Answer:
9.07
Explanation:
We have to start with the buffer system reaction, so:
![NH_4^+~~NH_3~+~H^+](https://tex.z-dn.net/?f=NH_4%5E%2B~%3C-%3E~NH_3~%2B~H%5E%2B)
When we have the hydrochloric acid (a <u>strong acid</u>) the
of the hydrochloric acid (
) <u>will interact with the base</u> of the buffer system (
) to produce more acid (
), so:
![HCl~+~NH_3->~NH_4^+~+Cl^-](https://tex.z-dn.net/?f=HCl~%2B~NH_3-%3E~NH_4%5E%2B~%2BCl%5E-)
Therefore the concentration of
will <u>decrease</u> and the concentration of
will <u>increase</u>. The next step then would be the calculation of the moles of the acid and base in the buffer system. So:
![M=\frac{#mol}{L}](https://tex.z-dn.net/?f=M%3D%5Cfrac%7B%23mol%7D%7BL%7D)
![#mol=0.353*0.125=0.044~mol~of~NH_4^+](https://tex.z-dn.net/?f=%23mol%3D0.353%2A0.125%3D0.044~mol~of~NH_4%5E%2B)
![#mol=0.352*0.125=0.044~mol~of~NH_3](https://tex.z-dn.net/?f=%23mol%3D0.352%2A0.125%3D0.044~mol~of~NH_3)
If we add 0.02 mol of
we can calculate the amount of <u>acid</u> and <u>base</u> that changes in the buffer system.
![0.044~mol~of~NH_3~-~0.02=0.024](https://tex.z-dn.net/?f=0.044~mol~of~NH_3~-~0.02%3D0.024)
![0.044~mol~of~NH_4^+~+~0.02=0.064](https://tex.z-dn.net/?f=0.044~mol~of~NH_4%5E%2B~%2B~0.02%3D0.064)
Now, we can calculate the <u>concentration of each species</u> if we divide by the number of moles:
![M=\frac{0.024~mol}{0.0125~L}=~0.192~M~of~NH_3](https://tex.z-dn.net/?f=M%3D%5Cfrac%7B0.024~mol%7D%7B0.0125~L%7D%3D~0.192~M~of~NH_3)
![M=\frac{0.064~mol}{0.0125~L}=~0.512~M~of~NH_4^+](https://tex.z-dn.net/?f=M%3D%5Cfrac%7B0.064~mol%7D%7B0.0125~L%7D%3D~0.512~M~of~NH_4%5E%2B)
If we use the <u>hendersson hasselbach equation</u> we can calculate the pH value again:
![pH=p{ K }_{ a }+log(\frac { { [A }^{ - }] }{ [HA] } )](https://tex.z-dn.net/?f=pH%3Dp%7B%20K%20%7D_%7B%20a%20%7D%2Blog%28%5Cfrac%20%7B%20%7B%20%5BA%20%7D%5E%7B%20-%20%7D%5D%20%7D%7B%20%5BHA%5D%20%7D%20%29)
![pH=9.5+log(\frac {0.192}{0.512} )](https://tex.z-dn.net/?f=pH%3D9.5%2Blog%28%5Cfrac%20%7B0.192%7D%7B0.512%7D%20%29)
![pH=9.07](https://tex.z-dn.net/?f=pH%3D9.07)
The final pH value is <u>9.07</u>