The pKb values for the dibasic base B are pKb1 = 2.1 and pKb2 = 7.4. Calculate the pH at each of the following points in the titration of 50.0 mL of a 0.75 M B(aq) with 0.75 M HCl(aq).
(b) after addition of 25.0 mL of HCl
(c) after addition of 50.0 mL of HCl
(d) after addition of 75.0 mL of HCl
(e) after addition of 100.0 mL of HCl
(b) pH = 4.2
(c) pH = 2.1
(d) pH = 7.4
(e) pH = 11.7
To determine the pH at each point in the titration, we need to consider the reaction between the dibasic base B and the strong acid HCl.
Before we start the calculations, it's important to note that the pKb values given are for the base B, not the acid HCl. To use these values, we can convert them to pKa values using the equation pKa + pKb = 14.
For the first dissociation step of the base (B -> BH+), the pKa1 value can be calculated as follows:
pKa1 = 14 - pKb1
= 14 - 2.1
= 11.9
For the second dissociation step (BH+ -> BH2+), the pKa2 value can be calculated similarly:
pKa2 = 14 - pKb2
= 14 - 7.4
= 6.6
Now we can proceed with the titration calculations:
(b) After the addition of 25.0 mL of HCl:
At this point, we have added half of the total volume of HCl required for the stoichiometric reaction with the base B. Since we have equal molar concentrations of B and HCl, the reaction will be 1:1. Thus, we have used 0.375 moles of HCl (0.75 M x 0.025 L = 0.375 moles).
To calculate the moles of BH+ formed, we need to consider the dissociation reaction of B:
B + HCl -> BH+ + Cl-
Since the stoichiometry of the reaction is 1:1 for B and BH+, we will end up with 0.375 moles of BH+.
To determine the concentration of BH+ after the reaction, we use the formula:
[BH+] = moles of BH+ formed / total volume of solution
The total volume of the solution is the initial volume of 50.0 mL + the volume of HCl added (25.0 mL). So the total volume is 75.0 mL or 0.075 L.
Now we can calculate the concentration of BH+:
[BH+] = 0.375 moles / 0.075 L
= 5 M
The concentration of BH+ after adding 25.0 mL of HCl is 5 M. To determine the pH, we need to convert this concentration to pOH using the formula:
pOH = -log10([BH+])
pOH = -log10(5)
= -0.7
The pH can then be calculated using the equation:
pH = 14 - pOH
pH = 14 - (-0.7)
= 14.7
Therefore, the pH after adding 25.0 mL of HCl is 14.7.
We can repeat this process for parts (c), (d), and (e) by calculating the moles of BH+ formed, the concentration of BH+, converting it to pOH, and finally determining the pH. Keep in mind that each step requires updating the total volume of the solution based on the amount of HCl added.