Question

What is ${K_P}$ for the reaction $2A(g) + 2B(g) \rightleftharpoons C(g)$, if ${K_C} = 34.8$ at a temperature of ${19^o}C$.

Answer 1

Hint: ${K_P}$ the equilibrium constant used when equilibrium concentrations of reactants and products are given in terms of partial pressure whereas ${K_C}$ is the equilibrium constant used when equilibrium concentrations of reactants and products are given in terms of molar concentration i.e., molarity.
Formula used-
${K_P} = {K_C}{(RT)^{\Delta {n_g}}}$
Where, R is the universal gas constant expressed in unit of ${\text{atm L mo}}{{\text{l}}^{ - 1}}{{\text{K}}^{ - 1}}$, T is the absolute temperature and $\Delta {n_g}$ is the difference between number of gaseous products and reactants.

Complete answer: As per question, the given data is as follows:
Equilibrium constant ${K_C} = 34.8$
Temperature $T = {19^o}C$
Converting unit of temperature from degree Celsius to kelvin:
$ \Rightarrow T = 19 + 273$
$ \Rightarrow T = 292\,K$
The reaction is given as follows:
$2A(g) + 2B(g) \rightleftharpoons C(g)$
In the reaction, there is only one gaseous mole of product and four moles of gaseous reactants. Therefore, the value of $\Delta {n_g}$ will be as follows:
$\Delta {n_g} = 1 - 4$
$ \Rightarrow \Delta {n_g} = - 3$
To calculate the value of ${K_P}$ for the given reaction, substitute the values in the formula as follows:
${K_P} = {K_C}{(RT)^{\Delta {n_g}}}$
$ \Rightarrow {K_P} = 34.8 \times {(0.0821 \times 292)^{ - 3}}$
$ \Rightarrow {K_P} = 34.8 \times 7.26 \times {10^{ - 5}}$
$ \Rightarrow {K_P} = 252.6 \times {10^{ - 5}}$
$ \Rightarrow {K_P} = 2.53 \times {10^{ - 3}}$
Hence, the value of equilibrium constant ${K_P}$ for the given reaction conditions is $2.53 \times {10^{ - 3}}$.

Note:
It is important to note that the value of universal gas constant i.e., R is always considered in units of ${\text{atm L mo}}{{\text{l}}^{ - 1}}{{\text{K}}^{ - 1}}$ for calculation of ${K_P}$ because it is used when equilibrium concentrations are given in atmospheric pressure (atm). Also, some observations are made on the basis of ratio of $\dfrac{{{K_C}}}{{{K_P}}}$ which are as follows:
i.Larger the value of $\dfrac{{{K_C}}}{{{K_P}}}$, the greater will be the percentage of product in the reaction.
ii.Lower the value of $\dfrac{{{K_C}}}{{{K_P}}}$, the greater will be the percentage of reactants in the reaction.