Read the passage given below and answer based it.

The rate of a reaction is concerned with decrease in concentration of reactants or increase in concentration of products per unit time. It can be expressed as instantaneous rate at a particular instant of time and average rate over a large interval of time. A number of factors such as temperature, concentration of reactants, catalyst, affect the rate of a reaction. Mathematical representation of rate of a reaction is given by rate law. It has to be determined experimentally and cannot be predicted. Order of a reaction with respect to a reactant is the power of its concentration which appears in the rate law equation. Molecularity is defined only for an elementary reaction. Molecularity and order of an elementary reaction are same.

75% of a first-order reaction was completed in 32 minutes. 50% of the reaction was completed in

16 minutes

The correct answer is option 2. 16 minutes.

We know, for first-order reaction,

\(k = \frac{2.303}{t}log\frac{a}{a − x}\)

Since the reaction is 75% complete in 32 min we can write,

\(k = \frac{2.303}{32}log\frac{100}{100 − 75}\)

⇒ \(k = \frac{2.303}{32}log\frac{100}{25}\)

⇒ \(k = \frac{2.303}{32}log(4)\)

⇒ \(k = \frac{2.303}{32} × 0.602\)

∴ \(k = 0.0433 min^{-1}\)

Now when the reaction is 50% complete, the time required will be

\(t_{50} = \frac{2.303}{k}log\frac{a}{a − x}\)

⇒\(t_{50} = \frac{2.303}{0.0433}log\frac{100}{100 − 50}\)

⇒\(t_{50} = \frac{2.303}{0.0433}log\frac{100}{50}\)

⇒\(t_{50} = \frac{2.303}{0.0433}log 2\)

⇒\(t_{50} = \frac{2.303}{0.0433} × 0.301\)

⇒\(t_{50} = 16.01\)

∴ \(t_{50} ≈ 16 min\)