Calculate the change in pH when 5.00 mL of 0.100 M HCl(aq) is added to 100.0 mL of a buffer solution that is 0.100 M in NH3(aq) and 0.100 M in NH4Cl(aq).
The pH at the beginning is
pH = pKa + log(base)/(acid)
Substitute pKa, base, and acid, and solve for initial pH.
You have 100 mL 0.100M NH3 and 0.100M NH4Cl = 10 millimoles of each. You're adding 5.00 mL of 0.100M HCl = 0.500 millimols.
.......NH3 + H^+ ==> NH4^+ + H2O
I......10.....0.......10........
add...........0.5...............
C......-0.5...-0.5.....+0.5
E......9.5.....0.......10.5
Now substitute the E line into the HH equation and solve for pH, then take the difference between the two pH values to arrive at the difference.
To calculate the change in pH when an acid is added to a buffer solution, we need to consider the Henderson-Hasselbalch equation. The Henderson-Hasselbalch equation is given by:
pH = pKa + log([A-]/[HA])
Where pH is the current pH value, pKa is the acid dissociation constant of the weak acid (NH4+ in this case) in the buffer, [A-] is the concentration of the conjugate base (NH3 in this case), and [HA] is the concentration of the weak acid (NH4+ in this case).
In this case, the weak acid is NH4+ and its pKa value is 9.25.
Step 1: Calculate the initial pH of the buffer solution.
Using the Henderson-Hasselbalch equation, we can calculate the initial pH of the buffer solution.
pH = pKa + log([A-]/[HA])
pH = 9.25 + log([NH3]/[NH4+])
pH = 9.25 + log(0.100/0.100)
pH = 9.25 + log(1)
pH = 9.25 + 0
pH = 9.25
Therefore, the initial pH of the buffer solution is 9.25.
Step 2: Calculate the concentration of NH4+ after adding HCl.
When HCl is added to the buffer solution, it reacts with the NH3 to form NH4+. The moles of NH4+ formed can be calculated using the equation:
moles of NH4+ = concentration of HCl × volume of HCl
moles of NH4+ = 0.100 M × 5.00 mL
moles of NH4+ = 0.100 × (5.00/1000) mol
moles of NH4+ = 5.00 × 10^-4 mol
Since the volume of the buffer solution is much larger than the volume of HCl added, we can assume that the change in the volume of the buffer is negligible. Therefore, the concentration of NH4+ can be calculated as:
concentration of NH4+ = (moles of NH4+)/volume of buffer solution
concentration of NH4+ = (5.00 × 10^-4 mol)/(100.0 mL + 5.00 mL)
concentration of NH4+ = (5.00 × 10^-4 mol)/(105.0 mL)
concentration of NH4+ = 4.76 × 10^-3 M
Step 3: Calculate the new concentration of NH3.
The concentration of NH3 can be calculated using the equation:
concentration of NH3 = initial concentration of NH3 + concentration of NH4+
concentration of NH3 = 0.100 M + 4.76 × 10^-3 M
concentration of NH3 = 0.10476 M
Step 4: Calculate the new pH of the buffer solution.
Using the Henderson-Hasselbalch equation, we can calculate the new pH of the buffer solution.
pH = pKa + log([A-]/[HA])
pH = 9.25 + log([NH3]/[NH4+])
pH = 9.25 + log(0.10476/4.76 × 10^-3)
pH = 9.25 + log(21.98)
pH = 9.25 + 1.343
pH = 10.593
Therefore, the new pH of the buffer solution after adding 5.00 mL of 0.100 M HCl is approximately 10.593.
Step 5: Calculate the change in pH.
The change in pH can be calculated as the difference between the initial pH and the new pH.
Change in pH = new pH - initial pH
Change in pH = 10.593 - 9.25
Change in pH = 1.343
Therefore, the change in pH when 5.00 mL of 0.100 M HCl is added to 100.0 mL of the buffer solution is approximately 1.343.
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.