To begin, let's first calculate the pH of the buffer (part a) using the Henderson-Hasselbalch equation:
pH = pKa + log (base)/(acid)
In this case, the acid is H2PO4^-, and the base is HPO4^2-. The pKa value we need to use is the pK2 value, which corresponds to the dissociation of the second H+ from phosphoric acid.
1) Determine the pK2 value:
Since phosphoric acid (H3PO4) has three ionizable hydrogens, we need to find pK2 specifically. The pK2 value for phosphoric acid is approximately 7.2.
2) Calculate the molar concentrations:
The volume of the buffer is 0.300 L. To calculate the moles of the acid and the base, we use the molarity of each component and multiply it by the volume of the buffer.
Moles of acid (H2PO4^-) = (0.500 M) * (0.300 L) = 0.150 moles
Moles of base (HPO4^2-) = (0.317 M) * (0.300 L) = 0.0951 moles
3) Calculate the ratio of base/acid:
ratio = (moles of base)/(moles of acid)
ratio = 0.0951/0.150 = 0.634
4) Apply the Henderson-Hasselbalch equation:
pH = 7.2 + log (0.634)
pH ≈ 6.7
Therefore, the pH of the buffer is approximately 6.7.
Now, let's move on to part b and part c:
b) When HCl is added to the buffer, it reacts with the base (HPO4^2-) and forms more acid (H2PO4^-). The moles of HCl added to the buffer will be equal to the moles of base consumed and the moles of acid formed.
In this case, 0.0500 mol of HCl is added to 0.600 L of the buffer. This means that the moles of acid will increase by 0.0500 mol and the moles of base will decrease by the same amount. Adjust the moles of acid and base accordingly and recalculate the ratio using the new values.
Once you get the new ratio, plug it into the Henderson-Hasselbalch equation with the pK2 value to calculate the new pH.
c) When NaOH is added to the buffer, it reacts with the acid (H2PO4^-) and forms more base (HPO4^2-). Similar to part b, the moles of NaOH added will be equal to the moles of acid consumed and the moles of base formed.
In this case, 0.0500 mol of NaOH is added to 0.600 L of the buffer. Adjust the moles of acid and base accordingly and recalculate the ratio using the new values.
Once you get the new ratio, plug it into the Henderson-Hasselbalch equation with the pK2 value to calculate the new pH.
Remember, the Henderson-Hasselbalch equation can be used in cases where the concentration of the acid and base is known, and the pKa value is also known. You can use this equation to calculate the pH of a buffer before and after the addition of acids or bases.