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Chemical Kinetics and Nuclear Chemistry question

2004 · Shift 0 · Q42

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Chemical Kinetics and Nuclear Chemistry
2004 · Shift 0 · Q42

Chemical Kinetics and Nuclear Chemistry question

2004 · Shift 0 · Q42

JEE MainChemistryChemical Kinetics and Nuclear ChemistryMCQ+4 / −1

The rate equation for the reaction 2A + B

\to

C is found to be: rate k[A][B]. The correct statement in relation to this reaction is that the

A
unit of K must be s-1
B
values of k is independent of the initial concentration of A and B
C
rate of formation of C is twice the rate of disappearance of A
D
t1/2 is a constant

View written solutionFree

Correct answer: B

Given rate law

For the reaction $2A + B \to C$ we are told that the rate equation is $\text{rate} = k[A][B]$

So the reaction is:

first order in $A$
first order in $B$
overall order $= 1+1 = 2$

Check option A: unit of $k$

For a second-order reaction, $\text{rate} = k(\text{concentration})^2$

Since rate has unit $\text{mol L}^{-1}\text{s}^{-1}$ and concentration has unit $\text{mol L}^{-1}$

Therefore,

= \text{L mol}^{-1}\text{s}^{-1}$$ So $k$ does **not** have unit $\text{s}^{-1}$. ✅ **Option A is false.** --- 3. **Check option B: dependence of $k$ on initial concentration** For a given reaction at fixed temperature, $$k$$ is a constant and does **not depend on initial concentrations** of reactants. It depends mainly on temperature and catalyst, not on initial amounts. ✅ **Option B is true.** --- 4. **Check option C: relation between rate of formation of $C$ and disappearance of $A$** For $$2A + B \to C$$ by stoichiometry, $$-\frac{1}{2}\frac{d[A]}{dt} = -\frac{d[B]}{dt} = \frac{d[C]}{dt}$$ Thus, $$\frac{d[C]}{dt} = -\frac{1}{2}\frac{d[A]}{dt}$$ So the **rate of disappearance of $A$ is twice the rate of formation of $C$**, not the other way round. ✅ **Option C is false.** --- 5. **Check option D: half-life** A constant half-life is characteristic of a **first-order** reaction only. Here overall order is 2, so in general $t_{1/2}$ is **not constant**. ✅ **Option D is false.** --- 6. **Final conclusion** The only correct statement is: $$\boxed{\text{B}}$$ --- 7. **Comparison with stored correct answer** Stored correct answer: **B** My derived answer: **B** So, the answers agree.

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