Question

You need to prepare 100.0mL of a pH=4.00 buffer solution using 0.100 M benzoic acid (pKa=4.20) and 0.240 M sodium benzoate. How much of each solution should be mixed to prepare the buffer?

a) Add 50.0 mL of 0.100 M benzoic acid and 50.0 mL of 0.240 M sodium benzoate.
b) Add 60.0 mL of 0.100 M benzoic acid and 40.0 mL of 0.240 M sodium benzoate.
c) Add 40.0 mL of 0.100 M benzoic acid and 60.0 mL of 0.240 M sodium benzoate.
d) Add 70.0 mL of 0.100 M benzoic acid and 30.0 mL of 0.240 M sodium benzoate.

Answer 1

To prepare a pH=4.00 buffer solution, we can use the Henderson-Hasselbalch equation and the dilution formula. The volumes of the stock solutions that contain the required concentrations can be calculated by solving the equation derived from the dilution formula.

Step-by-step explanation:

To prepare a pH=4.00 buffer solution, we need to use the Henderson-Hasselbalch equation, which is pH = pKa + log[(conjugate base)/(conjugate acid)].

First, calculate the ratio of sodium benzoate to benzoic acid: (0.240 M)/(0.100 M) = 2.4. Next, calculate the log of the ratio: log(2.4) = 0.3802. Now, substitute the values into the equation: 4.00 = 4.20 + 0.3802. Finally, solve for the concentration of the conjugate base: [conjugate base] = 10^(4.00 - 4.20 - 0.3802) = 0.174 M.

To prepare 100.0 mL of the buffer solution, we need to find the volumes of the stock solutions that contain the required concentrations of the benzoic acid and sodium benzoate. Let x be the volume of the 0.100 M benzoic acid, so the volume of the 0.240 M sodium benzoate will be (100 - x) mL. We can set up an equation based on the dilution formula: (0.100 M)(x mL) + (0.240 M)(100 - x mL) = (0.174 M)(100 mL). Solving this equation will give us the correct volumes of each stock solution to prepare the buffer solution.