Question

Two substances R and S decompose in solution independently, both following first order kinetics. The rate constant of R is twice that of S. Initially 0.5 millimoles of R and 0.25 of S. The molarities of R and S will be equal at the end of time equal to:

• A. twice the half-life of R
• B. twice the half-life of S
• C. the half-life of S
• D. the half-life of R

Hint:

For first order reactions, half-life is independent of initial concentration.

Answer 1

The Correct Option is D

Step 1: First order decay: \[ [R]=R_0 e^{-k_R t},\quad [S]=S_0 e^{-k_S t} \]
Step 2: Given \(k_R=2k_S\) and \(R_0=2S_0\).
Step 3: Equality occurs when: \[ t = \frac{\ln 2}{k_R} = t_{1/2}(R) \]