What is the pH of a 150 mL buffer solution containing 0.5 M NaH2PO4 with 0.5 M K2HPO4?
Determine the new pH of the solution upon the addition of 10 mL of 1.2 M strong acid to the 150 mL buffer solution above.
To find the pH of a buffer solution, you need to consider the acid-base equilibrium of the buffering agents present in the solution. In this case, the buffer is a mixture of NaH2PO4 and K2HPO4.
1. Calculate the pH of the buffer solution before the addition of the strong acid:
a. NaH2PO4 is a weak acid and will partially dissociate in water:
NaH2PO4 ⇌ Na+ + H2PO4-
b. K2HPO4 is a weak base and will partially dissociate in water:
K2HPO4 ⇌ 2K+ + HPO42-
2. The buffer solution is formed by the reaction between the acidic form (H2PO4-) and basic form (HPO42-):
H2PO4- ⇌ H+ + HPO42-
Since both NaH2PO4 and K2HPO4 are present in equal concentrations, the concentrations of H2PO4- and HPO42- will also be equal.
3. Calculate the concentrations of H2PO4- and HPO42-:
The initial concentration of each buffer component is 0.5 M. Since they are present in equal amounts, the concentration of H2PO4- and HPO42- in the buffer solution will be 0.5 M.
4. Determine the pKa of the H2PO4- / HPO42- system:
The pKa value can be found in a reference table or calculated using the Henderson-Hasselbalch equation.
5. Use the Henderson-Hasselbalch equation to calculate the pH of the buffer solution:
pH = pKa + log([A-]/[HA])
where [A-] is the concentration of the conjugate base (HPO42-) and [HA] is the concentration of the acid (H2PO4-).
6. Add 10 mL of the 1.2 M strong acid to the 150 mL buffer solution:
Calculate the moles of strong acid added:
Moles of strong acid = concentration of strong acid * volume of strong acid
Moles of strong acid = 1.2 M * 0.01 L = 0.012 moles
7. Determine the new total volume of the buffer solution:
Total volume = initial volume of buffer solution + volume of strong acid added
Total volume = 150 mL + 10 mL = 160 mL
8. Calculate the new concentrations of H2PO4- and HPO42- in the buffer solution:
The moles of H2PO4- and HPO42- are constant since they are provided by NaH2PO4 and K2HPO4. However, the total volume has increased, so the concentrations will be recalculated.
9. Use the Henderson-Hasselbalch equation to calculate the new pH of the solution:
pH = pKa + log([A-]/[HA])
Please provide the pKa value for the H2PO4- / HPO42- system so that we can proceed with the calculation.
To find the pH of a buffer solution, we need to consider the dissociation of the weak acid and its conjugate base in the solution.
In this case, we have a buffer solution containing NaH2PO4 (weak acid) and K2HPO4 (conjugate base), which are components of the phosphoric acid/phosphate buffer system.
Step 1: Calculate the moles of weak acid (NaH2PO4) and conjugate base (K2HPO4) in the solution.
Moles of NaH2PO4 = concentration (M) × volume (L) = 0.5 M × 0.150 L = 0.075 mol
Moles of K2HPO4 = concentration (M) × volume (L) = 0.5 M × 0.150 L = 0.075 mol
Step 2: Calculate the total moles of the weak acid and conjugate base.
Total moles = moles of weak acid + moles of conjugate base = 0.075 mol + 0.075 mol = 0.150 mol
Step 3: Calculate the concentrations of the weak acid and conjugate base in the buffer solution.
Concentration of NaH2PO4 = moles / volume (L) = 0.150 mol / 0.150 L = 1 M
Concentration of K2HPO4 = moles / volume (L) = 0.150 mol / 0.150 L = 1 M
Step 4: Calculate the pKa value of the weak acid. The pKa is the negative logarithm of the acid dissociation constant (Ka). In this case, the weak acid is phosphoric acid (H3PO4), and its pKa value is 2.15.
Step 5: Calculate the pH of the buffer solution using the Henderson-Hasselbalch equation:
pH = pKa + log ([conjugate base] / [weak acid])
pH = 2.15 + log (1 M / 1 M) = 2.15 + log(1) = 2.15
Therefore, the pH of the 150 mL buffer solution containing 0.5 M NaH2PO4 with 0.5 M K2HPO4 is 2.15.
Now, let's move on to determining the new pH of the solution upon the addition of 10 mL of 1.2 M strong acid.
Step 1: Calculate the moles of the strong acid (initially added).
Moles of strong acid = concentration (M) × volume (L) = 1.2 M × 0.010 L = 0.012 mol
Step 2: Calculate the change in moles of the weak acid and conjugate base due to the addition of strong acid.
The ratio of the weak acid and conjugate base in the buffer is 1:1. The addition of 0.012 mol of the strong acid will neutralize 0.012 mol of the weak acid (NaH2PO4) and form an equivalent amount of the conjugate base (HPO4^2-).
Step 3: Calculate the new moles of the weak acid and conjugate base.
New moles of NaH2PO4 = initial moles - moles neutralized = 0.075 mol - 0.012 mol = 0.063 mol
New moles of K2HPO4 = initial moles + moles formed = 0.075 mol + 0.012 mol = 0.087 mol
Step 4: Calculate the new concentrations of the weak acid and conjugate base.
New concentration of NaH2PO4 = moles / volume (L) = 0.063 mol / 0.150 L = 0.42 M
New concentration of K2HPO4 = moles / volume (L) = 0.087 mol / 0.150 L = 0.58 M
Step 5: Calculate the new pH of the solution using the Henderson-Hasselbalch equation:
pH = pKa + log ([conjugate base] / [weak acid])
pH = 2.15 + log (0.58 M / 0.42 M) = 2.15 + log(1.38) ≈ 2.15 + 0.138 = 2.29
Therefore, upon the addition of 10 mL of 1.2 M strong acid to the 150 mL buffer solution above, the new pH of the solution is approximately 2.29.