Final answer:
The initial pH of the buffer solution is calculated using the Henderson-Hasselbalch equation, which takes into account the dissociation constant of the acid and the concentrations of the weak acid and its salt. After performing the calculation, the initial pH is determined to be 2.601.
Step-by-step explanation:
The student is asking about the initial pH of a buffer solution that involves a weak acid HC₂H₂CIO₂ and its salt KC₂H₂CIO₂. The dissociation constant (Ka) of the acid is given as 1.30 x 10⁻³. To calculate the pH, we use the Henderson-Hasselbalch equation:
pH = pKa + log([A⁻]/[HA])
where pKa is the negative logarithm of Ka, [A⁻] is the concentration of the conjugate base, and [HA] is the concentration of the acid.
First, we need to calculate the moles of the weak acid and its salt. Given that the molar mass of KC₂H₂CIO₂ is approximately 128.17 g/mol, we can find the moles of salt:
Moles of KC₂H₂CIO₂ = 16.6 g / 128.17 g/mol = 0.1295 moles
The acid concentration is already provided as 0.500 M, which for a 500 mL solution amounts to 0.500 mol/L * 0.500 L = 0.250 moles.
Now we can calculate the pKa value:
pKa = -log(1.30 x 10⁻³) = 2.886
Applying the Henderson-Hasselbalch equation, we get:
pH = 2.886 + log(0.1295 / 0.250) = 2.886 + log(0.518) = 2.886 + (-0.285) = 2.601
Therefore, the initial pH of this buffer solution is 2.601.