Samuel O. answered 04/04/21
Ivy League Chemistry Graduate, Chemistry Researcher
We need to find Kc, which we can set up as Kc = [NH3]2/[H2]3[N2]. The brackets indicate concentrations (usually molarities = mol/L) of each species at equilibrium. This equation is given in a more generic form on the AP Chemistry equations sheet.
To find equilibrium concentrations, I'd set up a RICE Table: reaction, initial, change, and equilibrium!
R: N2(g) + 3H2(g) ⇆ 2NH3(g)
I: 0.4811 mol/4.50 L 1.761 mol / 4.50 L 0M
C: - x -3x +2x
E: 0.1069 - x M 0.3913 - 3x M 2x = 0.1201 mol / 4.50 L
From the RICE table, the equilibrium concentration of NH3 is 2x, which is given to be 0.1201 mol / 4.5 L:
2x = 0.1201 mol / 4.5 L = 0.026689 M → x = .013344 M
We can use this x for the other equilibrium concentrations from the RICE table and plug them into Kc:
Kc = [NH3]2/[H2]3[N2] = (2x)2/[(0.3913 - 3x)3(0.1069 - x)] = (0.1201)2/(.3513)3(0.09356) = 0.176