Question

A first order reaction takes 90 minutes for 75% decomposition. Calculate its rate constants.

• A. \(0.032\ \text{min}^{-1}\)
• B. \(0.015\ \text{min}^{-1}\)
• C. \(0.039\ \text{min}^{-1}\)
• D. \(0.045\ \text{min}^{-1}\)

Hint:

For first-order kinetics use k = (2.303 / t) log (initial / remaining), with 25% remaining.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
For a first-order reaction \(k = \dfrac{2.303}{t}\log\dfrac{[\text{A}]_{0}}{[\text{A}]}\).

Step 2: Values
After 75% decomposition, 25% is left, so \(\dfrac{[\text{A}]_{0}}{[\text{A}]} = \dfrac{100}{25} = 4\). Time \(t = 90\ \text{min}\).

Step 3: Calculation
\(k = \dfrac{2.303}{90}\log 4 = \dfrac{2.303\times 0.602}{90}\approx 0.0154\ \text{min}^{-1}\).

Final Answer:
The rate constant is about 0.015 per minute. \[ \boxed{\text{(B) }0.015\ \text{min}^{-1}} \]