Answer:
The rate law for second order unimolecular irreversible reaction is
![\frac{1}{[A]} = k.t + \frac{1}{[A]_{0} }](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5BA%5D%7D%20%3D%20k.t%20%2B%20%5Cfrac%7B1%7D%7B%5BA%5D_%7B0%7D%20%7D)
Explanation:
A second order unimolecular irreversible reaction is
2A → B
Thus the rate of the reaction is
![v = -\frac{1}{2}.\frac{d[A]}{dt} = k.[A]^{2}](https://tex.z-dn.net/?f=v%20%3D%20-%5Cfrac%7B1%7D%7B2%7D.%5Cfrac%7Bd%5BA%5D%7D%7Bdt%7D%20%3D%20k.%5BA%5D%5E%7B2%7D)
rearranging the ecuation
![-\frac{1}{2}.\frac{k}{dt} = \frac{[A]^{2}}{d[A]}](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B2%7D.%5Cfrac%7Bk%7D%7Bdt%7D%20%3D%20%5Cfrac%7B%5BA%5D%5E%7B2%7D%7D%7Bd%5BA%5D%7D)
Integrating between times 0 to <em>t </em>and between the concentrations of
to <em>[A].</em>
![\int\limits^0_t -\frac{1}{2}.\frac{k}{dt} =\int\limits^A_{0} _A\frac{[A]^{2}}{d[A]}](https://tex.z-dn.net/?f=%5Cint%5Climits%5E0_t%20-%5Cfrac%7B1%7D%7B2%7D.%5Cfrac%7Bk%7D%7Bdt%7D%20%3D%5Cint%5Climits%5EA_%7B0%7D%20_A%5Cfrac%7B%5BA%5D%5E%7B2%7D%7D%7Bd%5BA%5D%7D)
Solving the integral
![\frac{1}{[A]} = k.t + \frac{1}{[A]_{0} }](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5BA%5D%7D%20%3D%20k.t%20%2B%20%5Cfrac%7B1%7D%7B%5BA%5D_%7B0%7D%20%7D)
Answer:
The pH of the final solution is 0.16 .
Explanation:
The pH of the solution is defined as negative logarithm of hydrogen ion concentration in a solution.
![pH=-\log[H^+]](https://tex.z-dn.net/?f=pH%3D-%5Clog%5BH%5E%2B%5D)
Concentration of HCl = 0.16 M

HCl is a string acid .1 molar of HCl gives 1 molar of of hydrogen ions.
![[H^+]=0.16 M](https://tex.z-dn.net/?f=%5BH%5E%2B%5D%3D0.16%20M)
Concentration of
= 0.52 M

Nitric is a string acid .1 molar of nitric acid gives 1 molar of of hydrogen ions.
![[H^+]'=0.52 M](https://tex.z-dn.net/?f=%5BH%5E%2B%5D%27%3D0.52%20M)
Total hydrogen ion concentration:
![[H^+]''=[H^+]+[H^+]'](https://tex.z-dn.net/?f=%5BH%5E%2B%5D%27%27%3D%5BH%5E%2B%5D%2B%5BH%5E%2B%5D%27)
=0.16 M+0.52 M=0.68 M
The pH of the solution:
![\pH=-\log[H^+]''=-\log[0.68 M]](https://tex.z-dn.net/?f=%5CpH%3D-%5Clog%5BH%5E%2B%5D%27%27%3D-%5Clog%5B0.68%20M%5D)
pH = 0.16
The pH of the final solution is 0.16 .
250 --> 125 --> 62.5 --> 31.25
each arrow equals one half life, so 3 half lives
14 days/ 3 half lives =
4.67 days = half life