Thermodynamics

Question 1

Define and give an example of:

A Thermodynamic System

Answer 1

A thermodynamic system is a macroscopic body which is engaged in mass and/or energy exchange with its surroundings.

Ex: The classic example of a themodynamic system is a piston filled with gas.

Question 2

Define and give an example of:

An open thermodynamic system

Answer 2

An open system can exchange both mass and energy with the environment.

Ex: An bottle of gas with no lid is an open thermodynamic system.

Question 3

Define and give an example of:

A closed thermodynamic system

Answer 3

A closed system cannot exchange mass with the environment, but can exchange energy.

Ex: A bottle of gas with the lid securely on is a closed thermodynamic system.

Question 4

Define and give an example of:

An isolated thermodynamic system

Answer 4

An isolated system can not exchange either energy or mass with the environment.

Ex: A closed, double-walled (insulated) container which is temperature-independent of its environment is an isolated system.

Question 5

Define “the surroundings” in a thermodynamic problem.

Answer 5

The surroundings (also known as the environment) are everything capable of exchanging mass and/or energy with the system.

Question 6

Define:

A State Function

Answer 6

A state function is any property of a thermodynamic system that depends only on comparing the characteristics of the system at that moment compared to a prior 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 between a system’s values X₁ and X₂?

Answer 7

ΔX = X₂ - X₁

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

Question 8

Define:

Enthalpy, H

Answer 8

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

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

Question 9

What are the properties of an exothermic reaction?

Answer 9

An exothermic reaction is any reaction whose products have a lower enthalpy than the reactants. Therefore, ΔH < 0, and heat is lost from the system to the environment.

(Exo = exit)

Question 10

What are the properties of an endothermic reaction?

Answer 10

An endothermic reaction is any reaction whose products have a higher enthalpy than the reactants. Therefore, ΔH > 0, and heat is absorbed by the system from the environment.

(Endo = into)

Question 11

Define:

A material’s standard enthalpy of formation, ΔH^o_f

Answer 11

The standard enthalpy of formation (ΔH^o_f) is the enthalpy change of the formation reaction for the material from its fundamental elements under standard conditions.

Ex: 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

Zero.

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

Question 13

What are standard conditions?

Answer 13

• Pressure = 1 atm
• Temperature = 25 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 the sub-reactions

(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 sub-reactions which add up to the overall reaction.

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

Question 15

rxn1: 2H₂(g)⇒4H(g)
ΔH_rxn= -870 kJ/mol

rxn2: C(s) + 4H(g)⇒CH₄(g)
ΔH= +794 kJ/mol

What is the enthalpy change when 2 moles of CH₄ are formed?

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 were combined.

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

3) Finally, multiply by the number of moles (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)

Sum the enthalpies of formation of the products, and subtract the sum of the enthalpies of formation of the reactants.

Question 17

Is this reaction endothermic or exothermic?

CH₄+ 2O₂ ⇒ CO₂+ 2H₂0

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

Answer 17

The reaction is 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 kJ)]

= -891 kJ/mol

Question 18

Define:

Bond Enthalpy

Answer 18

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 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

Question 21

Define:

Specific Heat, c

Answer 21

Specific heat 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 1ºC.

The higher the value of c, the more heat it takes to raise the substance’s temperature.

Question 22

What is the formula for necessary quantity of heat in a specific heat problem?

Answer 22

q = mcΔT

Where q is the necessary heat, m is the mass of substance present, c is the substance’s specific heat, and ΔT is the desired temperature change.

Question 23

What is the specific heat of water?

Answer 23

4.184 J/g-K

This is a value the MCAT expects you to have memorized. It means that it takes 4.184 J to raise 1 g of water by 1ºK.

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

Question 24

The specific heat of water is 4.184 J/g-K.

The specific heat of iron is 0.46 J/g-K.

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

Answer 24

The iron changes its temperature 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 = 45ºC), while the water will only increase by 2 degrees (final T = 27ºC).

