Energetics & Equilibria 3: Chemical changes

Question 1

Define the standard state of a substance

Answer 1

The pure form at pressure = 1 bar and at the specified temperature.

Question 2

Define:

• Δ_rH^o
• Δ_rG^o
• Δ_rS^o

Answer 2

Δ_rH^o is the standard enthalpy change: the enthalpy change when one mole of reaction occurs at a specified, constant composition, and at standard conditions.

Δ_rG^o is the standard Gibbs energy change: the Gibbs energy change when one mole of reaction occurs at a specified, constant composition, and at standard conditions.

Δ_rS^o is the standard entropy change: the entropy change when one mole of reaction occurs at a specified, constant composition, and at standard conditions.

Standard state implies pure substance: i.e. pure reactants form pure products

Important: constant composition means the mixture is big enough that the concentrations of species don’t change throughout the reaction

Question 3

Define Δ_fH^o, the standard enthalpy of formation of a compound.

Answer 3

The standard enthalpy change of a reaction where one mole of the compound is formed from its constituent elements, each in their reference states (i.e. most stable state at 1 bar), at a specified temperature.

by definition, the standard enthalpy of elements in their reference states = 0, since no energy is required to put them into a state they’re already in (since stablest)

Question 4

Draw a cycle which can be used to find the standard enthalpy change for generic reaction v_AA + v_BB –> v_pP + v_qQ.

Answer 4

Question 5

Give the expression for the standard entropy change for the generic reaction v_AA + v_BB –> v_pP + v_qQ.

Answer 5

Δ_rS^o = v_pS^o_m(P) + v_QS^o_m​(Q) - v_AS^o_m​(A) - v_BS^o_m​(B)

Question 6

Give the expression for the standard Gibbs energy of a reaction.

Answer 6

Δ_rG^o = Δ_rH^o - TΔ_rS^o

Question 7

Δ_rH^o varies with temperature. Give the relationship giving Δ_rH^o at temperature 2, given knowledge of Δ_rH^o at temperature 1.

Answer 7

Δ_rH^o(T₂) = Δ_rH^o(T₁) + Δ_rC_p^o[T₂ - T₁]

Question 8

Δ_rH^o varies with temperature. Derive a relationship giving Δ_rH^o at temperature 2, given knowledge of Δ_rH^o at temperature 1.

State any assumptions made.

Answer 8

Define standard molar heat capacity at constant pressure:

Consider generic reaction v_AA + v_BB –> v_pP + v_QQ

Δ_rC_p^o = ν_PC^o_p,m(P) + ν_QC^o_p,m​(Q) - ν_AC^o_p,m​(A) - ν_BC^o_p,m​(B)

Definition of heat capacity at constant pressure:

C_p,m = (∂Hm/∂T)p (constant pressure)

C_p,m = dH_m/dT (constant pressure)

(Everything is under standard conditions so can drop molar subscript)

So Δ_rC_p^o = dΔ_rH^o/dT

Assume heat capacity is constant in range T₁ to T₂, so:

Return to C_p,m = dH_m/dT (constant pressure)

So dH_m = C_p,mdT (constant pressure)

Then integrate (image)

Apply integrated relationship to definition of molar heat capacity at standard pressure:

Δ_rH^o(T₂) = Δ_rH^o(T₁) + Δ_rC_p^o[T₂ - T₁]

Question 9

Δ_rS^o varies with temperature. State the relationship giving Δ_rS^o at temperature 2, given knowledge of Δ_rS^o at temperature 1.

Answer 9

Δ_rS^o(T₂) = Δ_rS^o(T₁) + Δ_rC_p^oln(T₂/T₁)

Question 10

Δ_rS^o varies with temperature. Derive a relationship giving Δ_rS^o at temperature 2, given knowledge of Δ_rS^o at temperature 1.

State any assumptions made.

Answer 10

Define standard molar heat capacity at constant pressure:

Consider generic reaction vAA + vBB –> vpP + vQQ

ΔrCpo = νPCop,m(P) + νQCop,m​(Q) - νACop,m​(A) - νBCop,m​(B)

Then derive relationship

Recall dS_M = C_p,mdT/T (constant pressure)

Integrate between T₁ and T₂ (image)

assumption: temperatures are not very different, so Cp is constant and can be taken out of the integral

(Everything is under standard conditions so can drop molar subscript)

Δ_rS^o(T₂) = Δ_rS^o(T₁) + Δ_rC_p^oln(T₂/T₁)

Question 11

Convert 1 bar to Pa

Answer 11

1 bar = 10⁵ Pa