Explanation:
It is known that
of
=
.
(a) Relation between
and
is as follows.
![pK_{a} = -log (K_{a})](https://tex.z-dn.net/?f=pK_%7Ba%7D%20%3D%20-log%20%28K_%7Ba%7D%29)
Putting the values into the above formula as follows.
![pK_{a} = -log (K_{a})](https://tex.z-dn.net/?f=pK_%7Ba%7D%20%3D%20-log%20%28K_%7Ba%7D%29)
= ![-log(4.5 \times 10^{-4})](https://tex.z-dn.net/?f=-log%284.5%20%5Ctimes%2010%5E%7B-4%7D%29)
= 3.347
Also, relation between pH and
is as follows.
pH = ![pK_{a} + log\frac{[conjugate base]}{[acid]}](https://tex.z-dn.net/?f=pK_%7Ba%7D%20%2B%20log%5Cfrac%7B%5Bconjugate%20base%5D%7D%7B%5Bacid%5D%7D)
= ![3.347+ log \frac{0.15}{0.12}](https://tex.z-dn.net/?f=3.347%2B%20log%20%5Cfrac%7B0.15%7D%7B0.12%7D)
= 3.44
Therefore, pH of the buffer is 3.44.
(b) No. of moles of HCl added = ![Molarity \times volume](https://tex.z-dn.net/?f=Molarity%20%5Ctimes%20volume)
=
= 0.0116 mol
In the given reaction,
will react with
to form ![HNO_{2}](https://tex.z-dn.net/?f=HNO_%7B2%7D)
Hence, before the reaction:
No. of moles of
= ![0.15 M \times 1.0 L](https://tex.z-dn.net/?f=0.15%20M%20%5Ctimes%201.0%20L)
= 0.15 mol
And, no. of moles of
= ![0.12 M \times 1.0 L](https://tex.z-dn.net/?f=0.12%20M%20%5Ctimes%201.0%20L)
= 0.12 mol
On the other hand, after the reaction :
No. of moles of
= moles present initially - moles added
= (0.15 - 0.0116) mol
= 0.1384 mol
Moles of
= moles present initially + moles added
= (0.12 + 0.0116) mol
= 0.1316 mol
As,
= ![4.5 \times 10^{-4}](https://tex.z-dn.net/?f=4.5%20%5Ctimes%2010%5E%7B-4%7D)
![pK_{a} = -log (K_{a})](https://tex.z-dn.net/?f=pK_%7Ba%7D%20%3D%20-log%20%28K_%7Ba%7D%29)
= ![-log(4.5 \times 10^{-4})](https://tex.z-dn.net/?f=-log%284.5%20%5Ctimes%2010%5E%7B-4%7D%29)
= 3.347
Since, volume is both in numerator and denominator, we can use mol instead of concentration.
As, pH = ![pK_{a} + log \frac{[conjugate base]}{[acid]}](https://tex.z-dn.net/?f=pK_%7Ba%7D%20%2B%20log%20%5Cfrac%7B%5Bconjugate%20base%5D%7D%7B%5Bacid%5D%7D)
= 3.347+ log {0.1384/0.1316}
= 3.369
= 3.37 (approx)
Thus, we can conclude that pH after the addition of 1.00 mL of 11.6 M HCl to 1.00 L of the buffer solution is 3.37.