Calculate the pH after 0.013 mole of gaseous HCl is added to 272.0 mL of each of the following buffered solutions. (Assume that all solutions are at 25°C.)
(a) 0.080 M C5H5N and 0.19 M C5H5NHCl
(b) 0.72 M C5H5N and 1.52 M C5H5NHCl
To calculate the pH after adding HCl to a buffered solution, we need to determine the effect of the HCl on the solution's pH. This can be done by considering the Henderson-Hasselbalch equation, which relates the pH of a buffered solution to the concentrations of the weak acid and its conjugate base.
The Henderson-Hasselbalch equation is given by:
pH = pKa + log([A-]/[HA])
Where:
- pH is the logarithmic measure of the hydrogen ion concentration in the solution.
- pKa is the logarithmic measure of the acid dissociation constant.
- [A-] is the concentration of the conjugate base.
- [HA] is the concentration of the weak acid.
Let's calculate the pH for both scenarios:
(a) 0.080 M C5H5N and 0.19 M C5H5NHCl
In this case, C5H5N acts as a weak base and C5H5NHCl acts as its conjugate acid. Before addition of HCl, the solution contains C5H5N and C5H5NHCl.
To find the pH, we need to determine the concentration of C5H5NH+ (conjugate acid), which is formed by the reaction of HCl with C5H5N.
Given that 0.013 moles of HCl is added to 272.0 mL, we can find the new concentration of C5H5NHCl:
0.19 M × (272.0 mL / 1000 mL) = 0.05168 moles
This means that 0.05168 moles of C5H5NHCl is present in the solution after the addition of HCl.
Now, let's calculate the concentration of C5H5N (weak base) in the solution:
0.080 M × (272.0 mL / 1000 mL) = 0.02176 moles
With these values, we can calculate the concentration of C5H5NH+ (conjugate acid):
0.05168 moles - 0.013 moles = 0.03868 moles
Now, we can apply the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
The pKa of C5H5NH+ (conjugate acid) can be found in the literature, and for C5H5NH+, it is approximately 4.75.
pH = 4.75 + log(0.02176/0.03868)
Using a calculator, evaluate the logarithm and perform the addition:
pH ≈ 4.75 + log(0.562) ≈ 4.75 + (-0.250) ≈ 4.50
Hence, the pH after adding 0.013 moles of gaseous HCl to the buffered solution of 0.080 M C5H5N and 0.19 M C5H5NHCl is approximately 4.50.
You can follow a similar procedure for scenario (b) by substituting the given concentrations (0.72 M C5H5N and 1.52 M C5H5NHCl) and using the Henderson-Hasselbalch equation to find the pH after adding 0.013 moles of gaseous HCl.