The given question is incomplete. The complete question is:
The decomposition of carbon disulfide, [tex]CS_2[/tex], to carbon monosulfide, CS, and sulfur is first order with k = [tex]2.8\times 10^{-7}s^{-1}[/tex] at 1000oC.
[tex]CS_2\rightarrow CS+S[/tex]
What is the half-life of this reaction at 1000oC?
Answer: The half-life of this reaction at 1000oC is 2400000s.
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
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.
[tex]t_{\frac{1}{2}}=\frac{0.693}{k}[/tex]
[tex]t_{\frac{1}{2}}=\frac{0.693}{2.8\times 10^{-7}s^{-1}}=0.24\times 10^7s[/tex]
The half-life of this reaction at 1000oC is 2400000s.
