Question

What is the equilibrium constant expression for the reaction $ {{P}_{4\left( s \right)}}+5{{O}_{2}}\rightleftharpoons {{P}_{4}}{{O}_{10(s)}} $
(A) $ {{K}_{C}}=\dfrac{\left[ {{P}_{4}}{{O}_{10}} \right]}{\left[ {{P}_{4}} \right]{{\left[ {{O}_{2}} \right]}^{5}}} $
(B) $ {{K}_{C}}=\dfrac{\left[ {{P}_{4}}{{O}_{10}} \right]}{5\left[ {{P}_{4}} \right]\left[ {{O}_{2}} \right]} $
(C) $ {{K}_{C}}={{\left[ {{O}_{2}} \right]}^{5}} $
(D) $ {{K}_{C}}=\dfrac{1}{{{\left[ {{O}_{2}} \right]}^{5}}} $

Answer 1

Hint: We know that the equilibrium represents the state of a process in which the properties like temperature, pressure, concentration of the system does not show any change with the passage of time.

Complete answer:
Equilibrium is a state of chemical reaction where the rate of forward and backward reaction is the same. Moreover, equilibrium can be of two types: homogeneous equilibrium and heterogeneous equilibrium. The main difference between the two equilibrium constants is that they are used for the different concentrations. $ {{K}_{P}} $ specifically represents equilibrium constant at partial pressure during a reaction. In terms of calculation, these values can be found from the reactant and products, using the formulae and using the specific values of those formulae.
A homogeneous equilibrium is defined as a homogeneous mixture (reactants and products in a single solution) in one phase. The reactants are on the left side of the equation and the products are on the right side of the equation. The given equilibrium reaction is $ {{P}_{4\left( s \right)}}+5{{O}_{2}}\rightleftharpoons {{P}_{4}}{{O}_{10(s)}} $
The following equilibrium reaction expression for $ {{K}_{C}} $ is given as; $ {{K}_{C}}=\dfrac{\left[ {{P}_{4}}{{O}_{10}} \right]}{\left[ {{P}_{4}} \right]{{\left[ {{O}_{2}} \right]}^{5}}}=\dfrac{1}{{{\left[ {{O}_{2}} \right]}^{5}}}. $
Here, $ \left[ {{P}_{4}}{{O}_{10}} \right]=\left[ {{P}_{4}} \right]=1~ $ as the partial pressures of the solid substances are considered as unity.
Therefore, the correct answer is option D.

Note:
Remember that the chemical equilibrium which involves equilibrium between ions in aqueous solution is called ionic equilibrium. Equilibrium can be established for both physical processes and chemical reactions. When the condition arrives in which there is no change in the concentrations of reactants and products and rate of forward reaction becomes equal to the rate of backward reaction then this type of equilibrium is called dynamic equilibrium.