Question: The equilibrium constant at 298 K for a reaction\[A + B \rightleftharpoons C + D\;\]is 100. If the i...

Question

The equilibrium constant at 298 K for a reaction $A + B \rightleftharpoons C + D\;$ is 100. If the initial concentration of all the four species were 1 M each, then equilibrium concentration of D (in molL −1 ) will be
A: 0.818
B: 1.818
C: 1.182
D: 0.182

Answer 1

Solution

Equilibrium refers to a condition when the rate of forward reaction is equal to the rate of reverse reaction. The equilibrium constant, denoted by K, expresses the relationship between reactants and products of a reaction at an equilibrium condition with respect to a specific unit.

Complete Step by step answer:
For a generalised chemical reaction taking place in a solution:
$aA + bB \rightleftharpoons cC + dD\;$
The equilibrium constant can be expressed as follows:
$K = \dfrac{{{{[C]}^c}{{[D]}^d}}}{{{{[A]}^a}{{[B]}^b}}}$
where [A], [B], [C] and [D] refer to the molar concentration of species A, B, C, D respectively at equilibrium. The coefficients like a, b, c, and d in the generalised chemical equation become exponents as seen in the above expression.
We are given the following chemical equation:
$A + B \rightleftharpoons C + D\;$
It is given that initial concentration of all four species i.e. A, B, C and D are 1 M each. The final concentration of all four species will be as listed in the following table:

Species	Initial concentration	Final concentration
A	1	1-x
B	1	1-x
C	1	1+x
D	1	1+x

Now substitute the values of initial and final concentration of each species in the equilibrium constant expression as mentioned below:
$K = \dfrac{{{{[1 + x]}^1}{{[1 + x]}^1}}}{{{{[1 - x]}^1}{{[1 - x]}^1}}}$
We are given the value of equilibrium constant as 100
Therefore,
$100 = {(\dfrac{{1 + x}}{{1 - x}})^2}$
$\therefore 10 = \dfrac{{1 + x}}{{1 - x}} \\\ \Rightarrow x = \dfrac{9}{{11}} \\\$
Equilibrium concentration of D = $1 + x = 1 + \dfrac{9}{{11}} = \dfrac{{20}}{{11}} = 1.818$ mol/L

Hence, the correct answer is Option B.

Note: While calculating the value of K, always remember few points such as (i) K is constant for a particular reaction at a particular temperature. K changes on changing the temperature, (ii) Pure solids or pure liquids are not generally included in the expression of equilibrium and (iii) The chemical reaction must always be balanced including the coefficients (lowest possible integer values) to attain the correct value for K.