A 23.9 mL sample of 0.283 M trimethylamine, (CH3)3N, is titrated with 0.207 M hydrochloric acid.
At the equivalence point, the pH is?
I started off by doing
0.283 X 2.39e-2 = 6.76e-3
Then I did 6.76e-3 / 0.207 = 3.36e-2
2.39e-2 + 3.36e-2 = 5.65e-2
6.76e-3/5.65e-2 = 0.119
I do not know where to got from here. Thank you for your help!
The titration is
MeN + HCl ==> MeNH^+ + Cl^- so at the equivalence point you have the salt; i.e., trimethylamine hydrochloride. So the salt will hydrolyze.
........MeNH^+ + HOH ==> (H3O+)+ + MeN
i......0.119.../////.......0........0
c........-x..............x.........x
e.....0.119-x...........x.........x
Ka for MeNH^+ = (Kw/Kb for MeN) = etc.
I did 1.0e-14 / 6.3e-5 = 1.58e-10
Then would I do (1.58e-10)(0.119)?
1.58E-10 = (x)(x)/(0.119)
Solve for x = (H3O^+) and convert to pH.
I multiplied 0.119 by 1.58e-10 and then took the square root, is that correct?
yes
To determine the pH at the equivalence point of the titration, we need to consider the reaction that occurs between trimethylamine ((CH3)3N) and hydrochloric acid (HCl). The balanced chemical equation for this reaction is:
(CH3)3N + HCl -> (CH3)3NH+ + Cl-
At the equivalence point, the moles of trimethylamine will be equal to the moles of hydrochloric acid added.
From your calculations, you determined that the volume of trimethylamine solution used is 23.9 mL and the concentration is 0.283 M. Using this information, we can calculate the moles of trimethylamine as follows:
moles of (CH3)3N = volume (in L) * concentration
moles of (CH3)3N = 23.9 mL * (1 L / 1000 mL) * 0.283 M
moles of (CH3)3N = 0.0067627 mol
Since the reaction between (CH3)3N and HCl is in a 1:1 ratio, the moles of HCl required to react with (CH3)3N is also 0.0067627 mol.
Now, we can calculate the volume of HCl solution needed to react with trimethylamine:
volume HCl (in L) = moles of HCl / concentration
volume HCl = 0.0067627 mol / 0.207 M
volume HCl = 0.032678 L
Since the volume of HCl used is 0.032678 L, we need to calculate the moles of HCl remaining after the reaction with trimethylamine:
moles of HCl remaining = moles of HCl added - moles of HCl reacted
moles of HCl remaining = (0.032678 L) * (0.207 M) - (0.0067627 mol)
moles of HCl remaining = 0.006917 mol
We can now determine the concentration of HCl remaining in the solution by dividing the moles of HCl remaining by the total volume of the solution (23.9 mL + volume of HCl):
concentration of HCl remaining = moles of HCl remaining / total volume of solution
concentration of HCl remaining = 0.006917 mol / (23.9 mL + 0.032678 L)
concentration of HCl remaining = 0.119 M
Finally, to find the pH at the equivalence point, we can use the fact that at the equivalence point, the solution contains a weak base and its conjugate acid. In this case, we have (CH3)3N and (CH3)3NH+.
The pH can be calculated using the Henderson-Hasselbalch equation:
pH = pKa + log ([salt] / [acid])
Where pKa is the negative logarithm (base 10) of the acid dissociation constant (Ka), [salt] is the concentration of the conjugate base, and [acid] is the concentration of the weak acid.
The pKa value for (CH3)3NH+ can vary, but assuming a pKa value around 9.8, we can calculate the pH:
pH = 9.8 + log ([ (CH3)3N ] / [ (CH3)3NH+ ])
pH = 9.8 + log (0.119 / 0.119)
pH = 9.8 + log (1)
pH = 9.8
Therefore, at the equivalence point, the pH is approximately 9.8.