Core 2: Entropy

Question 1

How does G change at constant temperature but changing pressure? How does this apply to solids/liquids and gases?

Answer 1

dG=Vdp

For solids and liquids, volume is effectivally constant so ΔG=VΔp (integration from above)

For gases, V changes with pressure so it is substituted using pV=nRT. This integrates to ΔG=nRTln(p_f/p_i)

Question 2

How are C_p,m and C_V,m related? What are their values for monoatomic and polyatomic gases? What are these values based on?

Answer 2

C_p,m=C_V,m+R

Monoatomic: C_p,m=R5/2 C_V,m=R3/2

Polyatomic: C_p,m>R5/2 C_V,m>R3/2

They are based on the degrees of freedom of the gas.

Question 3

What is the entropy change from a fusion reaction?

Answer 3

Δ_fusS=Δ_fusH(T_f)/T_f

Question 4

What is the equation for change in G when the pressure and temperature change?

Answer 4

dG=Vdp-SdT

Question 5

What is Trouton’s rule?

Answer 5

Δ_vapS is approximately the same for all liquids, around 85 J K^-1 mol^-1

Question 6

What is the Clapeyron equation for phase diagrams?

Answer 6

m=dp/dT=Δ_trsS/Δ_trsV=Δ_trsH/TΔ_trsV

Question 7

State the equation for S using the number of microstates

Answer 7

S=k_Bln(W)

Question 8

What is the entropy change when a gas is heated between two temperatures?

What if the is only a very small change between these temperatures? Why does this equation work?

What assumption as been made?

Answer 8

ΔS=nC_p,mln(T_f/T_i)

dS=nC_p,mdT/T, q_rev is being estimated to C_pΔT

C_p,m is not dependant on temperature, this can be improved by taking C_p,m=a+bT² +c/T²

Question 9

How is the entropy change of the surroundings related to the entropy change of the system?

Answer 9

ΔS_surr=-ΔS_system

ΔS_surr=-q_rev/T

Question 10

How can the absolute entropy of a gas be adapted when the pressure is changed from 1 bar?

How can this be adapted for real gases?

Answer 10

Using the equation ΔG=nRTln(p_f/p_i), p_i is p^⦵

The change of entropy can then be added to G^⦵_m to find the new G_m value at p.

G_m(p)=G^⦵_m+nRTln(p/p^⦵)

The p term is changed to f=øp for real gases.

Question 11

How does entropy change for a gas expanding isothermally at:

1. Constant pressure
2. Constant volume

Answer 11

1. ΔS=nRln(V_f/V_i)
2. ΔS=nRln(p_i/p_f)

Question 12

What is the Clausius-Clapeyron equation for the liquid-gas phase boundary?

What does this integrate to? How is it useful?

Answer 12

d(lnp)/dT=Δ_vapH/RT²

lnp=(Δ_vapH/RT)+c but this is useful for finding vapour pressure at different temperatures.

Question 13

What is the van’t Hoff isochore?

How can its alternate forms be used?

Answer 13

lnK=(Δ_rH^⦵/RT)+Δ_rS^⦵/R

This can be used to calculate K at different temperatures. It can also be used to find Δ_rH^⦵ and Δ_rS^⦵ from a graph of lnK and 1/T

Question 14

What is the equation for ΔU?

What can work be broken down into?

When is ΔU=0

Answer 14

ΔU=q+w

w=-pΔV

For an isothermal process

Question 15

What is K for evapouration or sublimation of water?

Answer 15

K=p_H2O(g)/p^⦵

Question 16

Define the 2nd law of thermodynamics in writing and by equation. How can changes in temperature be accounted for?

Answer 16

The entropy of the universe tends to increase.

ΔS=q_rev/T

ΔS=int_Ti^T_f(dq_rev/T)

Question 17

How are G and the equlibrium constant related?

How can this be derived?

Answer 17

Δ_rG^⦵=-RTlnK

Using the change of Gibbs free energy for a reaction and the change in G when p changes at constant temperature.

Question 18

What does ΔG represent?

Answer 18

The maximum non-expansion work that can be obtained from a process at constant T and p such as electrical work.

Question 19

What is the equation for Gibbs free energy?

Where is this derived from?

Answer 19

ΔG=ΔH-TΔS

The equation for ΔS_total, substitute out ΔS_surr, multiply by T. -ΔG=TΔS_total

Question 20

What is the Debye T³ law and when is it used?

Answer 20

C_V,m=aT³

Used when temperatures are very close to zero.

Question 21

How does G change when temperature changes at constant pressure?

Answer 21

dG_m=-S_mdT