If the rate constant of a reaction is 0.03 s^-1, how much time does it take for 7.2 mol L^-1 concentration of the reactant to get…

Question

If the rate constant of a reaction is 0.03 s^-1, how much time does it take for 7.2 mol L^-1 concentration of the reactant to get reduced to 0.9 mol L^-1? (Given: log 2 = 0.301)

1. A. 69.3 s (Correct answer)
2. B. 23.1 s
3. C. 210 s
4. D. 21.0 s

Correct Answer

Option A — 69.3 s

Detailed Solution & Explanation

The correct answer is 69.3 s.

Key Points

• The unit of $k$ (s$^{-1}$) shows it is a first order reaction: $t=\dfrac{2.303}{k}\log\dfrac{a}{a-x}$.
• $t=\dfrac{2.303}{0.03}\log\dfrac{7.2}{0.9}=\dfrac{2.303}{0.03}\log 8=\dfrac{2.303}{0.03}\times3\log2$.
• $=\dfrac{2.303}{0.03}\times3\times0.301=69.3$ s.