Question

A first order reaction has a half life period \(69.3\) seconds. Calculate the rate of reaction if the concentration of reactant is \(0.1\) M.

• A. \(1.0\times 10^{-1}\) mol dm\({}^{-3}\) s\({}^{-1}\)
• B. \(1.0\times 10^{-2}\) mol dm\({}^{-3}\) s\({}^{-1}\)
• C. \(1.0\times 10^{-3}\) mol dm\({}^{-3}\) s\({}^{-1}\)
• D. \(1.0\times 10^{-4}\) mol dm\({}^{-3}\) s\({}^{-1}\)

Hint:

Find the rate constant from the half life, then multiply it by the reactant concentration.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
For a first order reaction the rate constant depends only on the half life, and the rate equals the rate constant times the concentration.

Step 2: Find the rate constant
\(k=\dfrac{0.693}{t_{1/2}}=\dfrac{0.693}{69.3\ \text{s}}=1.0\times 10^{-2}\ \text{s}^{-1}\)

Step 3: Find the rate
\(\text{Rate}=k[A]=1.0\times 10^{-2}\times 0.1=1.0\times 10^{-3}\ \text{mol dm}^{-3}\text{ s}^{-1}\)

Step 4: Compare the options
The calculated rate matches the third option.

Final Answer:
The rate of reaction is 1.0 x 10^-3 mol dm^-3 s^-1. \[ \boxed{\text{(C) }1.0\times 10^{-3}\ \text{mol dm}^{-3}\text{ s}^{-1}} \]