Question

I need help solving these equations:

AG° = -RTInk , where R = 8.134 AG° = AH® - TAS° In Krı = = AH<>) + au InK12= ct** *2 + InK12– InKnı= lng k73) = 4H , KT2 AH KT1 AH°= go=AH°-AG°

This is what I got in the lab:

Answer 1

Room temperature = 21ºC = (21 + 273) K = 294 K

K_T1 = 3.446*10^-5

Determine ΔG⁰ (standard free energy change at room temperature) as

ΔG⁰ = - RTln K_T1

======> ΔG⁰ = -(8.314 J/mol.K)*(294 K)*ln (3.446*10^-5)

======> ΔG⁰ = -(2444.316 J/mol)*(-10.276)

======> ΔG⁰ = 25117.791 J/mol = (25117.791 J/mol)*(1 kJ)/(1000 J)

======> ΔG⁰ = 25.117791 kJ/mol ≈ 25.1 kJ/mol (ans, correct to 3 sig. figs).

Give T₂ = 356 K and K_T2 = 3.38*10^-4

Use the Vant Hoff equation to determine ΔH⁰.

ln K_T2/K_T1 = -ΔH⁰/R*(1/T₂ – 1/T₁)

======> ln (3.38*10^-4)/(3.446*10^-5) = -ΔH⁰/(8.314 J/mol.K)*[1/(386 K) – 1/(294 K)]

======> ln (9.8085) = -ΔH⁰/(8.314 J/mol.K)*(0.002591 K^-1 – 0.003401 K^-1)

======> 2.2832 = -ΔH⁰/(8.314 J/mol.K)*(-0.00045 K^-1)

======> 2.2832 = ΔH⁰/(8.314 J/mol.K)*(0.00045 K^-1)

======> ΔH⁰ = (2.2832)*(8.314 J/mol.K)/(0.00045 K^-1)

======> ΔH⁰ = 42183.388 J/mol

======> ΔH⁰ = (42183.388 J/mol)*(1 kJ)/(1000 J) = 42.183388 kJ/mol

======> ΔH⁰ ≈ 42.2 kJ/mol (ans, correct to 3 sig. figs).

The standard entropy change is given as

ΔS⁰ = (ΔH⁰ – ΔG⁰)/T

======> ΔS⁰ = [(42.2 kJ/mol) – (25.1 kJ/mol)]/(294 K)

======> ΔS⁰ = 0.05816 kJ/mol.K

======> ΔS⁰ = (0.05816 kJ/mol.K)*(1 kJ)/(1000 J)

======> ΔS⁰ = (0.05816 kJ/mol.K)*(1000 J)/(1 kJ)

======> ΔS⁰ = 58.16 J/mol.K ≈ 58.2 J/mol.K (ans, correct to 3 sig. figs)