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JEE Chemistry 2025 Question with Solution

Consider an elementary reaction: A(g)+B(g)→C(g)+D(g)A(g) + B(g) \rightarrow C(g) + D(g) If the volume of the reaction mixture is suddenly reduced to 13\frac{1}{3} of its initial volume, the reaction rate will become xx times of the original reaction rate. The value of xx is:

  • A

    19\frac{1}{9}

  • B

    99

  • C

    33

  • D

    13\frac{1}{3}

Answer

Correct answer:B

Step-by-step solution

Standard Method

Given: The elementary reaction is A(g)+B(g)→C(g)+D(g)A(g) + B(g) \rightarrow C(g) + D(g) and the volume is reduced to 13\frac{1}{3} of its initial value.

Find: The factor xx by which the reaction rate changes.

For an elementary reaction, the rate law is determined directly from the stoichiometric coefficients of the reactants:

Rate=k[A][B]\text{Rate} = k[A][B]

When the volume is reduced to 13\frac{1}{3} of the initial volume, the concentration of each gaseous reactant becomes 33 times its original value because concentration is inversely proportional to volume.

So the new rate is

R2=k(3[A])(3[B])=9k[A][B]R_2 = k(3[A])(3[B]) = 9k[A][B]

while the original rate is

R1=k[A][B]R_1 = k[A][B]

Therefore,

R2R1=9k[A][B]k[A][B]=9\frac{R_2}{R_1} = \frac{9k[A][B]}{k[A][B]} = 9

Hence, the reaction rate becomes 99 times the original rate. The correct option is B.

Stepwise Ratio Method

Given: A(g)+B(g)→C(g)+D(g)A(g) + B(g) \rightarrow C(g) + D(g) is an elementary reaction.

Find: The value of xx when the volume becomes 13\frac{1}{3} of the initial volume.

Since the reaction is elementary, the rate law is

R1=k[A][B]R_1 = k[A][B]

After volume reduction, the new concentrations become

[A]′=3[A],[B]′=3[B][A]' = 3[A], \qquad [B]' = 3[B]

Therefore, the new rate is

R2=k[A]′[B]′=k(3[A])(3[B])=9k[A][B]R_2 = k[A]'[B]' = k(3[A])(3[B]) = 9k[A][B]

Taking the ratio,

R2R1=9k[A][B]k[A][B]=9\frac{R_2}{R_1} = \frac{9k[A][B]}{k[A][B]} = 9

So, x=9x = 9 and the correct option is B.

Common mistakes

  • Using only one concentration factor of 33 and concluding the rate becomes 33 times. This is wrong because both [A][A] and [B][B] increase by a factor of 33. Multiply both factors to get 3×3=93 \times 3 = 9.

  • Assuming the rate law must be guessed separately from experiment. This is wrong here because the reaction is explicitly stated to be elementary, so the stoichiometric coefficients directly give Rate=k[A][B]\text{Rate} = k[A][B].

  • Thinking the rate decreases because the volume decreases to 13\frac{1}{3}. This is wrong because decreasing volume increases concentration for gases. Higher reactant concentrations increase the rate in this second-order elementary reaction.

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