Question

Calculate the rate constant of first order reaction \(\text{A}\rightarrow \text{B}\) having rate \(5.4\times 10^{-6} \text{mol dm}^{-3}\text{s}^{-1}\) and \([\text{A}] = 0.3\) M.

• A. \(1.52\times 10^{-5} \text{s}^{-1}\)
• B. \(1.68\times 10^{-5} \text{s}^{-1}\)
• C. \(1.72\times 10^{-5} \text{s}^{-1}\)
• D. \(1.80\times 10^{-5} \text{s}^{-1}\)

Hint:

For a first-order reaction, rate = k[A].

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
For a first-order reaction the rate is proportional to the concentration of the reactant to the first power.

Step 2: Key Formula or Approach
\[ \text{rate}=k[\text{A}] \]

Step 3: Substitute
\[ k=\frac{\text{rate}}{[\text{A}]}=\frac{5.4\times10^{-6}\ \text{mol dm}^{-3}\text{s}^{-1}}{0.3\ \text{mol dm}^{-3}} \]

Step 4: Calculate
\[ k=1.8\times10^{-5}\ \text{s}^{-1} \]

Step 5: Units check
The unit of \(k\) for a first-order reaction is \(\text{s}^{-1}\), matching the options. The other values, 1.52, 1.68 and 1.72 (all times \(10^{-5}\)), would come from a different rate or concentration.

Final Answer:
The rate constant is \(1.8\times10^{-5}\ \text{s}^{-1}\), option (D). \[ \boxed{1.80\times10^{-5}\ \text{s}^{-1}} \]