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In a first-order reaction, if the half-life is 10 minutes, what will be the conc

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Question: In a first-order reaction, if the half-life is 10 minutes, what will be the concentration after 30 minutes if the initial concentration is 1 M?

Options:

  1. 0.125 M
  2. 0.5 M
  3. 0.75 M
  4. 0.25 M

Correct Answer: 0.125 M

Solution: 

For a first-order reaction, the concentration after n half-lives is given by [A] = [A]0 * (1/2)^n. After 30 minutes (3 half-lives), [A] = 1 M * (1/2)^3 = 0.125 M.

In a first-order reaction, if the half-life is 10 minutes, what will be the conc

Practice Questions

Q1
In a first-order reaction, if the half-life is 10 minutes, what will be the concentration after 30 minutes if the initial concentration is 1 M?
  1. 0.125 M
  2. 0.5 M
  3. 0.75 M
  4. 0.25 M

Questions & Step-by-Step Solutions

In a first-order reaction, if the half-life is 10 minutes, what will be the concentration after 30 minutes if the initial concentration is 1 M?
  • Step 1: Identify the half-life of the reaction, which is given as 10 minutes.
  • Step 2: Determine how many half-lives fit into the total time of 30 minutes. Since 30 minutes divided by 10 minutes equals 3, there are 3 half-lives.
  • Step 3: Use the formula for concentration after n half-lives: [A] = [A]0 * (1/2)^n.
  • Step 4: Substitute the initial concentration [A]0 = 1 M and n = 3 into the formula: [A] = 1 M * (1/2)^3.
  • Step 5: Calculate (1/2)^3, which equals 1/8 or 0.125.
  • Step 6: Multiply 1 M by 0.125 to find the final concentration: [A] = 1 M * 0.125 = 0.125 M.
  • First-order reaction kinetics – Understanding how the concentration of a reactant decreases over time in a first-order reaction, specifically using the concept of half-lives.
  • Half-life calculation – Applying the formula for concentration after a certain number of half-lives to determine the remaining concentration of a reactant.
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