If the rate constant of a reaction is 0.03 s⁻¹, how much time does it take for 7.2 mol L⁻¹ concentration of the reactant to get reduced to 0.9 mol L⁻¹?
(Given: log 2 = 0.301)

CONCEPT:

First-Order Kinetics and Time Calculation

ln([A]_t / [A]₀) = -kt

• The rate constant (k) for a first-order reaction is related to the time taken for a reactant to decrease to a specific concentration using the integrated first-order rate equation:
• Where:
  • [A]_t is the concentration of the reactant at time t.
  • [A]₀ is the initial concentration of the reactant.
  • k is the rate constant.
  • t is the time.
• Rearranging the equation to solve for time (t):

  t = - (1 / k) × ln([A]_t / [A]₀)

EXPLANATION:

Substitute the values into the formula:

t = - (1 / 0.03) × ln(0.9 / 7.2)​

• Take the natural logarithm (ln):

  ln(0.125) = -2.079

• Substitute into the equation:

  t = - (1 / 0.03) × (-2.079)

• Simplify:

  t = (1 / 0.03) × 2.079

  t = 69.3 s

Therefore, the time taken for the concentration to reduce from 7.2 mol L⁻¹ to 0.9 mol L⁻¹ is 69.3 seconds.