# A sample of carbon is placed in a rigid 1.50 L flask. Dinitrogen monoxide is added and the flask heated to 800C. When the system reached equilibrium the partial pressure of the carbon dioxide is found to be 0.030 atm and the partial pressure of the dinitrogen monoxide to be 1.48 atm. What is the Gibbs free energy change, delta G, for the reaction at 800C?

Apr 27, 2015

The value of ΔG is 88.5 kJ/mol.

I presume that the reaction is

${\text{C"(s) + "2N"_2"O"(g) ⇌ "CO"_2(g) + "2N}}_{2} \left(g\right)$

Step 1. Calculate ${K}_{\text{p}}$

From the ICE table, we see that $x = 0.030$.

So ${P}_{\text{N₂" = 2x = "0.060 atm}}$

K_"p" = (P_"CO₂"P_"N₂"^2)/(P_"N₂O"^2) = (0.030 × 0.060^2)/1.48^2 = 4.93 × 10^-5

Step 2. Calculate ΔG^°.

ΔG^° = -RTlnK_"p" = "-8.314 J"·cancel("K⁻¹")"mol⁻¹" × 1073.15 cancel("K") × ln(4.93 × 10^-5) = "+88 500 J·mol"^-1 = "+88.5 kJ/mol"