Answer:
The balanced chemical equation for the reaction between nitrogen and hydrogen to form ammonia is:
N2 (g) + 3H2 (g) ⇌ 2NH3 (g)
The equilibrium constant expression for this reaction is:
Kp = (P(NH3)^2) / (P(N2) * P(H2)^3)
where P is the partial pressure of each gas in the equilibrium mixture.
We are given that the volume ratio of nitrogen to hydrogen is 1:3. This means that for every 1 volume of nitrogen, there are 3 volumes of hydrogen.
At equilibrium, let's assume that the total volume of the mixture is V. Then, the volume of nitrogen in the mixture is V/4, and the volume of hydrogen is (3/4)V.
Since the total pressure of the mixture is 10 atm, we can use the partial pressures of nitrogen and hydrogen to calculate the partial pressure of ammonia:
P(N2) = (1/4) * 10 atm = 2.5 atm
P(H2) = (3/4) * 10 atm = 7.5 atm
P(NH3) = 0.15 * 10 atm = 1.5 atm
Substituting these values into the equilibrium constant expression, we get:
Kp = (1.5^2) / (2.5 * 7.5^3) = 1.33 x 10^-4
Therefore, the value of Kp is 1.33 x 10^-4.