Question

After four half-life periods for a first-order reaction, what fraction of reactant remains?

Answer 1

`(1)/(16)` or 6.25%

Step-by-step explanation:

Half-life describes how long it takes for half of a reactant to react.

First-Order Reactions

The question describes the reaction as first-order. In first-order reactions, half-lives are not dependent on concentration. This means that the half-life remains constant throughout the entire reaction. The equation for first-order half-life is:

• 
  `\displaystyle t_(1/2)=(ln(2))/(k)`

In this equation, t is the length of the half-life and k is the rate constant. As you can see, concentration is not a variable in half-life

Half-life

After each half-life, 50% of the reactant forms the product. This means that 50% of the reactant is gone after 1 half-life. So, starting with 100%, we can divide by 2, 4 times.

• 100% ÷ 2⁴ = 6.25%

In fraction form, 6.25% = 1/16. So, after 4 half-lives 1/16th of the reactant remains.