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

A calorimeter 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 via a system’s temperature change, using the equation

q = mcΔT

Question 26

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

Answer 26

During a phase change, temperature stays constant as heat is added. The added heat causes the material to go through the phase change, 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

What is the equation for calculating the heat of a phase change?

Answer 27

q = mΔH_L

where q = necessary heat, m = mass of the substance present, and ΔH_L is the latent heat of the phase change.

The higher the ΔH_L, the more heat it takes to force the substance to go through the phase change.

Question 28

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

Answer 28

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

Question 29

The curve below represents a sample’s temperature vs. heat added. What heat (q) formula would need to be applied, in order to calculate heat added to the system at each labeled point on the plot?

Answer 29

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

Question 30

Define:

Entropy of a system

Answer 30

Entropy 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, and this definition is effective enough for most entropy questions on the MCAT.

Question 31

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

Answer 31

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

Systems spontaneously tend towards arrangements with higher entropy.

Question 32

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

S_solid, S_gas, S_liquid

Answer 32

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 33

What is the entropy change for this chemical reaction?

2H₂(g) + O₂(g) ⇒ 2H₂O(l)

Answer 33

ΔS < 0

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 lower final entropy.

Question 34

What are the enthalpy and entropy changes for this reaction?

H₂O (l) ⇒ H₂O (g)

Answer 34

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 35

What are the enthalpy and entropy changes for this reaction?

CO₂ (g) ⇒ CO₂ (s)

Answer 35

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 36

Define and give the formula for calculating:

Gibbs’ Free Energy, ΔG

Answer 36

ΔG is a measure of the work which can be extracted from a thermodynamic system.

ΔG = ΔH- TΔS

It also is used to measure the spontaneity of a system; chemical systems will always tend to move in a direction of decreasing ΔG.

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Question 37

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

Answer 37

If ΔG < 0 for a chemical reaction, then the forward reaction is spontaneous, favoring the creation of more products.

Question 38

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

Answer 38

If ΔG > 0 for a chemical reaction, then the forward reaction is non-spontaneous, and the reverse reaction is spontaneous, favoring the creation of more reactants.

Question 39

Define:

An Exergonic Reaction

Answer 39

An exergonic reaction is any reaction for which ΔG < 0; hence 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.

(Exerg = exit G)

Question 40

Define:

An Endergonic Reaction

Answer 40

An endergonic reaction is any reaction for which ΔG > 0; hence all exergonic 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.

(Enderg = enter G)

Question 41

Describe the spontaneity of a reaction where:

ΔH_rxn > 0
ΔS_rxn < 0

Answer 41

This reaction will always be non-spontaneous.

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

Question 42

Describe the spontaneity of a reaction where:

ΔH_rxn < 0
ΔS_rxn < 0

Answer 42

This reaction will be spontaneous at low temperatures, and non-spontaneous at significantly high temperatures.

Remember, ΔG = ΔH - TΔS. When T is low (near zero Kelvin), the second term can be ignored, and ΔG will be negative due to ΔH<0. But when T becomes large enough, the positive sign of the -TΔS term dominates, and ΔG becomes positive.

Question 43

Describe the spontaneity of a reaction where:

ΔH_rxn > 0
ΔS_rxn < 0

Answer 43

This reaction will be spontaneous at high temperatures and non-spontaneous at low enough temperatures.

Remember, ΔG = ΔH - TΔS. When T is low (near zero Kelvin), the second term can be ignored, and ΔG will be positive due to ΔH>0. But when T becomes large enough, the negative sign of the -TΔS term dominates, and ΔG becomes negative.

Question 44

Describe the spontaneity of a reaction where:

ΔH_rxn < 0
ΔS_rxn > 0

Answer 44

This reaction will always be spontaneous.

Remember, 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.

Question 45

What is the difference between ΔG and ΔGº?

Answer 45

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 will be compared, since this gives a common point of reference between them.

Question 46

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

Answer 46

Temperature and internal energy 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; i.e. they are at the same temperature.

