Answer:
a) 6.12
b) 1.87
Explanation:
At the onset of the equivalence point (i.e the first equivalence point); alaninate is being converted to alanine.
------> 
1 mole of alaninate react with 1 mole of acid to give 1 mole of alanine;
therefore 50.0 mL of 0.160 M alaninate required 50.0 mL of 0.160M HCl to reach the first equivalence point.
The concentration of alanine can be gotten via the following process as shown below;
= 
= 
= 
= 0.08 M
Alanine serves as an intermediary form, however the concentration of
and the pH can be determined as follows;
= ![\sqrt{\frac{K_{a1}K_{a2}{[H_3}^+NC_2H_5CO^-_2]+K_{a1}K_w}{ K_{a1}{[H_3}^+NC_2H_5CO^-_2] } }](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7BK_%7Ba1%7DK_%7Ba2%7D%7B%5BH_3%7D%5E%2BNC_2H_5CO%5E-_2%5D%2BK_%7Ba1%7DK_w%7D%7B%20%20K_%7Ba1%7D%7B%5BH_3%7D%5E%2BNC_2H_5CO%5E-_2%5D%20%20%7D%20%7D)
= 
= 
= 
pH = - log
pH = ![-log[7.63*10^{-7}]](https://tex.z-dn.net/?f=-log%5B7.63%2A10%5E%7B-7%7D%5D)
pH= 6.12
Therefore, the pH of the first equivalent point = 6.12
b) At the second equivalence point; all alaninate is converted into protonated alanine.
-----> 
-----> 
Here; we have a situation where 1 mole of alaninate react with 2 moles of acid to give 1 mole of protonated alanine;
Moreover, 50.0 mL of 0.160 M alaninate is needed to produce 100.0mL of 0.160 M HCl in order to achieve the second equivalence point.
Thus, the concentration of protonated alanine can be determined as:
= 
= 
= 
= 0.053 M
The pH at the second equivalence point can be calculated via the dissociation of protonated alanine at equilibrium which is represented as:
⇄
(0.053 - x) x x
= ![\frac{[H^+] [H^+_3NC_2H_5CO^-_2]}{[H^+_3NC_2H_5CO_2H]}](https://tex.z-dn.net/?f=%5Cfrac%7B%5BH%5E%2B%5D%20%5BH%5E%2B_3NC_2H_5CO%5E-_2%5D%7D%7B%5BH%5E%2B_3NC_2H_5CO_2H%5D%7D)
= 




Using quadratic equation formula;

we have:
OR 
= 0.0134 OR -0.0179
So; we go by the positive integer which says
x = 0.0134
So ![[H^+]=[H_3^+NC_2H_5CO^-_2]= 0.0134 M](https://tex.z-dn.net/?f=%5BH%5E%2B%5D%3D%5BH_3%5E%2BNC_2H_5CO%5E-_2%5D%3D%200.0134%20M)
pH = ![-log[H^+]](https://tex.z-dn.net/?f=-log%5BH%5E%2B%5D)
pH = ![-log[0.0134]](https://tex.z-dn.net/?f=-log%5B0.0134%5D)
pH = 1.87
Thus, the pH of the second equivalent point = 1.87