Respuesta :
Answer:
15.1 seconds is the half life of the reaction when concentration of the substrate is 2.77 M.
Explanation:
A → B + C
The rate law of the reaction will be :
[tex]R=k[A]^x[/tex]
Initial rate of the reaction when concentration of the substrate was 0.4 M:
[tex]0.183 M/s=k[0.4 M]^x[/tex]..[1]
Initial rate of the reaction when concentration of the substrate was 0.8 M:
[tex]0.183 M/s=k[0.8 M]^x[/tex]...[2]
[1] ÷ [2] :
[tex]\frac{0.183 M/s}{0.183 M/s}=\frac{k[0.4 M]^x}{k[0.8 M]^x}[/tex]
x = 0
The order of the reaction is zero.
For the value of rate constant ,k:
[tex]0.183 M/s=k[0.4 M]^x[/tex]..[1]
x = 0
[tex]0.183 M/s=k[0.4 M]^0[/tex]
k= 0.183 M/s
The half life of the zero order kinetics is given by :
[tex]t_{1/2}=\frac{[A_o]}{2k}[/tex]
Where:
[tex][A_o][/tex] = Initial concentration of A
k = Rate constant of the reaction
So, the half-life for the decomposition of substrate 1 when the initial concentration of the substrate is 2.77 M:
[tex]t_{1/2}=\frac{2.77 M}{0.183 M/s}=15.1 s[/tex]
15.1 seconds is the half life of the reaction when concentration of the substrate is 2.77 M.
