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MCQEasyJEE 2025Rate of Reaction

JEE Chemistry 2025 Question with Solution

Rate law for a reaction between AA and BB is given by R=k[A]n[B]mR = k[A]^n[B]^m. If concentration of A is doubled and concentration of B is halved from their initial value, the ratio of new rate of reaction to the initial rate of reaction (r2r1)\left(\frac{r_2}{r_1}\right) is

  • A

    2(n−m)2^{(n-m)}

  • B

    (n−m)(n-m)

  • C

    (m+n)(m+n)

  • D

    12(m+n)\frac{1}{2^{(m+n)}}

Answer

Correct answer:A

Step-by-step solution

Standard Method

Given: The rate law is

R=k[A]n[B]mR = k[A]^n[B]^m

Initially,

r1=k[A]n[B]mr_1 = k[A]^n[B]^m

The concentration of AA is doubled and the concentration of BB is halved.

Find: The ratio r2r1\frac{r_2}{r_1}.

Using the changed concentrations,

[A]′=2[A],[B]′=12[B][A]' = 2[A], \qquad [B]' = \frac{1}{2}[B]

So the new rate is

r2=k(2[A])n(12[B])mr_2 = k(2[A])^n\left(\frac{1}{2}[B]\right)^m

Now simplify:

r2=k⋅2n[A]n⋅(12)m[B]mr_2 = k \cdot 2^n [A]^n \cdot \left(\frac{1}{2}\right)^m [B]^m r2=k⋅2n⋅12m⋅[A]n[B]mr_2 = k \cdot 2^n \cdot \frac{1}{2^m} \cdot [A]^n[B]^m r2=k⋅2n−m⋅[A]n[B]mr_2 = k \cdot 2^{n-m} \cdot [A]^n[B]^m

Therefore,

r2r1=k⋅2n−m⋅[A]n[B]mk[A]n[B]m=2n−m\frac{r_2}{r_1} = \frac{k \cdot 2^{n-m} \cdot [A]^n[B]^m}{k[A]^n[B]^m} = 2^{n-m}

Therefore, the correct option is A.

Factor Change Method

Given: Rate is proportional to [A]n[B]m[A]^n[B]^m.

Find: How the rate changes when [A][A] becomes doubled and [B][B] becomes halved.

A doubling of [A][A] multiplies the rate by 2n2^n, and a halving of [B][B] multiplies the rate by (12)m\left(\frac{1}{2}\right)^m.

Hence, the overall factor is

r2r1=2n×(12)m=2n−m\frac{r_2}{r_1} = 2^n \times \left(\frac{1}{2}\right)^m = 2^{n-m}

Therefore, the correct option is A.

Common mistakes

  • Using 2n+m2^{n+m} instead of 2n−m2^{n-m}. This is wrong because halving [B][B] contributes a factor of (12)m\left(\frac{1}{2}\right)^m, not 2m2^m. Multiply by 2n2^n and divide by 2m2^m.

  • Treating the orders nn and mm as coefficients instead of exponents. This is wrong because the rate law depends on concentrations raised to powers. Apply the concentration change directly inside the exponents.

  • Writing the new rate as k(2[A]n)([B]m2)k(2[A]^n)\left(\frac{[B]^m}{2}\right). This is wrong because the whole concentration term changes before exponentiation. First substitute 2[A]2[A] and [B]2\frac{[B]}{2}, then raise them to nn and mm respectively.

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