Chapter 16, Problem 1SAQ

What is the correct expression for the equilibrium constant (Kc) for the reaction between carbon and hydrogen gas to form methane shown here?

$C(s)+2H_2(g)\rightleftharpoons C{H}_4(g)$

• ${\text{K}}_{\text{c}}=\frac{\left[{\text{CH}}_{\text{4}}\right]}{\left[{\text{H}}_{\text{2}}\right] }$
• ${\text{K}}_{\text{c}}=\frac{\left[{\text{CH}}_{\text{4}}\right]}{\left[\text{C}\right]\left[{\text{H}}_{\text{2}}\right] }$
• ${\text{K}}_{\text{c}}={\frac{\left[{\text{CH}}_{\text{4}}\right]}{{\left[{\text{H}}_{\text{2}}\right]}^{\text{2}}}}^{ }$
• ${\text{K}}_{\text{c}}=\frac{\left[{\text{CH}}_{\text{4}}\right]}{\left[\text{C}\right]{\left[{\text{H}}_{\text{2}}\right]}^2 }$

Interpretation Introduction

Interpretation: What is the correct expression for the equilibrium constant $(\text{Kc)}$ for the reaction.

Concept introduction: For the reaction type:

  $\text{xA+yB}\rightleftarrows \text{mC+nD}$

where A, B, C and D represent chemical species and x, y, m and n are coefficients of the balanced chemical equation. The equilibrium constant for such reactions are given as:

  ${\text{K}}_{\text{a}}\text{=}\frac{{\text{[C]}}^{\text{m}}{\text{[D]}}^{\text{n}}}{{\text{[A]}}^{\text{x}}{\text{[B}\text{]}}^{\text{y}}}$

The square brackets represent concentration of the species in equilibrium.

Correct answer:

Correct answer is option (c).

Explanation of Solution

Reason for correct option:

  ${\text{K}}_{\text{a}}\text{=}\frac{{\text{[C]}}^{\text{m}}{\text{[D]}}^{\text{n}}}{{\text{[A]}}^{\text{x}}{\text{[B}\text{]}}^{\text{y}}}$

Substitute the values in the equilibrium constant equation for the law of mass action and calculate the equilibrium constant $({\text{K}}_{\text{c}}\text{)}$ for the reaction between carbon and hydrogen gas to from the equilibrium methane ${\text{C(s) + 2H}}_{\text{2}}\text{ (g) }\rightleftarrows {\text{CH}}_{\text{4}}\text{(g)}$ the concentration of elements in the solid is taken to be zero.

$\begin{array}{l}{\text{K}}_{\text{a}}\text{=}\frac{{\text{[C]}}^{\text{m}}{\text{[D]}}^{\text{n}}}{{\text{[A]}}^{\text{x}}{\text{[B}\text{]}}^{\text{y}}}\\ \text{=}\frac{\left[{\text{CH}}_{\text{4}}\right]}{{\left[{\text{H}}_{\text{2}}\right]}^{\text{2}}}\end{array}$

Therefore, the correct answer is option (c).

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