A buffer solution contains 0.200 M NH3 and 0.250 M NH4Cl. What is the pH of the buffer solution after the addition of 10.0 mL of 0.100 M NaOH to 50.0 mL of the buffer? Kb for NH3 is 1.8 x 10-5.
To determine the pH of the buffer solution after the addition of NaOH, we need to consider the reaction between NH3 (ammonia) and NaOH (sodium hydroxide). The reaction between NH3 and NaOH will result in the formation of NH4+ (ammonium ion) and OH- (hydroxide ion).
NH3 + NaOH → NH4+ + OH-
Since we are given the concentrations of NH3 and NH4Cl in the buffer solution, we need to calculate the final concentrations of NH3 and NH4+ after the addition of NaOH.
Step 1: Calculate the moles of NaOH added.
Moles of NaOH = volume (in L) × concentration (in M)
Moles of NaOH = 0.010 L × 0.100 M = 0.001 mol
Step 2: Calculate the moles of NH3 and NH4+ initially in the buffer.
Moles of NH3 = volume (in L) × concentration (in M)
Moles of NH3 = 0.050 L × 0.200 M = 0.010 mol
Moles of NH4+ = volume (in L) × concentration (in M)
Moles of NH4+ = 0.050 L × 0.250 M = 0.0125 mol
Step 3: Calculate the moles of NH3 and NH4+ after the reaction with NaOH.
Since the reaction is in a 1:1 ratio, the number of moles of NH3 will decrease by the same number of moles of NaOH added.
Moles of NH3 after reaction = Moles of NH3 initially - Moles of NaOH
Moles of NH3 after reaction = 0.010 mol - 0.001 mol = 0.009 mol
Since the reaction is in a 1:1 ratio, the number of moles of NH4+ will increase by the same number of moles of NaOH added.
Moles of NH4+ after reaction = Moles of NH4+ initially + Moles of NaOH
Moles of NH4+ after reaction = 0.0125 mol + 0.001 mol = 0.0135 mol
Step 4: Calculate the final concentrations of NH3 and NH4+.
Concentration of NH3 = Moles of NH3 after reaction / volume (in L)
Concentration of NH3 = 0.009 mol / (0.050 L + 0.010 L) = 0.150 M
Concentration of NH4+ = Moles of NH4+ after reaction / volume (in L)
Concentration of NH4+ = 0.0135 mol / (0.050 L + 0.010 L) = 0.225 M
Step 5: Calculate the concentration of OH- ions.
Since NaOH is a strong base, it will completely dissociate in water to form OH- ions. The concentration of OH- ions can be calculated using the moles of NaOH added and the total volume of the solution after adding NaOH.
Concentration of OH- = Moles of NaOH / volume (in L)
Concentration of OH- = 0.001 mol / (0.050 L + 0.010 L) = 0.0167 M
Step 6: Calculate the concentration of NH4OH (ammonium hydroxide).
NH4OH is formed from the reaction between NH3 and OH-. Since the reaction is in a 1:1 ratio, the concentration of NH4OH can be determined using the concentration of NH3 and OH- ions.
Concentration of NH4OH = Concentration of NH3 × Concentration of OH-
Concentration of NH4OH = 0.150 M × 0.0167 M = 0.00251 M
Step 7: Calculate the concentration of NH3 remaining after the reaction.
Since NH3 reacts with OH- to form NH4OH, the concentration of NH3 remaining can be determined by subtracting the concentration of NH4OH from the initial concentration of NH3.
Concentration of NH3 remaining = Concentration of NH3 - Concentration of NH4OH
Concentration of NH3 remaining = 0.150 M - 0.00251 M = 0.147 M
Step 8: Calculate the pOH of the solution.
pOH = -log10([OH-])
pOH = -log10(0.0167) = 1.78
Step 9: Calculate the pH of the solution.
Since pH + pOH = 14 (at 25°C), we can calculate the pH.
pH = 14 - pOH
pH = 14 - 1.78 = 12.22
Therefore, the pH of the buffer solution after the addition of 10.0 mL of 0.100 M NaOH is 12.22.