The equilibrium constant Kp of the Haber reaction, N2 (g) + 3 H2(g) ⇌ 2 NH3 (g), at 200C is 6.78 × 105. Initially, 0.0020 moles N2, 0.010 moles H2, and 0.090 moles NH3 are present in a sealed 1 L reaction vessel. In which direction will the reaction proceed?

We are given moles and 1 L so we can calculate Qc with the initial concentrations. Remember the only difference between Q and K is that for K we use equilibrium values but for Q we use non equilibrium values such as initial concentrations. To calculate Qc we do concentrations of products to the power of their coefficients over concentrations of reactants to the power of their coefficients.

Qc = __[NH3]^2__

([N2][H2]^3

Let's plug in the values given,

Qc = __(0.090M)^2 __ = 4050000

(0.0020)(0.010)^3

We are given Kp, so we need to convert Qc to Qp to be able to compare it to Kc.

Qp = Qc(RT)^∆n where R is the ideal gas constant, T is temperature in Kelvin and ∆n = moles of gas in the product - moles of gas in the reactant. We can use the coefficients in the equation to calculate ∆n = 2- (1+3) = -2

Answer: Qp = 4.05 × 10^6 × [0.08206 × (25 + 273.15)]^-2 = 6766 < 6.78 × 105 = Kp

If Q<K, **the reaction will proceed to the right.**

Ps: If Q>K, the reaction will proceed to the right.

If Q=K, the reaction is at equibrium.