Using a 0.20 M phosphate buffer with a pH of 6.7, you add 0.71 mL of 0.55 M HCl to 52 mL of the buffer. What is the new pH of the solution?
To find the new pH of the solution, we need to calculate the change in pH caused by the addition of HCl to the buffer. Here are the steps to solve the problem:
Step 1: Calculate the moles of HCl added.
Moles HCl = concentration (M) × volume (L)
Moles HCl = 0.55 M × 0.00071 L
Step 2: Calculate the initial concentration of the buffer.
Initial concentration = 0.20 M
Step 3: Calculate the overall volume of the solution after mixing.
Overall volume = volume of buffer + volume of HCl
Overall volume = 52 mL + 0.71 mL
Step 4: Calculate the new concentration of the buffer after mixing.
New concentration of buffer = (initial concentration × volume of buffer) / overall volume
Step 5: Calculate the new concentration of HCl after mixing.
New concentration of HCl = (moles HCl) / overall volume
Step 6: Calculate the new concentration of phosphate ion (HPO4^2-) after mixing.
New concentration of phosphate ion = initial concentration of buffer - new concentration of HCl
Step 7: Calculate the new concentration of dihydrogen phosphate ion (H2PO4^-) after mixing.
New concentration of dihydrogen phosphate ion = new concentration of HCl
Step 8: Calculate the new pH using the Henderson-Hasselbalch equation.
pH = pKa + log([HPO4^2-]/[H2PO4^-])
In this case, phosphate acts as a buffer, and its pKa value can be determined from the Henderson-Hasselbalch equation using the known pH of 6.7 and the concentration of the phosphate buffer.
By following these steps and plugging in the values, you can find the new pH of the solution.