Question

For what order reaction does the half-life get longer as the initial concentration increases?

Answer 1

The half-life gets longer as the initial concentration increases in zero-order reaction.

The amount of time it takes for the concentration of a given reactant to reach 50% of its initial concentration is known as the half-life of a chemical reaction (i.e. the time taken for the reactant concentration to reach half of its initial value).

For zero order reaction:

The half-life is given as:

$t_{1/2}=\frac{[A]_{0}}{2k}$ where k is the rate constant of the reaction and $[A]_{0}$ is the initial concentration.

As we can see that the half-life is directly proportional to the initial concentration. Therefore, when the initial concentration increases the half-life gets longer.

For the first-order reaction,

The half-life is given as:

$t_{1/2}=\frac{\ln 2}{k}=\frac{0.693}{k}$

A first-order reaction's half-life is independent of the initial concentration.

For a second-order reaction,

The half-life is:

$t_{\frac{1}{2} }=\frac{1}{k[A]_{0}}$

The initial concentration is inversely proportional to the half-life, so when the initial concentration increases the half-life will get shorter.

Learn more about half life here:

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