Respuesta :
Answer:
The rate law of the reaction will be given as;
[tex]R=k[HNO_2]^2[/tex]
The value of rate constant of the reaction is :
[tex]k=4.11\times 10^{-4} \mu M^{-1}s^{-1}[/tex]
The half life for the decomposition of [tex]HNO_2[/tex] is 15,596.73 s
Explanation:
[tex]2HNO_2(aq)\rightarrow NO(g) + NO_2(g) + H_2O(l)[/tex]
Given that reaction follows second order kinetics;
The rate law of the reaction will be given as;
[tex]R=k[HNO_2]^2[/tex]
Integrated rate law for second order kinetics is given by:
[tex]\frac{1}{A}=kt+\frac{1}{A_o}[/tex]
[tex]A_o[/tex] = initial concentration
A = concentration left after time t
k = rate constant of the reaction
Concentration at 0 second:
[tex]A_o=0.1560 \mu M[/tex]
Concentration at 1000 second:
[tex]A=0.1466 \mu M[/tex]
t = 1000 s - 0 s = 1000 s
[tex]\frac{1}{0.1466 \mu M}=k\times 1000 s+\frac{1}{0.1560 \mu M}[/tex]
[tex]k\times 1000 s=\frac{1}{0.1466 \mu M}-\frac{1}{0.1560 \mu M}[/tex]
[tex]k=4.11\times 10^{-4} \mu M^{-1}s^{-1}[/tex]
Half life for second order kinetics is given by:
[tex]t_{\frac{1}{2}=\frac{1}{k\times A_o}[/tex]
So, the half life for the decomposition of [tex]HNO_2[/tex]:
[tex]t_{\frac{1}{2}=\frac{1}{4.11\times 10^{-4} \mu M^{-1}s^{-1}\times0.1560 \mu M}[/tex]
[tex]t_{1/2}=15,596.73 s[/tex]
The half life for the decomposition of [tex]HNO_2[/tex] is 15,596.73 s
