Calculate the pH of 100.00 mL of an ammonia buffer (pKb = 4.76), prepared by placing 55.0 mL of concentrated NH4OH (i.e., NH3; 14.5 M) into a volumetric flask, adding 6.76 g of ammonium chloride, and diluting to the mark with DI water.
What size flask? I will assume 100 mL volumetric flask AND I will assume adding solid NH4Cl does not change the volume.
M NH3 = 14.5 x 55 mL/100 mL = ?
mols NH4Cl = grams/molar mass = ?
M NH4Cl = mols/L
pH = pKa + log(base)/(acid)
You are given pKb.
PKa + pKb = pKw = 14
Post your work if you get stuck.
To calculate the pH of an ammonia buffer, we need to consider the equilibrium between ammonia (NH3) and ammonium (NH4+) in water. The pKb value provided (4.76) represents the equilibrium constant for this reaction.
Here's how you can calculate the pH of the ammonia buffer:
Step 1: Calculate the concentration of NH3 and NH4+ in the buffer solution.
- Concentration of NH3 (ammonia):
First, we need to calculate the number of moles of NH3 (ammonia) in the solution.
Number of moles of NH3 = Volume (in L) × Concentration (in mol/L)
The volume of concentrated NH4OH added is 55.0 mL, which is equivalent to 0.055 L (since 1 L = 1000 mL). The concentration of NH4OH is 14.5 M.
Number of moles of NH3 = 0.055 L × 14.5 mol/L = 0.7975 mol
- Concentration of NH4+ (ammonium):
To calculate the concentration of NH4+ (ammonium), we need to convert the mass of ammonium chloride (NH4Cl) added into moles.
Number of moles of NH4Cl = Mass (in g) ÷ Molar mass (NH4Cl)
The mass of ammonium chloride added is 6.76 g. The molar mass of NH4Cl is 53.49 g/mol (14.01 g/mol for NH3 + 1.01 g/mol for H × 4 + 35.45 g/mol for Cl).
Number of moles of NH4Cl = 6.76 g ÷ 53.49 g/mol = 0.1264 mol
Since NH4Cl dissociates 1:1, the number of moles of NH4+ (ammonium) is also 0.1264 mol.
Step 2: Calculate the concentration of NH3 and NH4+ after the buffer is prepared.
The total volume of the buffer solution is 100.00 mL, which is equivalent to 0.1000 L.
- Concentration of NH3 (ammonia):
Concentration of NH3 = Number of moles of NH3 ÷ Total volume (in L)
Concentration of NH3 = 0.7975 mol ÷ 0.1000 L = 7.975 M
- Concentration of NH4+ (ammonium):
Concentration of NH4+ = Number of moles of NH4+ ÷ Total volume (in L)
Concentration of NH4+ = 0.1264 mol ÷ 0.1000 L = 1.264 M
Step 3: Calculate the pOH of the buffer solution.
pOH = -log10 [OH-]
Since NH4OH is a weak base, it will react with water to produce OH- ions. The concentration of OH- can be calculated using the Kb value.
Kb = [NH4+][OH-] / [NH3]
Rearranging the equation:
[OH-] = Kb × [NH3] / [NH4+]
[OH-] = 10^(-pKb) × [NH3] / [NH4+]
We are given the pKb value as 4.76. Substituting the values, we get:
[OH-] = 10^(-4.76) × 7.975 M / 1.264 M
Now, we have the concentration of OH-. To find the pOH, we can take the negative logarithm of [OH-]:
pOH = -log10 [OH-]
Step 4: Calculate the pH of the buffer solution.
To calculate the pH, we can use the fact that the sum of pH and pOH is always 14.
pH = 14 - pOH
Now, substitute the calculated pOH value into the equation to find the pH of the buffer solution.
Note: The concentration values obtained should be double-checked for accuracy, as small errors can impact the final pH calculation.