Final answer:
To calculate the pH at the equivalence point in a titration of methylamine with HCl, find the concentration of the conjugate acid formed, use the Kb to calculate the pKb, derive the pKa, and then apply the Henderson-Hasselbalch equation to determine the pH.
Step-by-step explanation:
Calculating pH at the Equivalence Point in a Titration
To calculate the pH at the equivalence point for the titration of 0.180 M methylamine (CH₃NH₂) with 0.180 M HCl, we first recognize that at the equivalence point, all the methylamine has reacted with the HCl to form the methylammonium ion (CH₃NH₃⁺). The pH calculation involves finding the concentration of CH₃NH₃⁺ and then using the Kb of methylamine to find the pOH, and subsequently the pH.
As HCl is a strong acid, it will react completely with methylamine, a weak base, to produce the conjugate acid CH₃NH₃⁺. The concentration of CH₃NH₃⁺ will be equal to the initial concentration of methylamine since we're at the equivalence point, so it is 0.180 M. The Kb of methylamine is given as 5.0 x 10⁻³; thus, the pKb is -log(5.0 x 10⁻³). We can find the pKa of the conjugate acid by using the relationship pKa + pKb = 14. Once we have the pKa, we calculate the pH of the methylammonium ion solution using the Henderson-Hasselbalch equation.