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The half-life of a first-order reaction is independent of the initial concentrat

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Question: The half-life of a first-order reaction is independent of the initial concentration of the reactant. What is the expression for the half-life (t₁/₂)? (2022)

Options:

  1. t₁/₂ = 0.693/k
  2. t₁/₂ = k/0.693
  3. t₁/₂ = 1/k
  4. t₁/₂ = k/1

Correct Answer: t₁/₂ = 0.693/k

Exam Year: 2022

Solution: 

The half-life of a first-order reaction is given by t₁/₂ = 0.693/k.

The half-life of a first-order reaction is independent of the initial concentrat

Practice Questions

Q1
The half-life of a first-order reaction is independent of the initial concentration of the reactant. What is the expression for the half-life (t₁/₂)? (2022)
  1. t₁/₂ = 0.693/k
  2. t₁/₂ = k/0.693
  3. t₁/₂ = 1/k
  4. t₁/₂ = k/1

Questions & Step-by-Step Solutions

The half-life of a first-order reaction is independent of the initial concentration of the reactant. What is the expression for the half-life (t₁/₂)? (2022)
  • Step 1: Understand what a first-order reaction is. In a first-order reaction, the rate of the reaction depends only on the concentration of one reactant.
  • Step 2: Learn about half-life. The half-life (t₁/₂) is the time it takes for half of the reactant to be consumed.
  • Step 3: Recognize that for first-order reactions, the half-life does not depend on the initial concentration of the reactant.
  • Step 4: Know the formula for the half-life of a first-order reaction, which is t₁/₂ = 0.693/k, where k is the rate constant.
  • Step 5: Remember that 0.693 is derived from the natural logarithm of 2 (ln(2)), which is used in the calculation of half-life.
  • First-Order Reactions – First-order reactions have a constant half-life that does not depend on the initial concentration of the reactant.
  • Half-Life Expression – The half-life of a first-order reaction can be calculated using the formula t₁/₂ = 0.693/k, where k is the rate constant.
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