In a first-order reaction \(A \longrightarrow P\), the ratio of \(\frac{a}{a – x}\) was found to be 8 after 60 minutes. If the concentration is 0.1 Μ then the rate of reaction in moles of A reacted per minutes is:

3.466 × 10^–3 mol litre^–1 min^–1

The correct answer is option 2. 3.466 × 10^–3 mol litre^–1 min^–1

Given,

$\frac{a}{a − x} = 8$

\(t  = 60 min\)

We know,

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

\( ⇒ k = \frac{2.303}{60} log 8\)

\( ⇒ k = 3.466 × 10^{−2} \text{min}^{−1}\)

Rate of a reaction,

\(\frac{dx}{dt} = k[A]\)

or, \(\frac{dx}{dt} =3.466 × 10^{−2} × 0.1\)

or, \(\frac{dx}{dt} =3.466 × 10^{−3} × 0.1\text{ mol L}^{−1}\text{min}^{−1}\)