# What is the half-life of a first-order reaction with a rate constant of #7.80xx10^-4 s^(-1)#?

##### 1 Answer

#### Explanation:

The **half-life**, *first-order reaction* is * independent* of the initial concentration of the reactant, which is why the problem doesn't provide you with one.

In fact, all you need to know in order to calculate the half-life of a first-order reaction is the **rate constant**,

#k = 7.80 * 10^(-4)"s"^(-1)#

So, the half-life of a first-order reaction can be calculated by using the equation

#color(blue)(|bar(ul(color(white)(a/a)t_"1/2" = ln(2)/kcolor(white)(a/a)|)))#

Plug in your values to find

#t_"1/2" = ln(2)/(7.80 * 10^(-4)"s"^(-1)) = color(green)(|bar(ul(color(white)(a/a)color(black)("889 s")color(white)(a/a)|)))#

The answer is rounded to three **sig figs**.

You can thus say that for your reaction, it takes **half** of the concentration of the reactant to be consumed.