 for all adiabatic processes. Furthermore, during any compression, work is being done on the system, raising ΔE. Since T and ΔE are proportional, the system’s temperature will increase as well.

Question 56

What happens to the system’s temperature during an adiabatic expansion?

Answer 56

The system’s temperature must decrease.

Remember, Δq = 0 for all adiabatic processes. Furthermore, during any expansion, the system is doing work, causing it to lose energy. Since T and ΔE are proportional, the system’s temperature will decrease as well.

Question 57

What are the characteristics of an isothermal thermodynamic process?

Answer 57

It is one in which temperature is held constant. In such processes, ΔE = 0 and Δq = -Δw. Any heat flow into or out of the system is compensated by work done by or on the system, respectively.

Isothermal processes usually happen slowly enough that the system’s temperature can constantly equilibrate.

Question 58

In what direction does heat flow during an isothermal compression?

Answer 58

out of the system

Remember, during any compression, work is being done on the system, raising ΔE. Since an isothermal compression must have an overall ΔE = 0, Δq must be negative to compensate.

Question 59

In what direction does heat flow during an isothermal expansion?

Answer 59

into the system

Remember, during any expansion, the system is doing work and losing energy. Since any isothermal process must have an overall ΔE = 0, Δq must be positive to compensate.

Question 60

Explain the Second Law of Thermodynamics.

Answer 60

It states that for any thermodynamic process, the total entropy of the universe must increase.

ΔS_universe > 0
ΔS_system+ ΔS_surroundings > 0

The universe can be defined as a system and its surroundings. Therefore, if the entropy of a system decreases, the entropy of its surroundings must increase by a greater amount in order for the universal law to hold true.

Question 61

If System X is completely isolated from its surroundings, what must be true of ΔS_X for any process that occurs inside the system?

Answer 61

ΔS_X > 0

Since System X is isolated, it cannot exchange energy or entropy with its surroundings. For the Second Law to hold, the entropy of the system itself must increase.

Question 62

What formula can be used to convert between temperatures in Celsius and Kelvin?

Answer 62

T_K = T_C + 273

Where:

T_K = Kelvin temperature
T_C = Celsius temperature

Some standard temperatures to memorize:

• 0º C = 273 K
• 25º C = 298 K
• 100º C = 373 K

Question 63

What formula can be used to convert between temperatures in Celsius and Fahrenheit?

Answer 63

T_F = (9/5)*T_C + 32

Where:

T_F = Fahrenheit temperature
T_C = Celsius temperature

Some standard conversions to memorize:

• 32º F = 0º C
• 77º F = 25º C
• 212º F = 100º C

Question 64

Define:

conduction

Answer 64

It is the transfer of thermal energy via molecular collisions. It requires physical contact between the systems that are exchanging energy.

When the molecules collide, molecules of the higher-energy system transfer some of their energy to the lower-energy molecules of the other system, cooling the first and heating the second.

Question 65

Define:

convection

Answer 65

It is the thermal energy transfer via the movement of fluid in currents. It requires at least one medium that is capable of motion.

Differences in pressure or density drive warm fluid in the direction of cooler fluid, transferring heat away from a warmer object or towards a cooler one.

Question 66

Define:

radiation

Answer 66

It is the thermal energy transfer via emission or absorption of electromagnetic waves.

Radiation does not require a medium, so it can occur through a vacuum.

Question 67

When a hot piece of metal is placed on a wooden table, causing the table to start to smoke, what is the primary form of heat transfer being exhibited?

Answer 67

Conduction

Conduction is the most efficient form of heat transfer. Since the metal and table are in direct physical contact, conduction will dominate.

Question 68

When the upstairs rooms of a house are warmer than the basement, what form of heat transfer is being exhibited?

Answer 68

Convection

The decreased density of the warmer air causes it to rise to the top of the house, a classic example of a convection current.

Question 69

When the sun rises above the horizon, warming the ground, what form of heat transfer is being exhibited?

Answer 69

Radiation

For the heat to move from the sun to the earth, it must travel across millions of miles of near-empty space. Only electromagnetic radiation can carry energy across this distance, and electromagnetic waves transfer heat through radiation.

Question 70

What equation gives the work done on a thermodynamic system as a function of its pressure and volume?

Answer 70

Work = PΔV

At constant pressure, W = PΔV can be calculated by simple multiplication. More generally, the work done during a thermodynamic process is the area under the curve of a P vs, V diagram.