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NEET CHEMISTRYMedium

Consider the following reaction taking place in 1 L1\text{ L} capacity container at 300 K300\text{ K}: A+BC+D\text{A} + \text{B} \rightleftharpoons \text{C} + \text{D} If one mole each of A and B are present initially and at equilibrium 0.7 mol0.7\text{ mol} of C is formed, then the equilibrium constant (KcK_c) for the reaction is:

A

9.7

B

1.2

C

6.2

D

5.4

Step-by-Step Solution

For the given reversible reaction: A+BC+D\text{A} + \text{B} \rightleftharpoons \text{C} + \text{D}

Initial moles: nA=1n_A = 1 nB=1n_B = 1 nC=0n_C = 0 nD=0n_D = 0

Let xx be the number of moles of C formed at equilibrium. The moles of each species at equilibrium will be: nA=1xn_A = 1 - x nB=1xn_B = 1 - x nC=xn_C = x nD=xn_D = x

We are given that 0.7 mol0.7\text{ mol} of C is formed at equilibrium, so x=0.7x = 0.7. Since the volume of the container is 1 L1\text{ L}, the molar concentrations at equilibrium are equal to the number of moles : [A]=10.7=0.3 M[\text{A}] = 1 - 0.7 = 0.3\text{ M} [B]=10.7=0.3 M[\text{B}] = 1 - 0.7 = 0.3\text{ M} [C]=0.7 M[\text{C}] = 0.7\text{ M} [D]=0.7 M[\text{D}] = 0.7\text{ M}

The equilibrium constant expression (KcK_c) is: Kc=[C][D][A][B]K_c = \frac{[\text{C}][\text{D}]}{[\text{A}][\text{B}]}

Substituting the equilibrium concentrations into the expression: Kc=0.7×0.70.3×0.3=0.490.09=4995.44K_c = \frac{0.7 \times 0.7}{0.3 \times 0.3} = \frac{0.49}{0.09} = \frac{49}{9} \approx 5.44

Therefore, the equilibrium constant (KcK_c) is approximately 5.45.4.

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