If 16 8 g of sodium lactate (molar mass = 112 g/mol) are dissolved in 1 L of 0 20 M lactic acid, what is the pH of the resulting buffer solution? (K_a = 1.4 times 10^-4)
The correct answer and explanation is :
To calculate the pH of the buffer solution formed by sodium lactate and lactic acid, we use the Henderson-Hasselbalch equation. The equation is as follows:
[
\text{pH} = \text{pKa} + \log \left( \frac{[\text{Base}]}{[\text{Acid}]} \right)
]
Where:
- pKa is the negative logarithm of the acid dissociation constant (Ka) of lactic acid.
- [Base] is the concentration of the conjugate base (lactate ion from sodium lactate).
- [Acid] is the concentration of the acid (lactic acid).
Step 1: Calculate the pKa of lactic acid
Given that the ( K_a ) of lactic acid is ( 1.4 \times 10^{-4} ), we calculate the pKa:
[
\text{pKa} = -\log(K_a) = -\log(1.4 \times 10^{-4}) \approx 3.85
]
Step 2: Find the concentration of the acid and base
- Concentration of Lactic Acid (Acid): We are told the lactic acid solution has a concentration of ( 0.20 \, \text{M} ).
- Concentration of Sodium Lactate (Base): To find the concentration of the lactate ion from sodium lactate:
- Molar mass of sodium lactate = 112 g/mol.
- Moles of sodium lactate = ( \frac{16.8 \, \text{g}}{112 \, \text{g/mol}} = 0.15 \, \text{mol} ).
- The volume of the solution is 1 L, so the concentration of lactate ions is:
[
[\text{Base}] = \frac{0.15 \, \text{mol}}{1 \, \text{L}} = 0.15 \, \text{M}
]
Step 3: Apply the Henderson-Hasselbalch equation
Now, substitute the values into the equation:
[
\text{pH} = 3.85 + \log \left( \frac{0.15}{0.20} \right)
]
[
\text{pH} = 3.85 + \log(0.75)
]
[
\text{pH} = 3.85 + (-0.125)
]
[
\text{pH} = 3.725
]
Final Answer:
The pH of the resulting buffer solution is 3.73.
Explanation:
In this buffer system, sodium lactate provides the lactate ion (the conjugate base) that can react with any excess H(^+) ions, while lactic acid (a weak acid) can donate H(^+) ions when needed. The Henderson-Hasselbalch equation is ideal for calculating the pH of such buffer solutions, where both the acid and its conjugate base are present in significant amounts. This equation shows that the pH depends on the ratio of the concentrations of the conjugate base to the acid, and we find that the pH is slightly acidic (around 3.73).