For a reaction of the type X k₂k₁⇌ Y, the correct rate expression is ([X]₀. and [X] corresponds to the concen… · ABC26PH0364

Subject: Physical Chemistry · Chapter: Chemical Kinetics · Topic: Chemical Kinetics – General · Exam: GATE 2005-2021 · Marks: 2 · Difficulty: Medium

For a reaction of the type $\mathrm{X} \underset{\mathrm{k}_{2}}{\stackrel{\mathrm{k}_{1}}{\rightleftharpoons}} \mathrm{Y}$, the correct rate expression is $\left([\mathrm{X}]_{0}\right.$ and $[\mathrm{X}]$ corresponds to the concen tration of X at time $\mathrm{t}=0$ and $\mathrm{t}=\mathrm{t}$, respectively)
(a)$-\frac{\mathrm{d}[\mathrm{X}]}{\mathrm{dt}}=\mathrm{k}_{1}[\mathrm{X}]_{0}-\left(\mathrm{k}_{1}+\mathrm{k}_{2}\right)[\mathrm{X}]$
(b)$-\frac{\mathrm{d}[\mathrm{X}]}{\mathrm{dt}}=\left(\mathrm{k}_{1}+\mathrm{k}_{2}\right)[\mathrm{X}]-\mathrm{k}_{2}[\mathrm{X}]_{0}$
(c)$-\frac{\mathrm{d}[\mathrm{X}]}{\mathrm{dt}}=\left(\mathrm{k}_{1}+\mathrm{k}_{2}\right)[\mathrm{X}]_{0}-\mathrm{k}_{1}[\mathrm{X}]$
(d)$-\frac{\mathrm{d}[\mathrm{X}]}{\mathrm{dt}}=\left(\mathrm{k}_{1}-\mathrm{k}_{2}\right)[\mathrm{X}]-\mathrm{k}_{1}[\mathrm{X}]_{0}$
Answer
Answer: B ✓ checked by 4AB · confidence high
Explanation
−d[X]/dt = k₁[X] − k₂[Y], with [Y] = [X]₀ − [X]. That gives (k₁ + k₂)[X] − k₂[X]₀ (b).

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