Question

A particular reactant decomposes with a half-life of 105 s when its initial concentration is 0.272 m. the same reactant decomposes with a half-life of 223 s when its initial concentration is 0.128 m. what is the value and units of the rate constant for this reaction?

Answer 1

The rate constant for the reaction is 0.0066 s^-1 for the first reaction and 0.0031 s^-1 for the second reaction.

Step-by-step explanation:

The half-life of a reaction is the time required for the reactant concentration to decrease to one-half its initial value. For a first-order reaction, the half-life is given by the equation t1/2 = 0.693/k, where k is the rate constant. In this case, we have two different reactions with different initial concentrations and half-lives. We can use the half-life equation to find the rate constant for each reaction.

For the first reaction with an initial concentration of 0.272 M and a half-life of 105 s, we have 105 s = 0.693/k. Solving for k gives us 0.0066 s-1.

For the second reaction with an initial concentration of 0.128 M and a half-life of 223 s, we have 223 s = 0.693/k. Solving for k gives us 0.0031 s-1.

Therefore, the rate constant for the first reaction is 0.0066 s-1 and for the second reaction is 0.0031 s-1.