Final answer:
The pH of the carbonate buffer solution is approximately 10.601.
Step-by-step explanation:
To determine the pH of a carbonate buffer solution prepared by mixing 1.5 mol Na2CO3 and 1 mol NaHCO3, we need to consider the dissociation of the acidic species in water. Na2CO3 will dissociate into two moles of Na+ ions and one mole of CO3^2- ions, while NaHCO3 will dissociate into one mole of Na+ ions, one mole of HCO3- ions, and one mole of H+ ions. The HCO3- ions will act as a weak acid and the CO3^2- ions will act as a weak base in the buffer solution.
The pH of the buffer solution can be calculated using the Henderson-Hasselbalch equation: pH = pKa + log ([A-]/[HA]), where [A-] is the concentration of the conjugate base and [HA] is the concentration of the weak acid. In this case, the weak acid is HCO3- and the conjugate base is CO3^2-. The pKa for the HCO3-/CO3^2- system is 10.3. To calculate the concentrations of [A-] and [HA], we need to take into account the moles of NaHCO3 and Na2CO3 used to prepare the buffer solution.
Given that 1.5 mol of Na2CO3 and 1 mol of NaHCO3 are mixed to make a 1L buffer solution, the total moles of the weak acid and conjugate base are:
- [A-] = 2 mol (from the Na2CO3)
- [HA] = 1 mol (from the NaHCO3)
Substituting the values into the Henderson-Hasselbalch equation:
pH = 10.3 + log (2/1)
pH = 10.3 + 0.301 = 10.601
Therefore, the pH of the carbonate buffer solution is approximately 10.601.