Thermodynamics: the second law

Question 1

Define spontaneous change

Answer 1

Spontaneous change is change that requires no work to bring about. The mixing of gases in an isolated system

Question 2

Define entropy, S

Answer 2

Entropy, S, is a measure of molecular disorder

Question 3

Give the second law of thermodynamics

Answer 3

The total entropy (ie the entropy of the system, ΔS, + the entropy of the surroundings, ΔS_Sur) increases in the course of a spontaneous change.

Note: ΔS can be negative as long as ΔS_Sur is positive enough so that overall S_total > 0

Question 4

Give the equation for dS_total, taking temperatures of the system and the surroundings into account

Answer 4

Define T_h, the higher temperature, as the temperature of the system and T_c, the lower temperature, as the temperature of the surroundings. dq is the heat transfer.

Question 5

Give the equation linking dS and dq^reversible

Answer 5

Question 6

Give the equation of ΔS as a state function

Answer 6

Question 7

Derive the equation of ΔS for the isothermal expansion of an ideal gas

Answer 7

Question 8

Derive the equation for Δ_TrsS at constant temperature and pressure

(Trs = phase transition)

Answer 8

Remember that reversible phase transitions of pure substances take place at constant temperatures, and dq = dH at constant pressure

Question 9

Describe Trouton’s rule

Answer 9

Trouton observed that the standard molar entropy of vaporisation. Δ_vapS⁰m _~ 85JK^-1mol^-1 for a wide range of liquids.

This is due to similar changes in disorder when going from a liquid to a gas. Water is an exception due to the structural order (ie lower entropy) of hydrogen bonds.

Question 10

Derive the equation of ΔS when a material is heated at constant pressure

Answer 10

Note that C_p is assumed to be independent of temperature

Question 11

State the third law of thermodynamics

Answer 11

The entropy of all perfect crystalline substances is zero at T = 0

Question 12

Derive an equation to work out the entropy for any given temperature

Answer 12

Combining entropy changed upon heating and during phase transitions, we can calculate the entropy for any given temperature

Question 13

Give the equation for standard reaction entropy

Answer 13

Question 14

Give the equation for the standard reaction enthalpy at T₂ if we know the quantity at T₁

Answer 14

Question 15

Describe the total entropy change for any irreversible reaction

Answer 15

Question 16

Describe the total entropy change for any reversible reaction

Answer 16

Question 17

Give and describe the Clausius inequality

Answer 17

This is a criterion for irreversible/ spontaneous change. It is very useful in judging the spontaneity of chemical reactions

Question 18

Define G, the Gibbs free energy

Answer 18

G = H - TS

dG = dH - TdS

Temperature and pressure are constant

Question 19

Give dG for spontaneous processes

Answer 19

dG < 0

Question 20

Derive dG = Vdp - SdT by combining the first and second laws of thermodynamics

Answer 20

Note: use the product rule

Question 21

Derive the equation of the Gibb’s free energy at pressure p, where T is held constant.

Denote G⁰ as the standard Gibbs free energy

Question 22

Modify the equation for G(p) for a mixture of gasses, denoting p_A and p_B as the partial pressures of reactants

Answer 22