Calculate the pH of the resulting solution if 50 cm3 of 0.045mol dm-3 solution of C5H5N is mixed with 100 cm3 of 0.035 mol dm-3 of C5H5NH+
Use the Henderson-Hasselbalch eqauation.
To calculate the pH of the resulting solution, we need to consider the acid-base properties of the given compounds.
C5H5N is a weak base, while C5H5NH+ is its conjugate acid. When these two solutions are mixed, they will undergo a reaction, forming an equilibrium:
C5H5N + H2O ⇌ C5H5NH+ + OH-
To solve this problem, we can use the concept of Henderson-Hasselbalch equation, which relates the pH of a solution to the concentration of the acid and its conjugate base:
pH = pKa + log([conjugate acid] / [conjugate base])
In this case, C5H5NH+ acts as the conjugate acid, and C5H5N as the conjugate base.
First, let's determine the concentrations of the acid and its conjugate base after mixing the solutions:
For C5H5N:
Concentration = moles/volume
Concentration = (0.045 mol/dm^3) * (50 cm^3 / 1000 cm^3/dm^3)
Concentration = 0.045 * 0.05 mol/dm^3
For C5H5NH+:
Concentration = moles/volume
Concentration = (0.035 mol/dm^3) * (100 cm^3 / 1000 cm^3/dm^3)
Concentration = 0.035 * 0.1 mol/dm^3
Now, let's substitute the values into the Henderson-Hasselbalch equation:
pH = pKa + log([conjugate acid] / [conjugate base])
pH = pKa + log((0.035 * 0.1) / (0.045 * 0.05))
The pKa for the C5H5N/C5H5NH+ system is typically given (around 9.25), so we can assume this value.
pH = 9.25 + log((0.0035) / (0.00225))
pH = 9.25 + log(1.5556)
Using a calculator, log(1.5556) ≈ 0.192
pH = 9.25 + 0.192
pH = 9.442
Therefore, the pH of the resulting solution is approximately 9.442.