Final answer:
To find the pH of a Na2CO3/NaHCO3 buffer solution, we use the Henderson-Hasselbalch equation with the given masses of the buffer components converted to molarity. Moles of NaHCO3 and Na2CO3 are calculated and substituted into the equation. The final pH calculation yields a pH of approximately 10.50.
Step-by-step explanation:
To calculate the pH of the Na2CO3/NaHCO3 buffer solution, we use the Henderson-Hasselbalch equation, which is pH = pKa + log([A-]/[HA]). Here, pKa is the acid dissociation constant for the acid component of the buffer, NaHCO3, and [A-] and [HA] are the molar concentrations of the conjugate base and acid, respectively. For the carbonate system, pKa is 10.33 for the equilibrium between HCO3- (bicarbonate) and H2CO3 (carbonic acid).
First, we need to convert the masses of Na2CO3 and NaHCO3 into moles by dividing by their molar masses, which are 105.99 g/mol for Na2CO3 and 84.01 g/mol for NaHCO3. With 8.4 g of NaHCO3, this is 8.4 g / 84.01 g/mol = 0.1 moles of NaHCO3. And with 16.0 g of Na2CO3, this is 16.0 g / 105.99 g/mol = 0.151 moles of Na2CO3.
Since we have a solution volume of 0.500 L, the molar concentrations of the species are [HCO3-] = 0.1 moles / 0.500 L = 0.200 M and [CO32-] (which comes from Na2CO3 and serves as A- in the equation) = 0.151 moles / 0.500 L
= 0.302 M.
Inserting these values into the Henderson-Hasselbalch equation produces:
pH = 10.33 + log(0.302/0.200).
Calculating the log(0.302/0.200) gives us approximately 0.182, so the final pH is roughly 10.33 + 0.182 = 10.50