Answer: 36.5 minutes
Explanation:
Expression for rate law for first order kinetics is given by:
[tex]t=\frac{2.303}{k}\log\frac{a}{a-x}[/tex]
where,
k = rate constant
t = age of sample
a = let initial amount of the reactant = 100
a - x = amount left after decay process
a) for completion of 36.8 % of reaction
[tex]7.6=\frac{2.303}{k}\log\frac{100}{100-36.8}[/tex]
[tex]k=\frac{2.303}{7.6}\times 0.19[/tex]
[tex]k=0.060min^{-1}[/tex]
b) for completion of 88.8 % of reaction
[tex]t=\frac{2.303}{k}\log\frac{100}{100-88.8}[/tex]
[tex]t=\frac{2.303}{0.060}\log\frac{100}{11.2}[/tex]
[tex]t=\frac{2.303}{0.060}\times 0.95[/tex]
[tex]t=36.5min[/tex]
It will take 36.5 minutes for 88.8% of the compound to decompose.
