In a first-order reaction \(A \longrightarrow P\), the ratio \(\frac{a}{a - x}\) was found to be 8 after 60 minutes. When the concentration of A is 0.1 M, the rate of the reaction, in moles of A reacted per litre per minute, is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 3.466 × 10−3 mol L−1 min−1
For a first order reaction, the rate constant follows from the integrated rate equation, and the rate at any instant is k times the concentration at that instant.
\( \displaystyle k=\frac{2.303}{t}\log\frac{a}{a-x} \)
\( \displaystyle k=\frac{2.303}{60\,\mathrm{min}}\log 8=\frac{2.303\times0.9031}{60\,\mathrm{min}} \)
\( \displaystyle k=3.466\times10^{-2}\,\mathrm{min^{-1}} \)
Rate when [A] = 0.1 M:
\( \displaystyle \text{Rate}=k[A] \)
\( \displaystyle \text{Rate}=3.466\times10^{-2}\,\mathrm{min^{-1}}\times0.1\,\mathrm{mol\,L^{-1}} \)
\( \displaystyle \text{Rate}=3.466\times10^{-3}\,\mathrm{mol\,L^{-1}\,min^{-1}} \)
The rate is 3.466 × 10−3 mol L−1 min−1.