Calculate the pH of the buffer solution that results when 10 mL of 0.10 M NaH2PO4 is added to 3 mL of 0.05 M NaOH.
Chemistry help wanted
To calculate the pH of the buffer solution, you need to consider the equilibrium between the weak acid, NaH2PO4, and its conjugate base, HPO4^2-. The equation for the dissociation of NaH2PO4 is:
NaH2PO4 → Na+ + H2PO4^-
Since NaH2PO4 is a weak acid, it partially ionizes in water to produce H+ ions and H2PO4^- ions. The reaction can be represented by the equilibrium equation:
H2PO4^- ⇌ H+ + HPO4^2-
To solve this problem, we need to determine the concentrations of H2PO4^- and HPO4^2- in the buffer solution.
Step 1: Calculate the moles of NaH2PO4 and NaOH added.
Moles of NaH2PO4 = concentration (M) x volume (L)
= 0.10 M x 0.010 L
= 0.001 moles
Moles of NaOH = concentration (M) x volume (L)
= 0.05 M x 0.003 L
= 0.00015 moles
Step 2: Determine the limiting reagent.
Since the stoichiometric ratio between NaH2PO4 and NaOH is 1:2, we know that 2 moles of NaOH are required to react with 1 mole of NaH2PO4. Therefore, NaOH is the limiting reagent, and we will use up all of the 0.00015 moles of NaOH.
Step 3: Calculate the concentrations of H2PO4^- and HPO4^2- in moles per liter.
The total volume of the buffer solution is the sum of the volumes of NaH2PO4 and NaOH:
Total volume = 10 mL + 3 mL = 13 mL = 0.013 L
Concentration of H2PO4^- = moles of H2PO4^- / total volume (L)
= 0.001 moles / 0.013 L
= 0.0769 M
Concentration of HPO4^2- = moles of HPO4^2- / total volume (L)
= 2 x moles of NaOH / total volume (L)
= 2 x 0.00015 moles / 0.013 L
= 0.0023 M
Step 4: Apply the Henderson-Hasselbalch equation to calculate the pH.
The Henderson-Hasselbalch equation is given by:
pH = pKa + log ([A-] / [HA])
Where pKa is the negative logarithm of the acid dissociation constant, [A-] is the concentration of the conjugate base, and [HA] is the concentration of the weak acid.
For the phosphate buffer system, the pKa for the H2PO4^- / HPO4^2- equilibrium is around 7.2.
pH = 7.2 + log (0.0023 / 0.0769)
Using a calculator, the pH of the buffer solution is approximately 6.49.
Therefore, the pH of the buffer solution is 6.49.