Answer:
It will take 17.46 hours for the reaction to be 75% complete.
Explanation:
Half life for second order kinetics is given by:
[tex]t_{\frac{1}{2}=\frac{1}{k\times a_o}[/tex]
[tex]t_{\frac{1}{2}[/tex] = half life = 5.82 hour
k = rate constant =?
[tex]a_o[/tex] = initial concentration = 4.46 mol/L
[tex]5.82 hour=\frac{1}{k\times 4.46 mol/L}[/tex]
[tex]k=\frac{1}{5.82 hour\times 4.46 mol/L}=0.03852 L/mol hour[/tex]
Integrated rate law for second order kinetics is given by:
[tex]\frac{1}{[a]}=kt+\frac{1}{[a_o]}[/tex]
[a] = concentration left after time t = [tex]100\%-75\%=25\% of [a_o]=0.25[a_o][/tex]
[tex]\frac{1}{0.25\times 4.46 mol/L}=\frac{1}{0.03852 L/mol hour}\times t+\frac{1}{4.46 mol/L}[/tex]
[tex]t=17.46 hours[/tex]
It will take 17.46 hours for the reaction to be 75% complete.
It will take 17.7 hours for the reaction to be 75% complete.
From the question, we can see that;
Half life of the reaction = 5.82 hours
Initial concentration of NOCl = 4.46 mol/l
Half life of a second order reaction is given by;
t1/2 = 1/k[A]o
k = 1/t1/2[A]o
k = 1/5.82 × 4.46
k = 0.038 Mol-1 L hour-1
When the reaction is 75% complete, the amount of NOCl = 100 - 75 = 25%
[A]t = 0.25 × 4.46 mol/l = 1.115 mol/l
For a second order reaction;
1/[A]t = kt + 1/[A]o
1/[A]t - 1/[A]o = kt
Substituting values;
(1.115)^ -1 - (4.46)^-1 = 0.038t
0.897 - 0.224/ 0.038 = t
t = 17.7 hours
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