Final answer:
The pH of a buffer solution prepared with 0.155 mol of phosphoric acid and 0.250 mol of KH₂PO₄ in 0.500 L of water can be calculated using the Henderson-Hasselbalch equation. The solution is found to be basic with a pH greater than 7.
Step-by-step explanation:
To calculate the pH of a buffer solution prepared from 0.155 mol of phosphoric acid, 0.250 mol of KH₂PO₄, and enough water to make 0.500 L of solution, you can use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
Firstly, determine the pKa of phosphoric acid relevant to the dissociation of H₂PO₄- (as KH₂PO₄ provides the H₂PO₄- ions). The first dissociation step pKa is typically around 2.15, but since we are dealing with the second step, we need the second pKa which is around 7.2.
Convert moles to molarity by dividing moles of each species by the volume of the buffer. This gives you 0.155 M for H₂PO₄- and 0.250 M for KH₂PO₄.
Now, apply the values to the Henderson-Hasselbalch equation:
pH = 7.2 + log(0.250/0.155)
After calculating, you will find that the pH is greater than 7, which indicates that the solution is basic.
In regards to the final pH when hydrochloric acid is added, fresh calculations need to be made considering the change in concentration of H₂PO₄- and KH₂PO₄.