Calculate the pH after 0.010 mol gaseous HCl is added to 250.0 mL of each of the following buffered solutions:
a. .050 M NH3/.15 M NH4Cl
b. .5 M NH3/ 1.5 M NH4Cl
a. 7.97
b. 8.73
To calculate the pH after adding gaseous HCl to a buffered solution, you need to use the Henderson-Hasselbalch equation. The equation is given as:
pH = pKa + log ([A-]/[HA])
Where:
- pH is the expected pH after adding the acid to the buffered solution.
- pKa is the negative logarithm (base 10) of the acid dissociation constant.
- [A-] is the concentration of the conjugate base after the addition of the acid.
- [HA] is the concentration of the weak acid before the addition of the acid.
To solve the problem for each scenario, follow these steps:
a. .050 M NH3 / .15 M NH4Cl
1. Find the pKa value for NH4Cl. The pKa for NH4Cl is equal to the pKa of NH4+ (ammonium ion), which is approximately 9.25.
2. Calculate the concentration of NH3 and NH4+ after the addition of HCl.
- NH3 will react with HCl to form NH4+. So, after adding 0.010 mol of HCl to 250.0 mL of a 0.050 M NH3 solution, the concentration of NH3 will be reduced by 0.010 mol and the concentration of NH4+ will increase by 0.010 mol (assuming complete reaction).
- The new concentration of NH3 will be 0.050 - 0.010 = 0.040 M.
- The new concentration of NH4+ will be 0.15 + 0.010/(0.250 L) = 0.1504 M.
3. Substitute the values in the Henderson-Hasselbalch equation.
- pH = 9.25 + log(0.1504/0.040) = 9.25 + log(3.76) = 9.25 + 0.5763 = 9.8263.
So, the pH after adding 0.010 mol of gaseous HCl to the .050 M NH3 / .15 M NH4Cl buffered solution is approximately 9.8263.
b. .5 M NH3 / 1.5 M NH4Cl
1. Find the pKa value for NH4Cl, which is approximately 9.25.
2. Calculate the concentration of NH3 and NH4+ after the addition of HCl.
- After adding 0.010 mol of HCl to 250.0 mL of a 0.5 M NH3 solution, the concentration of NH3 will be reduced by 0.010 mol and the concentration of NH4+ will increase by 0.010 mol (assuming complete reaction).
- The new concentration of NH3 will be 0.5 - 0.010 = 0.490 M.
- The new concentration of NH4+ will be 1.5 + 0.010/(0.250 L) = 1.54 M.
3. Substitute the values in the Henderson-Hasselbalch equation.
- pH = 9.25 + log(1.54/0.490) = 9.25 + log(3.142) = 9.25 + 0.4972 = 9.7472.
So, the pH after adding 0.010 mol of gaseous HCl to the 0.5 M NH3 / 1.5 M NH4Cl buffered solution is approximately 9.7472.