For a first-order reaction, the half-life is independent of the initial concentration.

For a first-order reaction, the half-life is independent of the initial concentration.

• A. True
• B. False
• C. Only at high concentration
• D. Only at low temperature

Answer: (A)

For a first-order reaction, the time it takes to reach half the initial concentration depends only on the rate constant, not on how much reactant you started with. The integrated rate law is [A] = [A]0 e^{-kt}. At the half-life, [A] = [A]0/2, so 1/2 = e^{-kt1/2}, giving t1/2 = ln(2)/k. Since this value is set by k and not by [A]0, the half-life is independent of the initial concentration (though it can change with temperature because k changes with temperature). So the statement is true.

For a first-order reaction, the time it takes to reach half the initial concentration depends only on the rate constant, not on how much reactant you started with. The integrated rate law is [A] = [A]0 e^{-kt}. At the half-life, [A] = [A]0/2, so 1/2 = e^{-kt1/2}, giving t1/2 = ln(2)/k. Since this value is set by k and not by [A]0, the half-life is independent of the initial concentration (though it can change with temperature because k changes with temperature). So the statement is true.