Question

Steam reacts with iron at high temperature to give hydrogen gas and $F{e_3}{O_4}(s)$. The correct expression for the equilibrium constant is:
A. $\dfrac{{{P^2}_{{H_2}}}}{{{P^2}_{{H_2}O}}}$
B. $\dfrac{{{{({P_{{H_2}}})}^4}}}{{{{({P_{{H_2}O}})}^4}}}$
C. $\dfrac{{{{({P_{{H_2}}})}^4}[F{e_3}{O_4}]}}{{{{({P_{{H_2}O}})}^4}[Fe]}}$
D. $\dfrac{{[F{e_3}{O_4}]}}{{[Fe]}}$

Answer 1

Hint: For a chemical reaction, the equilibrium constant is defined as the ratio of the multiple of the molar concentration of products to the molar concentration of reactants at a given temperature, and the molar concentration of each substance is raised to the power equal to the number of the molecules of that in the balanced equation.

Complete answer:
When iron reacts with steam at high temperature, it gives hydrogen gas and ferrosoferric oxide i.e. $F{e_3}{O_4}$. The balanced chemical equation is written as:
$3Fe(s) + 4{H_2}O(steam)\overset {} \leftrightarrows F{e_3}{O_4} + 4{H_2}$
According to the law of chemical equilibrium,
$K = \dfrac{{[F{e_3}{O_4}]{{[{H_2}]}^4}}}{{{{[Fe]}^3}{{[{H_2}O]}^4}}}$
Since the concentration of pure solid or liquid is unity and iron and ferrosoferric oxide are in the pure state so their molar concentration will also be unity.
Hence K will be:
$K = \dfrac{{{{[{H_2}]}^4}}}{{{{[{H_2}O]}^4}}}$
Here, since both hydrogen and water are in gaseous form and the gaseous state, the concentration is expressed in terms of partial pressure. Let the partial pressure of hydrogen gas is ${p_{{H_2}}}$ and the partial pressure of the stream be ${p_{{H_2}}}_O$. Hence the equilibrium constant will be defined in terms of pressure and denoted by ${K_P}$, where
${K_P} = \dfrac{{{{[{p_{{H_2}}}]}^4}}}{{{{[{p_{{H_2}O}}]}^4}}}$

So, the correct answer is Option B .

Note:
Since the value of equilibrium constant is based on molar concentration or partial pressure but it is not truly constant and changes as the concentration changes. Therefore, we use a dimensionless quantity called activity in expression representing the equilibrium constant so we can say equilibrium constant has no unit.