Methylamine is a weak base, and hydrochloric acid (HCl) is a strong acid. The reaction between the two is:
CH3NH2 + HCl → CH3NH3+Cl-
At the equivalence point of the titration, the moles of HCl added will equal the moles of methylamine present in the solution. This means that all the methylamine will have been converted to its conjugate acid, CH3NH3+, and the solution will contain only CH3NH3+ and Cl- ions.
To calculate the pH at the equivalence point, we need to find the concentration of CH3NH3+ in the solution. This can be done by using the dissociation constant of the weak base, methylamine:
Kb = [CH3NH3+][OH-]/[CH3NH2]
At the equivalence point, [CH3NH2] = [CH3NH3+], so we can simplify the equation to:
Kb = [CH3NH3+]^2/[CH3NH2]
[CH3NH3+]^2 = Kb[CH3NH2]
[CH3NH3+] = sqrt(Kb[CH3NH2])
[CH3NH3+] = sqrt(5.0 x 10^-4 x 0.050)
[CH3NH3+] = 0.0224 M
Now we can use the equation for the ionization constant of a weak acid to find the pH:
Ka = [H+][A-]/[HA]
For the conjugate acid of methylamine, CH3NH3+, the Ka is:
Ka = Kw/Kb = 1.0 x 10^-14/5.0 x 10^-4 = 2.0 x 10^-11
At the equivalence point, [H+] = [CH3NH3+], so we can simplify the equation to:
Ka = [H+]^2/[CH3NH2+]
[H+]^2 = Ka[CH3NH2+]
[H+] = sqrt(Ka[CH3NH2+])
[H+] = sqrt(2.0 x 10^-11 x 0.0224)
[H+] = 4.2 x 10^-7 M
pH = -log[H+]
pH = -log(4.2 x 10^-7)
pH = 6.38
Therefore, the pH at the equivalence point of the titration of 0.100 M methylamine with 0.100 M HCl is 6.38.
*IG:whis.sama_ent*