In first order reaction the conc. of reactant decreases from 1.0 M to 0.25 M in 20 minutes, the value of k is -

CONCEPT:

First Order Reaction Kinetics

• For a first-order reaction, the rate of reaction is directly proportional to the concentration of the reactant.
• The integrated rate law for a first-order reaction is given by:
  \( \ln \left(\frac{[R]_0}{[R]}\right) = kt \), where:
  • \([R]_0\) is the initial concentration of the reactant.
  • [R] is the concentration of the reactant at time t.
  • k is the rate constant.
  • t is the time.

CALCULATION:

• Given data:
  • Initial concentration \([R]_0 = 1.0 \, M\)
  • Final concentration \([R] = 0.25 \, M\)
  • Time \(t = 20 \, minutes\)
• Using the first-order integrated rate law:
  • \(\ln \left(\frac{[R]_0}{[R]}\right) = kt \)
  • \(\ln \left(\frac{1.0}{0.25}\right) = k \times 20 \, minutes\)
  • \(\ln(4) = k \times 20\)
  • \(k = \frac{\ln(4)}{20} \approx \frac{1.386}{20} \approx 0.06932 \, \text{min}^{-1}\)

The correct answer is (1) 0.06932.