Acetone is one of the most important solvents in organic chemistry. It is used to dissolve everything from fats and waxes to airplane glue and nail polish. At high temperatures, it decomposes in a first-order process to methane and ketene (CH2═C═O). At 600°C, the rate constant is 8.7 * 10-3 s-1. (a) What is the half-life of the reaction? Give your answer in scientific notatio

The half-life time, the team equired for a quantity to reduce to half of its initial value, is 79.67 seconds.

Explanation:

The half-life time = the time required for a quantity to reduce to half of its initial value. Half of it's value = 50%.

To calculate the half-life time we use the following equation:

[At]=[Ai]*e^ (-kt)

with [At] = Concentration at time t

with [Ai] = initial concentration

with k = rate constant

with t = time

We want to know the half-life time = the time needed to have 50% of it's initial value

50 = 100 * e^ (-8.7 * 10^-3 s^ - * t)

50/100 = e^ (-8.7 * 10^-3 s^-1 * t)

ln (0.5) = 8.7 * 10^-3 s^-1 * t

t = ln (0.5) / - 8.7 * 10^-3 = 79.67 seconds

The half-life time, the team equired for a quantity to reduce to half of its initial value, is 79.67 seconds.