To calculate the pH at the equivalence point for the titration of 0.1 M NH3 and 0.1 M HCl, we need to determine the moles of NH3 and HCl present at the equivalence point.
Step 1: Write the balanced chemical equation for the reaction between NH3 and HCl.
NH3 + HCl -> NH4Cl
Step 2: Calculate the number of moles of NH3 and HCl using the given concentrations and volumes of the solutions.
At the equivalence point, the moles of NH3 equals the moles of HCl.
Let x be the volume of the NH3 and HCl solutions at the equivalence point (in liters).
Moles of NH3 = (0.1 mol/L) x (x L) = 0.1x mol
Moles of HCl = (0.1 mol/L) x (x L) = 0.1x mol
Step 3: Calculate the concentration of NH4+ (the conjugate acid of NH3) at the equivalence point.
The reaction between NH3 and HCl forms NH4+, so the concentration of NH4+ is equal to the moles of NH4+ divided by the total volume at the equivalence point.
NH4+ concentration = (0.1x mol) / (2x L) = 0.05 mol/L
Step 4: Use the given value of Kb for NH3 to determine the concentration of OH- ions.
Kb = [NH4+][OH-] / [NH3]
Given: Kb = 1.8 x 10^-5
Since we assume that the concentration of NH4+ is equal to the concentration of OH- at the equivalence point, we can rewrite the equation as:
Kb = [OH-]^2 / [NH3]
Plugging in the values:
1.8 x 10^-5 = [OH-]^2 / 0.05
Solving for [OH-]:
[OH-]^2 = (1.8 x 10^-5) x 0.05
[OH-]^2 = 9 x 10^-7
[OH-] = 3 x 10^-4 mol/L
Step 5: Calculate the pOH using the concentration of OH-.
pOH = -log[OH-]
pOH = -log(3 x 10^-4)
pOH ≈ 3.52
Step 6: Calculate the pH using the pOH.
pOH + pH = 14
pH = 14 - pOH
pH ≈ 10.48
Therefore, the pH at the equivalence point for the titration of 0.1 M NH3 and 0.1 M HCl is approximately 10.48.