Question

For the equilibrium $S{O_2}C{l_2}\left( g \right) \rightleftharpoons S{O_2}\left( g \right) + C{l_2}\left( g \right)$ , what is the temperature at which $\dfrac{{{K_p}\left( {atm} \right)}}{{{K_c}\left( M \right)}} = 3$ .
(A) $0.027K$
(B) $0.36K$
(C) $36.54K$
(D) $273K$

Answer 1

To answer this question we need to know the relationship between ${K_p}$ , ${K_c}$ and temperature. The answer to this question will be given by substituting the given values in a formula which relates ${K_c}$ , ${K_p}$ , $T$ (temperature) and $R$ (gas constant).
${K_p} = {K_c}{\left( {RT} \right)^{\Delta n}}$ ;
where
${K_p}$ is equilibrium at constant pressure,
${K_c}$ is equilibrium at constant concentration,
$R$ = gas constant (8.314
$T$ = temperature
$\Delta n$ = change in the number of moles of reaction.

Complete answer:
Chemical equilibrium is a condition where there is no net change in the amounts of reactants and products. The reaction given in this question is $S{O_2}C{l_2}\left( g \right) \rightleftharpoons S{O_2}\left( g \right) + C{l_2}\left( g \right)$ . Here we first need to calculate the value of $\Delta n$ . In this question the number of moles on the reactant side is 1, and the number of moles on the product side is 2.
$\Delta n$ is the change in number of moles in the reaction
$\Delta n = {n_p} - {n_r}$
$\Delta n$ = number of moles of product –number of moles of reactant.
$\Delta n$ =2-1
$\Delta n$ =1
We know that
${K_p} = {K_c}{\left( {RT} \right)^{\Delta n}}$
we can also write the above equations as
$\dfrac{{{K_p}}}{{{K_c}}} = R{T^{\Delta n}}$
substituting the values we get
$3 = R{T^1}$
Or, $T = \dfrac{3}{R}$
Also, putting the value of gas constant we have
$T = \dfrac{3}{{0,0821}}$
Finally, we get
$\Rightarrow T = 36.54K$ .
Hence the correct answer to this question is option C.

Note:
${K_p}$ and ${K_c}$ are the equilibrium constants in pressure and concentrations respectively, when the reactants and products are in gaseous state you can use ${K_p}$ . Also , $\Delta n$ is the difference of the number of moles and it can be positive, negative and even zero.
There are many applications of equilibrium constant.
1. It is a measure of the extent to which a reactant occurs.
2. It is used to calculate equilibrium concentrations
3. It also predicts the direction of reaction.