In 30 minutes, a first-order reaction is 50% complete. The time required to complete 87.5 percent of the reaction is   ____________________

The rate of a first-order reaction is directly proportional to the concentration of one of the reactants. The formula for the rate of a first-order reaction is:

k = ln(2) / t_half

where:

• k is the rate constant
• t_half is the half-life of the reaction, or the time it takes for half of the reactants to be used up

Given that the reaction is 50% complete in 30 minutes, we can say that the half-life of the reaction is 30 minutes. We can use this to find the rate constant:

k = ln(2) / 30 min = 0.0231 min^-1

The time required to complete a certain percentage of a first-order reaction can be found using the formula:

t = ln([A]0 / [A]) / k

where:

• t is the time
• [A]0 is the initial concentration
• [A] is the final concentration

If we want to find the time required to complete 87.5% of the reaction, we can say that the final concentration is 12.5% of the initial concentration (because 100% - 87.5% = 12.5%). Therefore, we can plug these values into the formula:

t = ln(1 / 0.125) / 0.0231 min^-1 = 100 minutes

So, the time required to complete 87.5% of the reaction is approximately 100 minutes.