Question 15.7: After a mixture of hydrogen and nitrogen gases in a reaction...

After a mixture of hydrogen and nitrogen gases in a reaction vessel is allowed to attain equilibrium at 472 °C, it is found to contain 7.38 bar H_{2}, 2.46 bar N_{2}, and 0.166 bar NH_{3}. From these data, calculate the equilibrium constant K_{p} for the reaction

N_{2}  (g) + 3  H_{2}  (g) ⇌ 2  NH_{3}  (g)
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Analyze We are given a balanced equation and equilibrium partial pressures and are asked to calculate the value of the equilibrium constant.
Plan Using the balanced equation, we write the equilibriumconstant expression. We then substitute the equilibrium partial pressures into the expression and solve for K_{p}.

Solve

K_{p}=\frac{(P_{NH_{3}})²}{P_{N_{2}}(P_{H_{2}})³} =\frac{0.166²}{(249.3)(747.8)³}= 2.71 × 10^{-9}

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