Question

For an equilibrium reaction, \[\Delta {n_g}\] value is positive, which of the following is correct?
A) \[{K_p} = {K_c}\]
B) \[{K_p} > {K_c}\]
C) \[{K_p} < {K_c}\]
D) \[{K_p} = {K_c} = 0\]

Answer 1

Hint:The equilibrium constant is the ratio of the amount of product to the amount of reactant raised to their respective stoichiometric coefficients when the reaction is at equilibrium. The equilibrium constant of aqueous reaction and gaseous reactions is denoted by \[{K_c}\] and \[{K_p}\] respectively. A \[\Delta {n_g}\] is the difference between the total number of moles of gaseous products and a total number of moles of gaseous reactants. Use the equation related to \[{K_c}\] and \[{K_p}\] and determine the relation between \[{K_c}\] and \[{K_p}\] when \[\Delta {n_g}\] value is positive.

Complete step-by-step answer:
The equilibrium constant \[{K_c}\] indicates the ratio of the equilibrium concentration of product to the equilibrium concentration of reactant raised to their respective stoichiometric coefficients.
For gaseous reactions, the concentrations of products and reactants are expressed in terms of partial pressure. So the equilibrium constant of a gaseous reaction is denoted by the symbol\[{K_p}\].
The mathematical equation related to \[{K_p}\]and \[{K_c}\]is as follows:
\[{K_p} = {K_c}{(RT)^{\Delta {n_g}}}\]
Here,
\[R\] = gas constant
\[T\]= temperature
\[\Delta {n_g}\]= total number of moles of gaseous products - total number of moles of gaseous reactants
So from the equation, we can say that the relation between \[{K_p}\]and \[{K_c}\] depends on the value of\[\Delta {n_g}\].
When\[\Delta {n_g} = 0\], \[{K_p} = {K_c}\]
So, option (A) \[{K_p} = {K_c}\] is an incorrect answer.
When\[\Delta {n_g} = {\text{positive}}\], \[{K_p} > {K_c}\]
So, the correct option is (B) \[{K_p} > {K_c}\].
When\[\Delta {n_g} = {\text{negative}}\], \[{K_p} < {K_c}\]
So, option (C) \[{K_p} < {K_c}\]is an incorrect answer.
Also, option (D) \[{K_p} = {K_c} = 0\] is incorrect as it indicates no reaction takes place.

Hence the correct answer is option ‘B’.
Note: The positive value of \[\Delta {n_g}\] indicates that there are more number of gaseous products than a number of gaseous reactants. The negative value of \[\Delta {n_g}\] indicates that there are less number of gaseous products than a number of gaseous reactants. When a number of gaseous products is equal to the number of gaseous reactants than\[\Delta {n_g} = 0\].