Question

What is the unit of \[{{\text{K}}_{\text{p}}}\] for the reaction?
(A) atm
(B) \[{\text{at}}{{\text{m}}^{{\text{ - 2}}}}\]
(C) \[{\text{at}}{{\text{m}}^{\text{2}}}\]
(D) \[{\text{at}}{{\text{m}}^{{\text{ - 1}}}}\]

Answer 1

Hint: To solve this question we must know about the equilibrium constant for a chemical reaction. The equilibrium constant for a chemical reaction can be defined as a relation between the corresponding product and the given reactants when the chemical equation reaches an equilibrium.

Complete step by step solution:
The equilibrium constant in terms of concentration \[{{\text{K}}_{\text{C}}}\] is defined as the ratio of the concentration of products to the concentration of the reactants.
The equilibrium constant in terms of partial pressure \[{{\text{K}}_{\text{p}}}\] is defined as the ratio of the partial pressure of products to the partial pressure of the reactants.
For the reaction,
\[
  {K_C} = \dfrac{{{{\left[ C \right]}^c}{{\left[ D \right]}^d}}}{{{{\left[ A \right]}^a}{{\left[ B \right]}^b}}} \\
  {K_p} = \dfrac{{{{\left[ {pC} \right]}^c}{{\left[ {pD} \right]}^d}}}{{{{\left[ {pA} \right]}^a}{{\left[ {pB} \right]}^b}}} \\
  \]
So for the reaction given in question \[{{\text{K}}_{\text{p}}}\] can be written as,

\[
  {K_p} = \dfrac{{{{\left[ {pC{H_4}} \right]}^1}{{\left[ {p{H_2}S} \right]}^2}}}{{{{\left[ {pC{S_2}} \right]}^1}{{\left[ {{H_2}} \right]}^4}}} \\
  {K_p} = \dfrac{{{{\left[ {atm} \right]}^1}{{\left[ {atm} \right]}^2}}}{{{{\left[ {atm} \right]}^1}{{\left[ {atm} \right]}^4}}} = {\left[ {atm} \right]^{ - 2}} \\
  \]
So the unit of \[{{\text{K}}_{\text{p}}}\] is \[{\left[ {{\text{atm}}} \right]^{{\text{ - 2}}}}\].

Hence the correct option is (B).

Note: Using the ideal gas equation i.e. pV = nRT, \[{{\text{K}}_{\text{p}}}\] can be written in terms of \[{{\text{K}}_{\text{C}}}\].
\[{K_p} = {K_C}{(RT)^{(c + d) - (a + b)}}\], where \[{{\Delta n = (c + d) - (a + b)}}\], the number of moles of product subtracted the number of moles reactants in gaseous phase in the balanced chemical equation.