Question

How much solid NaCH₃CO₂•3H₂O must be added to 0.300 L of a 0.50-M acetic acid solution to give a buffer with a pH of 5.00? (Hint: Assume a negligible change in volume as the solid is added.)

a) 0.00 g
b) Between 0.00 g and 5.00 g
c) 5.00 g
d) More than 5.00 g

Answer 1

To provide a buffer with a pH of 5.00 using acetic acid and sodium acetate trihydrate, the Henderson-Hasselbalch equation is utilized. Calculations based on the given concentration of acetic acid and the desired pH indicate that more than 5.00 g of solid NaCH₃CO₂•3H₂O is required.

Step-by-step explanation:

To determine how much solid NaCH₃CO₂•3H₂O must be added to a 0.300 L of 0.50-M acetic acid solution to give a buffer with a pH of 5.00, we can use the Henderson-Hasselbalch equation, which is pH = pKa + log([A-]/[HA]), where [A-] is the concentration of the acetate ion and [HA] is the concentration of acetic acid. The pKa of acetic acid is around 4.76. Since we are given a target pH of 5.00, we can arrange the equation as follows: 5.00 = 4.76 + log([A-]/[HA]).

The concentration of acetic acid [HA] is 0.50 M. To find the ratio of [A-]/[HA] for the desired pH, we rearrange the Henderson-Hasselbalch equation: ratio = 10^(pH-pKa) = 10^(5.00-4.76) = 10^(0.24). Once we have the ratio, we can calculate the moles of acetate ion needed as follows: moles of [HA] = 0.300 L × 0.50 M = 0.150 moles; moles of [A-] = 0.150 moles × ratio.

Now we can calculate the mass of NaCH₃CO₂•3H₂O (molar mass = 136.08 g/mol) required to achieve the desired moles of acetate ion and indirectly determine the range of mass needed. This calculation results in more than 5.00 g. Answer (d) More than 5.00 g is therefore correct.