# Problem: Acetone is one of the most important solvents in organic chemistry, 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 x 10−3 s−1. How long does it take for 90.% of a sample of acetone to decompose?

###### FREE Expert Solution

We’re being asked to determine the time it would take for 90.% of a sample of acetone to decompose. Since no concentration is given, we can use the given percentages in place of concentration.

The integrated rate law for a first-order reaction is as follows:

where:

[A]t = concentration at time t
k = rate constant
t = time
[A]0 = initial concentration

If we have [A]0 = 100% at the start of the reaction, this means after time, t,, we have [A]t = 100% – 90% = 10%

We’re given:

90% (171 ratings)
###### Problem Details

Acetone is one of the most important solvents in organic chemistry, 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 x 10−3 s−1. How long does it take for 90.% of a sample of acetone to decompose?