Question

Answer ALL parts. (a) The reaction B + C → D just becomes spontaneous at a temperature of 78.1 °C. When the temperature is increased to 220 °C: (i) Calculate Gibbs free energy (ii) Calculate equilibrium constant (iii) State whether the products or reactants are favoured at this temperature and explain your reasoning (iv) State the assumptions associated with your calculations.

Useful data for this question:

ΔSreaction (B + C → D) = 259.4 J K–1 mol–

Answer 1

Given transformation,

B + C → D

Given that, at 78.1 ⁰C reaction becomes just spontaneous that means ΔG⁰ attains least possible –Ve value [Because for spontaneous reaction Gibbs free energy change (ΔG⁰) is -ve.] Below that temperature reaction would be non-spontaneous with ΔG⁰ ≥ 0 (0 or +ve).

We can assume that at 78 ⁰C ΔG⁰ = 0.

We know the relation between ΔG⁰ , ΔH⁰ , ΔS⁰ and T as,

ΔG⁰ = ΔH⁰ -TΔS⁰ ……….. (1)

At T = 78 ⁰C = 78 + 273.15 = 351.15 K, ΔG⁰ = 0

Hence, eq. (1) takes form,

ΔH⁰ = TΔS⁰

With T = 351.15 K and ΔS⁰ = 259.4 J.K^-1.mol^-1 we get,

ΔH⁰ = 351.15 x 259.4

ΔH⁰ = +91088.31 J/mol

ΔH⁰ = +91.088 kJ/mol.

1)Calculation of ΔG⁰ at T = 220 ⁰C,

We have, ΔH⁰ = +91088.31 J/mol, ΔS⁰ = 259.4 J.K^-1.mol^-1 and T = 220 ⁰C = 273.15 + 220 = 493.15 K.

Using eq. (1) let us calculate ΔG⁰ for given transformation at given temperature 220 ⁰C,

ΔG⁰ = ΔH⁰ -TΔS⁰

ΔG⁰ = (+91088.31) - 493.15 x 259.4

ΔG⁰ = -36835 J/mol

ΔG⁰ = -36.835 kJ/mol

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2)Calculating equilibrium constant K,

Equilibrium constant K and ΔG⁰ related by formula,

ΔG⁰ = -RTln(K) …………. (2)

Where, R = 8.314 J.K^-1.mol^-1.

T = 220 ⁰C = 273.15 + 220 = 493.15 K

ΔG⁰ = -36835 J/mol

K = ?

Let us all the known things in eq. (2)

-36835 = - 8.314 x 493.15 ln(K)

36835 = 8.314 x 493.15 ln(K)

ln(K) = (36835) / (8.314 x 493.15)

ln(K) = 8.984

K = e^8.984

K = 7.97 x 10³

Equilibrium constant for given transformation at given temperature is 7.97 x 10³

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3)

As, ΔG⁰ = -36835 J/mol and K = 7.97 x 10³

i.e. ΔG⁰ = -ve and High equilibrium constant value

Hence, forward reaction will be favored i.e. Product (D) formation will be favored.

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4) Assumption is stated at the beginning only.

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