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Chemical Kinetics and Nuclear Chemistry question

2019 · 11 Jan · Shift 2 · Q13

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Chemical Kinetics and Nuclear Chemistry
2019 · 11 Jan · Shift 2 · Q13

Chemical Kinetics and Nuclear Chemistry question

2019 · 11 Jan · Shift 2 · Q13

JEE MainChemistryChemical Kinetics and Nuclear ChemistryMCQ+4 / −1

The reaction 2X

\to

B is a zeroth order reaction. If the initial concentration of X is 0.2 M, the half-life is 6 h. When the initial concentration of X is 0.5 M, the time required to reach its final concentration of 0.2 M will be:

A
18.0 h
B
9.0 h
C
7.2 h
D
12.0 h

View written solutionFree

Correct answer: A

Use the integrated rate law for a zero-order reaction

For a zero-order reaction, $[X]_t = [X]_0 - kt$

where:

$[X]_0$ = initial concentration
$[X]_t$ = concentration at time $t$
$k$ = zero-order rate constant

Use the given half-life to find $k$

For a zero-order reaction, half-life is: $t_{1/2} = \frac{[X]_0}{2k}$

Given:

$[X]_0 = 0.2\,\text{M}$
$t_{1/2} = 6\,\text{h}$

So, $6 = \frac{0.2}{2k} = \frac{0.1}{k}$

Hence, $k = \frac{0.1}{6} = \frac{1}{60}\,\text{M h}^{-1}$

Now calculate the time for concentration to fall from $0.5\,\text{M}$ to $0.2\,\text{M}$

Using $[X]_t = [X]_0 - kt$

Substitute: $0.2 = 0.5 - kt$ $kt = 0.5 - 0.2 = 0.3$

Thus, $t = \frac{0.3}{k} = \frac{0.3}{1/60} = 18\,\text{h}$

Evaluate the options

A: $18.0\,\text{h}$ ✅
B: $9.0\,\text{h}$ ❌
C: $7.2\,\text{h}$ ❌
D: $12.0\,\text{h}$ ❌

Therefore, the correct answer is: $\boxed{18.0\,\text{h}}$

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