Question

For the system $3A + 2B \to 2C$, the expression for equilibrium constant $K$is:
A.$\left[ {3A} \right] \times \left[ {2B} \right] \times \dfrac{1}{{\left[ C \right]}}$
B.${\left[ A \right]^3} \times \left[ B \right] \times \dfrac{1}{{\left[ C \right]}}$
C.\[\dfrac{{{{\left[ C \right]}^2}}}{{{{\left[ A \right]}^3}}} \times \dfrac{1}{{{{\left[ B \right]}^2}}}\]
D.$\dfrac{{\left[ C \right]}}{{\left[ {3A} \right]}} \times \dfrac{1}{{\left[ {2B} \right]}}$

Answer 1

Hint: Try to recollect the concept of reaction quotient at chemical equilibrium, which can be defined as a state, that a dynamic chemical system approaches when sufficient time has elapsed as a result of which its composition has no measurable tendency towards further change.

Complete step by step answer:
A reversible reaction can proceed in both the forward direction as well as backward direction. The state of Equilibrium is said to have been achieved when the rate of the forward reaction becomes equal to the rate of the reverse reaction. In this state, the concentration of all the reactants and products become constant.
Let us consider a general reversible reaction of the form,
$aA + bB \rightleftharpoons cC + dD$
For the above reaction, the expression for equilibrium constant can be written as,


  $K = \dfrac{{{{\left[ C \right]}^c} \times {{\left[ D \right]}^d}}}{{{{\left[ A \right]}^a} \times {{\left[ B \right]}^b}}}$ , …….. (1)


So, on substituting the values of concentrations of products and reactants, in equation (1) as per the equation given in question, we will have,
$K = \dfrac{{{{\left[ C \right]}^2}}}{{{{\left[ A \right]}^3} \times {{\left[ B \right]}^2}}}$

So, the correct option is C.

Note:
The value of equilibrium constant is always the same (provided that the temperature is not changing), irrespective of the amounts of reactants. It also remains unaffected by a change in pressure or whether or not we are using a catalyst.
For the reactions that are not at equilibrium, we can write a similar expression, by replacing equilibrium constant $K$ with the reaction quotient $Q$ . This $Q = K$ at equilibrium.