A solution is 0.10M in aqueous NH3. Calculate (a) the number of moles and (b) the number of grams of NH4Cl that must be added to 500mL of this solution to prepare a buffer solution with pH=9.15. You may neglect the volume change due to addition of solid NH4Cl. Kb=1.8x10^-5.
(atomic wts: N=14 H=1 Cl=35.45)
pH = pKa + log (base)/(acid)
You know pH, Ka is calculated from KaKb = Kw = 1E-14 and pKa = -log Ka.
You know base is 0.1, substitute into the above and solve for acid. Since the problem asks for mols and grams, the easy to do this is to substitute millimols into (base) and (acid) instead of concentrations so the unknown is millimols acid. Converted to mols that will give you part a. Then mols x molar mass will give you part b.
Concentration and mols is not the same but the math comes out to be the same answer so the shortcut saves sine time.
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.