Calculate the pH of the 0.20 M NH3/0.20 M NH4Cl buffer. What is the pH of the buffer after the addition of 10.0 mL of 0.10 M HCl to 65.0 mL of the buffer?
Use the Henderson-Hasselbalch equation.
How do I take into account the change in volume?
You calculate moles, then M = moles/L
To calculate the pH of a buffer solution, we need to consider the Henderson-Hasselbalch equation, which is given by:
pH = pKa + log ([A-]/[HA])
where pH is the negative logarithm of the concentration of H+ ions (acidity), pKa is the negative logarithm of the acid dissociation constant (a measure of the relative strength of an acid), [A-] is the concentration of the conjugate base (in this case, NH4+), and [HA] is the concentration of the weak acid (in this case, NH3).
Let's break down the problem step by step:
1. Calculate the pKa of NH4Cl:
NH4Cl is the conjugate acid-base pair of NH3 and NH4+. The pKa can be calculated by using the expression:
pKa = pH + log ([A-]/[HA])
Since we are dealing with the ammonium ion (NH4+), which is weakly acidic, we can assume that pKa is approximately equal to the pH of the solution. Therefore, the pKa for NH4+ is approximately 4.75.
2. Calculate the concentrations of NH3 and NH4+ in the buffer solution:
We are given that the buffer solution contains 0.20 M NH3 and 0.20 M NH4Cl. This means that the concentration of NH3 is 0.20 M and the concentration of NH4+ is also 0.20 M.
3. Calculate the ratio [A-]/[HA]:
[A-]/[HA] = [NH4+]/[NH3] = 0.20 M / 0.20 M = 1
4. Calculate the pH of the buffer initially:
pH = pKa + log ([A-]/[HA]) = 4.75 + log (1) = 4.75
Therefore, the pH of the buffer initially is 4.75.
5. Calculate the new concentrations of NH3 and NH4+ after the addition of HCl:
We are adding 10.0 mL of 0.10 M HCl to 65.0 mL of the buffer. However, since the volume of the HCl solution is much smaller compared to the buffer solution, we can neglect the dilution effect.
The number of moles of HCl added can be calculated as follows:
moles of HCl = concentration of HCl * volume of HCl = 0.10 M * 0.01 L = 0.001 mol
Since HCl completely dissociates in water, every mole of HCl will produce one mole of H+ ions. Therefore, the concentration of the newly formed H+ ions can be calculated as 0.001 mol/L.
The new concentration of NH4+ can be calculated by subtracting the moles of H+ ions from the initial concentration of NH4+:
concentration of NH4+ = initial concentration of NH4+ - moles of H+ ions
Using the stoichiometry, we can say that one mole of HCl reacts with one mole of NH4+. Therefore, the concentration of NH4+ after the addition of HCl is:
concentration of NH4+ = 0.20 M - 0.001 mol/L
6. Calculate the new ratio [A-]/[HA]:
[A-]/[HA] = [NH4+]/[NH3] = (concentration of NH4+) / (concentration of NH3)
Substituting the values, we have:
[A-]/[HA] = (0.20 M - 0.001 mol/L) / 0.20 M
7. Calculate the new pH of the buffer after the addition of HCl:
pH = pKa + log ([A-]/[HA]) = 4.75 + log [(0.20 M - 0.001 mol/L) / 0.20 M]
Using this equation, you can calculate the new pH of the buffer after the addition of HCl.