Question

For the reversible reaction, ${N_{2\left( g \right)}} + 3{H_{2\left( g \right)}} \rightleftharpoons 2N{H_{3\left( g \right)}}$ at ${500^0}C$ , the value of ${K_p}$ is $1.44 \times {10^{ - 5}}$ when partial pressure is measured in the atmosphere. The corresponding value of ${K_c}$ , with concentration in $mol{\left( {litre} \right)^{ - 1}}$
(A) $\dfrac{{1.44 \times {{10}^5}}}{{{{\left( {0.082 \times 500} \right)}^{ - 2}}}}$
(B) $\dfrac{{1.44 \times {{10}^{ - 5}}}}{{{{\left( {8.314 \times 773} \right)}^{ - 2}}}}$
(C) $\dfrac{{1.44 \times {{10}^{ - 5}}}}{{{{\left( {0.082 \times 773} \right)}^2}}}$
(D) $\dfrac{{1.44 \times {{10}^{ - 5}}}}{{{{\left( {0.082 \times 773} \right)}^{ - 2}}}}$

Answer 1

The equilibrium constant from partial pressure and equilibrium constant from concentrations were related as ${K_c} = \dfrac{{{K_p}}}{{{{\left( {RT} \right)}^{\Delta n}}}}$ where $\Delta n$ is the change in the concentration of gaseous products and gaseous reactants and the temperature must be in kelvins.

Complete Step By Step Answer:
Given reaction is ${N_{2\left( g \right)}} + 3{H_{2\left( g \right)}} \rightleftharpoons 2N{H_{3\left( g \right)}}$ the combination of nitrogen and hydrogen gas to form ammonia. All the reactants and products are in gaseous state. Thus, the factor $\Delta n$ is the change in the gaseous reactants from the gaseous products. The number of moles of products are two and the number of moles of gaseous reactants are four will be $\Delta n = 2 - 4 = - 2$
The number of moles of reactants i.e. nitrogen gas and hydrogen gas is four as these both are gaseous reactants.
The universal gas constant R has the value of $0.0821 Lit.atm.{K^{ - 1}}.mo{l^{ - 1}}$
The temperature is in kelvin given temperature is ${500^0}C$ which can be written as $500 + 273 = 773K$
Equilibrium constant from partial pressure is given as $1.44 \times {10^{ - 5}}$
Substitute the values of temperature, universal gas constant and change in moles in the term ${K_c}$
${K_c} = \dfrac{{1.44 \times {{10}^{ - 5}}}}{{{{\left( {0.082 \times 773} \right)}^{ - 2}}}}$
Thus, the value of equilibrium constant from concentrations will be $\dfrac{{1.44 \times {{10}^{ - 5}}}}{{{{\left( {0.082 \times 773} \right)}^{ - 2}}}}$
Option D is the correct one.

Note:
While calculating the change in moles of gaseous reactants and gaseous products the compounds in gaseous phase are only considered. If any solid and liquid compounds they should not be considered. The temperature must be in kelvins and the ideal gas constant must be in $Lit.atm.{K^{ - 1}}.mo{l^{ - 1}}$ .