To calculate the number of moles and grams of NH4Cl needed to prepare the buffer solution, we need to use the Henderson-Hasselbalch equation. The Henderson-Hasselbalch equation relates the pH, pKa (or pKb), and the ratio of the conjugate base (NH4Cl) and weak base (NH3) concentrations in a buffer solution.
The equation is as follows:
pH = pKa + log([A-]/[HA])
In this case, NH3 acts as the weak base (HA), and NH4Cl acts as the conjugate acid (A-).
Given:
- Solution concentration of NH3: 0.10 M
- pH of the buffer solution: 9.15
- Kb value for NH3: 1.8 x 10^-5
Step 1: Calculate the pKa
pKb + pKa = 14 (for NH3-NH4+ system)
So, pKb = 14 - pKa
pKa = 14 - pKb = 14 - (-log10(1.8 x 10^-5))
Step 2: Convert the pH to [A-]/[HA] ratio
pH = pKa + log([A-]/[HA])
9.15 = pKa + log([A-]/[HA])
log([A-]/[HA]) = 9.15 - pKa
[A-]/[HA] = antilog(9.15 - pKa)
Step 3: Calculate the concentration of NH4Cl needed
The concentration of NH4Cl needed can be calculated using the ratio obtained in Step 2.
Let's assume the final volume of the solution after adding NH4Cl is V liters.
[A-] = [NH4Cl] / V
[HA] = [NH3] = 0.10 M
Substituting these values in the ratio equation:
0.10 / V = antilog(9.15 - pKa)
Rearranging the equation for V:
V = 0.10 / antilog(9.15 - pKa)
Step 4: Calculate the number of moles of NH4Cl needed
To calculate the number of moles, we need to multiply the concentration of NH4Cl by the volume.
Number of moles = [NH4Cl] x V
Step 5: Calculate the number of grams of NH4Cl needed
To calculate the number of grams, we need to multiply the number of moles by the molar mass of NH4Cl.
Number of grams = Number of moles x Molar mass of NH4Cl
Considering the atomic weights provided:
Molar mass of NH4Cl = (1 x 4) + (14 + 1) + (35.45) = 53.45 g/mol
Now you can substitute the values calculated in the respective equations to find the number of moles and grams of NH4Cl required.