Question

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?
b. How much time is required for 32% of a sample of acetone to decompose?
c. How much time is required for 81% of a sample of acetone to decompose?

Answer 1

Answer: a. 79.6 s

b. 44.3 s

c. 191 s

Explanation:

Expression for rate law for first order kinetics is given by:

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

k = rate constant  

t = age of sample

a = let initial amount of the reactant  

a - x = amount left after decay process  

a) for completion of half life:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

$t_{\frac{1}{2}}=\frac{0.693}{k}$

$t_{\frac{1}{2}}=\frac{0.693}{8.7\times 10^{-3}s^{-1}}=79.6s$

b) for completion of 32% of reaction  

$t=\frac{2.303}{k}\log\frac{100}{100-32}$

$t=\frac{2.303}{8.7\times 10^{-3}}\log\frac{100}{68}$

$t=44.3s$

c) for completion of 81 % of reaction  

$t=\frac{2.303}{k}\log\frac{100}{100-81}$

$t=\frac{2.303}{8.7\times 10^{-3}}\log\frac{100}{19}$

$t=191s$