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Question: Steam reacts with iron at high temperature to give hydrogen gas and \(F{e_3}{O_4}(s)\). The correct ...

Steam reacts with iron at high temperature to give hydrogen gas and Fe3O4(s)F{e_3}{O_4}(s). The correct expression for the equilibrium constant is:
A. P2H2P2H2O\dfrac{{{P^2}_{{H_2}}}}{{{P^2}_{{H_2}O}}}
B. (PH2)4(PH2O)4\dfrac{{{{({P_{{H_2}}})}^4}}}{{{{({P_{{H_2}O}})}^4}}}
C. (PH2)4[Fe3O4](PH2O)4[Fe]\dfrac{{{{({P_{{H_2}}})}^4}[F{e_3}{O_4}]}}{{{{({P_{{H_2}O}})}^4}[Fe]}}
D. [Fe3O4][Fe]\dfrac{{[F{e_3}{O_4}]}}{{[Fe]}}

Explanation

Solution

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. Fe3O4F{e_3}{O_4}. The balanced chemical equation is written as:
3Fe(s)+4H2O(steam)⇆Fe3O4+4H23Fe(s) + 4{H_2}O(steam)\overset {} \leftrightarrows F{e_3}{O_4} + 4{H_2}
According to the law of chemical equilibrium,
K=[Fe3O4][H2]4[Fe]3[H2O]4K = \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=[H2]4[H2O]4K = \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 pH2{p_{{H_2}}} and the partial pressure of the stream be pH2O{p_{{H_2}}}_O. Hence the equilibrium constant will be defined in terms of pressure and denoted by KP{K_P}, where
KP=[pH2]4[pH2O]4{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.