Question

For the dissolution of thenardite shown below, calculate the following (at STP, 25 °C and 1 atm):Na2SO4 (s) ↔ 2Na+(aq) + SO42-(aq)

(a) standard??° enthalpy of reaction (∆????°), ??°
(b) standard Gibbs free energy of reaction (∆?? ) using standard Gibbs free energy of formation values (∆?? ), and
(c) equilibrium constant (K).
(d) Is this a spontaneous reaction [i.e., the dissolution reaction (left to right)]? Explain.

Answer 1

(a). The given reaction is :

Na₂SO₄ (s) <----------------> 2 Na⁺(aq) + SO₄^2-(aq), ΔH⁰_rxn = ?

By using the formula,

ΔH⁰_rxn = Σ Δ_fH⁰ of Products - Σ Δ_fH⁰ of Reactants

Here, Δ_fH⁰ = Standard change in enthalpy of formation.

Apply this formula for the given reaction :

ΔH⁰_rxn = [ 2 x Δ_fH⁰ of Na⁺ (aq) + Δ_fH⁰ of SO₄^2- (aq) ] -  [ Δ_fH⁰ of Na₂SO₄ (s) ]

From the table of Δ_fH⁰ substitute the values of Δ_fH⁰ for all the species :

ΔH⁰_rxn = [ 2 x (–240.3 KJ/mol ) + (–909.3 KJ/mol)] - [ -1387.1 kJ/mol]

= [ - 480.6 KJ - 909.3 KJ] + 1387.1 kJ

= - 1389.9 KJ + 1387.1 KJ

= - 2.8 KJ

Hence, ΔH⁰_rxn = - 2.8 KJ

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(b).

By using the formula,

ΔG⁰_rxn = Σ Δ_fG⁰ of Products - Σ Δ_fG⁰ ​​​​​​​ of Reactants

Here, Δ_fG⁰ = Standard change in Gibb's free energy.

Apply this formula for the given reaction :

ΔG⁰_rxn = [ 2 x Δ_fG⁰ of Na⁺ (aq) + Δ_fG⁰ of SO₄^2- (aq) ] -  [ Δ_fG⁰ of Na₂SO₄ (s) ]

From the table of Δ_fG⁰ substitute the values of Δ_fG⁰ for all the species :

ΔG⁰_rxn = [ 2 x (–261.905 KJ/mol ) + (–744.53 KJ/mol)] - [ -1270.2 kJ/mol]

= [ - 523.81 KJ - 744.53 KJ] + 1270.2 kJ

= - 1268.34 KJ + 1270.2 KJ

= + 1.86 KJ

Hence, ΔG⁰_rxn = + 1.86 KJ

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(c). Relationship between ΔG⁰_rxnand Equilibrium constant (k) is :

ΔG⁰_rxn = - 2.303 RT log k ..................(1)

Here, R = Universal gas constant = 8.314 x 10^-3 KJ K^-1mol^-1 and

T = Temperature = 298 K = 25 ⁰C

Substitute the values of ΔG⁰_rxn, R and T in equation (1) :

1.86 KJ = - 2.303 x 8.314 x 10^-3 KJ K^-1mol^-1​​​​​​​ x 298 K log K

log k = - 1.86 KJ /2.303 x 8.314 x 10^-3 KJ K^-1mol^-1​​​​​​​ x 298 K

log k = - 0.32598

k = 10^-0.32598  

k = 0.472

Hence, equilibrium constant = k = 0.472

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(d). Since the value of ΔG⁰_rxn is Positive that is + 1.86 KJ for the dissolution of Na₂SO₄ reaction (left to right) , therefore, the reaction is not a spontaneous reaction.