Question 47

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

Answer 47

U = KE_avg = (3/2)nkT

• k is Boltzmann’s constant(1.38x10^-23 J/K)
• T is the absolute temperature (in Kelvin)
• n is the number of moles of fluid molecules (in mol)

Question 48

Define:

Work (in thermodynamics)

Answer 48

Work 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.

Question 49

Define:

Heat (in thermodynamics)

Answer 49

Heat 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.

Question 50

What is the First Law of Thermodynamics?

Answer 50

In thermodynamics, heat and work are the only ways in which energy can flow, and energy is always conserved, hence energy change can be calculated:

ΔE = Δq + Δw

Question 51

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

Answer 51

During a compression, work is being done by the environment, and on the system.

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

Question 52

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

Answer 52

During an expansion, work is being done by the system, and on the environment.

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

Question 53

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

Answer 53

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.

Question 54

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

Answer 54

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 55

What are the characteristics of an adiabatic thermodynamic process?

Answer 55

An adiabatic process is any process where heat cannot flow. Hence, Δq = 0 and ΔE = Δw; all energy change is due to work being done on or by the system.

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

Question 56

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

Answer 56

The system’s temperature must increase during an adiabatic compression.

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 must gain temperature during an adiabatic compression.

Question 57

What are the characteristics of an isothermal thermodynamic process?

Answer 57

An isothermal process is any process where temperature is held constant. Hence, 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 are usually processes that happen slowly enough that the system’s temperature can constantly equilibrate.

Question 58

What is the direction of heat flow during an isothermal compression?

Answer 58

Heat flows out of the system during an isothermal compression.

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

Define:

The Second Law of Thermodynamics

Answer 59

The Second Law of Thermodynamics states that for any thermodynamic process, the total entropy of the universe increases.

ΔS_universe > 0

ΔS_system+ ΔS_{surroundings > 0}

since the universe can be defined as a system and its surroundings. If the entropy of a system decreases, therefore, the entropy of its surroundings must increase by an equal or greater amount in order for the universal law to still hold true.

Question 60

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

Answer 60

ΔS_X > 0

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

Question 61

What is the formula for converting between temperature in Celsius and Kelvin?

Answer 61

T_K = T_C + 273

T_K = Kelvin Temperature
T_C = Celcius Temperature

Some standard temperatures to memorize:

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

Question 62

What is the formula for converting between temperature in Centigrade and Fahrenheit?

Answer 62

T_F = (9/5)*T_C + 32

T_F = Farenheit Temperature
T_C = Celcius Temperature

Some standard conversions to memorize:

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

Question 63

Define:

Conduction

Answer 63

Conduction is the transfer of thermal energy via molecular collisions. It requires physical contact between the systems 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 64

Define:

Convection

Answer 64

Convection is the thermal energy transfer via the movement of fluid in currents. It requires at least one medium which 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 65

Define:

Radiation

Answer 65

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

Radiation does not require a medium and can occur through a vaccuum.

Question 66

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 66

Conduction

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

Question 67

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

Answer 67

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 68

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

Answer 68

Radiation

For the heat to get from the sun to the earth, it must travel across millions of miles of nearly empty space. Only electromagnetic radiation can carry energy across this distance.

Question 69

Define a material’s heat of vaporization, ΔH_vap.

Answer 69

ΔH_vap is the energy needed to vaporize one mole of a substance from its liquid phase to the gas phase at constant pressure.

ΔH_vap is always positive, since vaporization is an endothermic process.

Question 70

Define a material’s heat of fusion, ΔH_fus.

Answer 70

ΔH_fus is the energy needed to melt one mole of a substance from its solid phase to its liquid phase at constant pressure.

ΔH_fus is always positive, since melting is an endothermic process.

Question 71

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

Answer 71

Work = Δ(PV)

At constant pressure, W = PΔV

More generally, the work done during a thermodynamic process is the area under the curve of a P vs V diagram.