Question

Reactant ${\text{X}}{{\text{Y}}_2}$ dissociates as ${\text{X}}{{\text{Y}}_2}\left( {\text{g}} \right) \rightleftharpoons {\text{XY}}\left( {\text{g}} \right) + {\text{Y}}\left( {\text{g}} \right)$
Initial pressure of ${\text{X}}{{\text{Y}}_2}$ is 600 mm Hg. The total pressure at equilibrium is 800 mm Hg. Assuming volume of system to remain constant, the value of ${{\text{K}}_{\text{P}}}$ is:
A.50
B.100
C.20
D.400

Answer 1

The number of moles or pressure of reactant consumed and moles and pressure of product formed can be determined using the stoichiometric coefficient. These values can be used to determine the equilibrium constant in terms of pressure for the given reaction using the definition of equilibrium constant.

Formula: ${{\text{K}}_{\text{c}}} = \dfrac{{\left[ {{\text{Products}}} \right]}}{{\left[ {{\text{Reactants}}} \right]}}$

Complete step-by-step answer: We know the pressure is directly proportional to the number of moles so the pressure will change in the same proportion as the number of moles. From the given reaction we can see that one mole of a reactant that is ${\text{X}}{{\text{Y}}_2}$ decomposes to form one mole of product that is XY and Y.
The initial pressure for the reactant is given to us that is 600 mm Hg. writing the pressure at equilibrium according to the balanced chemical equation as:

Time	${\text{X}}{{\text{Y}}_{\text{2}}}\left( {\text{g}} \right){\text{ }} \to$	${\text{ XY}}\left( {\text{g}} \right){\text{ }} + {\text{ Y}}\left( {\text{g}} \right)$
Initially	600	$\,\,0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0\,\,\,$
Equilibrium	${\text{600}} - {\text{p}}$	$\,\,p\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,p$

Total pressure at equilibrium is given to us. So we will add all the pressure at equilibrium and that will be become:
$800 = 600 - {\text{p}} + {\text{p}} + {\text{p}}$
Solving this we will get the value of p as 200 mm Hg.
The pressure at equilibrium of Y will be p that is 200 mm Hg
The pressure at equilibrium of XY will be p that is 200 mm Hg
The pressure at equilibrium of ${\text{X}}{{\text{Y}}_2}$ will be $600 - 200 = 400$
The equilibrium constant in terms of pressure is defined as the ratio of the pressure of product each raised to the power of their respective stoichiometry to the pressure of reactant raise to the power of their respective stoichiometry. Hence the equilibrium constant will be:
${{\text{K}}_{\text{P}}} = \dfrac{{{{\left[ {{\text{XY}}} \right]}^1}{{\left[ {\text{Y}} \right]}^1}}}{{{{\left[ {{\text{X}}{{\text{Y}}_2}} \right]}^1}}}$
We have risen to the power 1 because of the stoichiometric coefficient in the reaction given is 1 for all.
${{\text{K}}_{\text{P}}} = \dfrac{{200 \times 200}}{{400}} = 100$
Hence, the correct option is B.

Note: The equilibrium is attained when the rate of forward reaction becomes equal to the rate of backward reaction, that is the rate at which the reactant converts into product becomes equal to rate at which product converted into reactant. The equilibrium constant is a constant which is a function of temperature. It remains constant throughout the reaction unless temperature changes.