To calculate the change in pH when an acid is added to a buffer solution, we need to use the Henderson-Hasselbalch equation. The Henderson-Hasselbalch equation is:
pH = pKa + log ( [A-] / [HA] )
where pH is the measure of acidity or alkalinity, pKa is the acid dissociation constant, [A-] represents the concentration of the conjugate base, and [HA] represents the concentration of the acid in the buffer solution.
In this case, the buffer solution contains NH3(aq) and NH4Cl(aq). NH3 acts as a weak base and NH4Cl acts as its conjugate acid.
Step 1: Calculate the initial concentrations of NH3 and NH4Cl:
The initial concentration of NH3 is given as 0.100 M, and the initial concentration of NH4Cl is also given as 0.100 M.
Step 2: Calculate the initial pH of the buffer solution:
To calculate the initial pH of the buffer solution, we need the pKa value of NH3. The pKa value for NH3 is 9.25.
Using the Henderson-Hasselbalch equation, we can calculate the initial pH:
pH = pKa + log ( [A-] / [HA] )
pH = 9.25 + log (0.100 / 0.100) = 9.25
Therefore, the initial pH of the buffer solution is 9.25.
Step 3: Calculate the concentration of NH4+ (conjugate acid):
When HCl is added, it will react with NH3 to form NH4+.
The balanced chemical equation for the reaction is:
NH3(aq) + HCl(aq) -> NH4+(aq) + Cl-(aq)
Since HCl is a strong acid, it will completely dissociate. Therefore, the moles of HCl added will be equal to the moles of NH4+ formed.
Moles of HCl = concentration (in mol/L) x volume (in L)
Moles of HCl = 0.100 mol/L x 0.005 L = 0.0005 mol
Therefore, the concentration of NH4+ after the reaction will be 0.0005 mol/L.
Step 4: Calculate the concentration of NH3 (conjugate base):
The moles of NH3 will decrease due to the reaction, so we need to calculate its concentration.
Initial moles of NH3 = concentration (in mol/L) x volume (in L)
Initial moles of NH3 = 0.100 mol/L x 0.100 L = 0.010 mol
Since 0.0005 mol of NH3 reacts with HCl, the remaining moles of NH3 will be:
Remaining moles of NH3 = Initial moles of NH3 - Moles of NH3 reacted
Remaining moles of NH3 = 0.010 mol - 0.0005 mol = 0.0095 mol
Therefore, the concentration of NH3 after the reaction will be:
Concentration of NH3 = Remaining moles of NH3 / Total volume (in L)
Concentration of NH3 = 0.0095 mol / (0.100 L + 0.005 L) = 0.0091 mol/L
Step 5: Calculate the final pH of the buffer solution:
Using the Henderson-Hasselbalch equation, we can calculate the final pH:
pH = pKa + log ( [A-] / [HA] )
pH = 9.25 + log ( 0.0091 mol/L / 0.0005 mol/L )
pH = 9.25 + log (18.2)
Using a calculator, log(18.2) ≈ 1.26
pH = 9.25 + 1.26 = 10.51
Therefore, the final pH of the buffer solution after the addition of 5.00 mL of 0.100 M HCl(aq) is approximately 10.51.
The change in pH can be calculated by subtracting the initial pH from the final pH:
Change in pH = Final pH - Initial pH
Change in pH = 10.51 - 9.25 = 1.26
Therefore, the change in pH is approximately 1.26.