what mass of sodium acetate, NaCH3CO2, must be added to 1.0 L of 0.10 M acetic acid to give a solution with a pH of 4.50?
If you have had work with the Henderson-Hasselbalch equation, you should use that equation. There are other ways to do it but they are longer.
To find out the mass of sodium acetate required to achieve a pH of 4.50 in a solution with acetic acid, we need to consider the acid-base equilibrium and the Henderson-Hasselbalch equation.
The Henderson-Hasselbalch equation is given as follows:
pH = pKa + log([A-]/[HA])
Where:
- pH is the desired pH of the solution
- pKa is the dissociation constant of the acid
- [A-] is the concentration of the conjugate base
- [HA] is the concentration of the acid
In this case, acetic acid (CH3CO2H) acts as the acid and the acetate ion (CH3CO2-) acts as the conjugate base.
Step 1: Determine the dissociation constant (pKa) of acetic acid:
The pKa of acetic acid is approximately 4.76. This information can be found in various reference sources.
Step 2: Set up the Henderson-Hasselbalch equation and rearrange it to solve for the ratio of [A-]/[HA]:
4.50 = 4.76 + log([A-]/[HA])
0.26 = log([A-]/[HA])
10^(0.26) = [A-]/[HA]
[A-]/[HA] ≈ 1.8
Step 3: Calculate the concentration of acetic acid (HA) and acetate ion (A-) in the solution:
Since the initial concentration of acetic acid is 0.10 M, we can assign [HA] = 0.10 M.
Using the ratio found in Step 2, we have [A-] = 1.8 * [HA] = 1.8 * 0.10 M = 0.18 M.
Step 4: Determine the molecular weight of sodium acetate (NaCH3CO2):
The molecular weight of sodium acetate (NaCH3CO2) is approximately 82.03 g/mol. This can be obtained from the periodic table and adding the atomic masses of the elements.
Step 5: Calculate the mass of sodium acetate needed:
Using the equation: Mass = moles × molecular weight
The moles of sodium acetate can be calculated by multiplying the volume of the solution (1.0 L) by the concentration of acetate ions ([A-]).
Moles = volume (L) × concentration (M) = 1.0 L × 0.18 M = 0.18 moles
Mass = 0.18 moles × 82.03 g/mol ≈ 14.77 g
Therefore, approximately 14.77 grams of sodium acetate (NaCH3CO2) must be added to the 1.0 liter of 0.10 M acetic acid solution to achieve a pH of 4.50.