Answer:
A) 0.065 M is its molarity after a reaction time of 19.0 hour.
B) In 52 hours
will react 69% of its initial concentration.
Explanation:
![Co(NH_3)_5(H_2O)_3+[Co(NH_3)5Br]^{2+}(Purple)(aq)+H_2O(l)\rightarrow [Co(NH_3)_5(H_2O)]^{3+}(Pinkish-orange)(aq)+Br^-(aq)](https://tex.z-dn.net/?f=Co%28NH_3%29_5%28H_2O%29_3%2B%5BCo%28NH_3%295Br%5D%5E%7B2%2B%7D%28Purple%29%28aq%29%2BH_2O%28l%29%5Crightarrow%20%5BCo%28NH_3%29_5%28H_2O%29%5D%5E%7B3%2B%7D%28Pinkish-orange%29%28aq%29%2BBr%5E-%28aq%29)
The reaction is first order in
:
Initial concentration of
= ![[A_o]=0.100 M](https://tex.z-dn.net/?f=%5BA_o%5D%3D0.100%20M)
a) Final concentration of
after 19.0 hours= ![[A]](https://tex.z-dn.net/?f=%5BA%5D)
t = 19.0 hour = 19.0 × 3600 seconds ( 1 hour = 3600 seconds)
Rate constant of the reaction = k = ![6.3\times 10^{-6} s^{-1}](https://tex.z-dn.net/?f=6.3%5Ctimes%2010%5E%7B-6%7D%20s%5E%7B-1%7D)
The integrated law of first order kinetic is given as:
![[A]=[A_o]\times e^{-kt}](https://tex.z-dn.net/?f=%5BA%5D%3D%5BA_o%5D%5Ctimes%20e%5E%7B-kt%7D)
![[A]=0.100 M\times e^{-6.3\times 10^{-6} s^{-1}\times 19.0\times 3600 s}](https://tex.z-dn.net/?f=%5BA%5D%3D0.100%20M%5Ctimes%20e%5E%7B-6.3%5Ctimes%2010%5E%7B-6%7D%20s%5E%7B-1%7D%5Ctimes%2019.0%5Ctimes%203600%20s%7D)
![[A]=0.065 M](https://tex.z-dn.net/?f=%5BA%5D%3D0.065%20M)
0.065 M is its molarity after a reaction time of 19.0 h.
b)
Initial concentration of
= ![[A_o]=x](https://tex.z-dn.net/?f=%5BA_o%5D%3Dx)
Final concentration of
after t = ![[A]=(100\%-69\%) x=31\%x=0.31x](https://tex.z-dn.net/?f=%5BA%5D%3D%28100%5C%25-69%5C%25%29%20x%3D31%5C%25x%3D0.31x)
Rate constant of the reaction = k = ![6.3\times 10^{-6} s^{-1}](https://tex.z-dn.net/?f=6.3%5Ctimes%2010%5E%7B-6%7D%20s%5E%7B-1%7D)
The integrated law of first order kinetic is given as:
![[A]=[A_o]\times e^{-kt}](https://tex.z-dn.net/?f=%5BA%5D%3D%5BA_o%5D%5Ctimes%20e%5E%7B-kt%7D)
![0.31x=x\times e^{-6.3\times 10^{-6} s^{-1}\t}](https://tex.z-dn.net/?f=0.31x%3Dx%5Ctimes%20e%5E%7B-6.3%5Ctimes%2010%5E%7B-6%7D%20s%5E%7B-1%7D%5Ct%7D)
t = 185,902.06 s =
≈ 52 hours
In 52 hours
will react 69% of its initial concentration.