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?
Practice Questions
1 question
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?
0.125 M
0.5 M
0.75 M
0.25 M
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.
Questions & Step-by-step Solutions
1 item
Q
Q: 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?
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.
Steps: 6
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.
