Answer :
Answer: The rate constant of a first-order reaction that takes 563 secondsseconds for the reactant concentration to drop to half of its initial value is [tex]1.23\times 10^{-3}s^{-1}[/tex]
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
a - x = amount left after decay process
Half life is the amount of time taken by a radioactive material to decay to half of its original value.
[tex]t_{\frac{1}{2}}=\frac{0.693}{k}[/tex]
[tex]k=\frac{0.693}{563s}=1.23\times 10^{-3}s^{-1}[/tex]
Thus rate constant of a first-order reaction that takes 563 secondsseconds for the reactant concentration to drop to half of its initial value is [tex]1.23\times 10^{-3}s^{-1}[/tex]