Respuesta :
The given question is incomplete. The complete question is :
The thermal decomposition of phosphine (PH3) into phosphorus and molecular hydrogen is a first-order reaction: [tex]4PH_3(g)\rightarrow P_4(g)+6H_2(g)[/tex] The half-life of the reaction is 35.0 s at 680°C. Calculate the first order rate constant.
Answer: a) The first order rate constant is [tex]0.0198s^{-1}[/tex]
b) The time after which 95% reactions gets completed is 151 seconds
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
a) for finding the rate constant
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}{35.0s}=0.0198s^{-1}[/tex]
The first order rate constant is [tex]0.0198s^{-1}[/tex]
b) for completion of 95 % of reaction
[tex]t=\frac{2.303}{k}\log\frac{100}{100-95}[/tex]
[tex]t=\frac{2.303}{0.0198}\log\frac{100}{5}[/tex]
[tex]t=151 s[/tex]
The time after which 95% reactions gets completed is 151 seconds
