a 25.0 mL sample of .050 M solution of aqueous trimethylamine is titrated with a .063 M solution of HCl. calculate pH the solution after 10.0 mL, 20.0 mL, 30.0 mL of acid have been added. pKb of (CH3)_3_N= 4.19 at 25 degrees C
First determine where the equivalence point is so you will know where you are on the titration curve with each of thes additions.
mL x M = mL x M
25.0 x 0.05 = mL x 0.063
mL = about 19 or so.
Therefore, 10 mL will be before the e.p. and you will have some base and some of its conjugate. Use the Henderson-Hasselbalch equation.
b. 20 mL will be just after the e.p. So you will have an excess of 20 mL-mL for e.p. That will be an excess of HCl
c. 30 mL is same as part b.
To calculate the pH of the solution after adding different volumes of acid, we need to consider the reaction between trimethylamine (CH3)3N and HCl. The reaction can be represented as follows:
(CH3)3N + HCl -> (CH3)3NH+ + Cl-
At each stage of titration, we can use the stoichiometry of the reaction to calculate the moles of reactants and products. Then, we can use the Henderson-Hasselbalch equation to find the pH, which relates the ratio of the concentrations of the conjugate acid and base to the pH.
Let's break down the calculation steps for each stage:
1. After adding 10.0 mL of HCl:
- Calculate the initial moles of trimethylamine in the 25.0 mL solution:
moles (CH3)3N = volume (L) x concentration (M)
moles (CH3)3N = 0.025 L x 0.050 M = 0.00125 moles
- Calculate the moles of HCl added:
moles HCl = volume added (L) x concentration (M)
moles HCl = 0.010 L x 0.063 M = 0.00063 moles
- Calculate the remaining moles of trimethylamine:
remaining moles (CH3)3N = initial moles (CH3)3N - moles HCl
remaining moles (CH3)3N = 0.00125 moles - 0.00063 moles = 0.00062 moles
- Calculate the concentration of trimethylamine after the reaction:
concentration (CH3)3N = remaining moles (CH3)3N / volume of solution (L)
concentration (CH3)3N = 0.00062 moles / 0.015 L = 0.0413 M
- Calculate the concentration of the conjugate acid (CH3)3NH+:
concentration (CH3)3NH+ = concentration (CH3)3N = 0.0413 M
- Calculate the pH using the Henderson-Hasselbalch equation:
pH = pKa + log(concentration of (CH3)3NH+ / concentration of (CH3)3N)
2. Repeat the same steps for 20.0 mL and 30.0 mL of added HCl, adjusting the volume and moles accordingly.
Keep in mind that the pKa of (CH3)3N is given as 4.19, but we can convert it to pKb using the relationship: pKa + pKb = 14.
Therefore, pKb = 14 - 4.19 = 9.81
Using these steps, you can calculate the pH at each stage of titration by substituting the values into the Henderson-Hasselbalch equation.