What mass of ammonium chloride must be added to a 0.500 L solution of 0.250 M ammonia to make a buffer with a pH of 9.26? Kb (NH3) = 1.8 × 10–5?
Would I use the Henderson-hasselbalch equation? And what would I do after that?
To solve this problem, we need to use the Henderson-Hasselbalch equation for calculating the pH of a buffer solution:
pH = pKa + log([A-]/[HA])
In this case, we have ammonia (NH3) acting as the weak base and ammonium chloride (NH4Cl) acting as the conjugate acid. The pKa value can be calculated from the Kb value using the equation: pKa = 14 - pKb.
Step 1: Calculate the pKa value.
pKa = 14 - pKb
pKa = 14 - log(Kb)
Step 2: Calculate the ratio of [A-] to [HA] using the Henderson-Hasselbalch equation.
pH = pKa + log([A-]/[HA])
9.26 = pKa + log([A-]/[HA])
Step 3: Calculate the ratio of [A-] to [HA].
[A-]/[HA] = 10^(pH - pKa)
Step 4: Calculate the concentration of ammonia (NH3).
Given:
Volume = 0.500 L
Concentration = 0.250 M
NH3 concentration = concentration * volume
NH3 concentration = 0.250 M * 0.500 L
Step 5: Calculate the concentration of ammonium chloride (NH4Cl).
Since we know the ratio of [A-] to [HA], we can set up the following proportion:
[A-]/[HA] = [NH4Cl]/[NH3]
NH4Cl concentration = NH3 concentration * ([A-]/[HA])
NH4Cl concentration = (0.250 M * 0.500 L) * ([A-]/[HA])
Step 6: Calculate the mass of ammonium chloride.
To convert the concentration to mass, we use the formula:
Mass = Concentration * Volume * Molar mass
The molar mass of NH4Cl is 53.49 g/mol. Thus, the mass of ammonium chloride can be calculated as follows:
Mass of NH4Cl = NH4Cl concentration * 53.49 g/mol
By following these steps, you should be able to determine the mass of ammonium chloride needed to make the buffer with a pH of 9.26.