What mass of solid sodium acetate, NaCH3COO, must be added to 2.50 L of an aqueous solution of 0.55 M acetic acid, CH3COOH, in order to make a buffer solution whose pH is 4.50? Assume that adding the solid does not change the volume of the solution.
Use the Henderson-Hasselbalch equation.
114g
To determine the mass of solid sodium acetate required to make a buffer solution with a specific pH, we need to use the Henderson-Hasselbalch equation for buffers:
pH = pKa + log([A-]/[HA])
In this case, acetic acid (CH3COOH) is the weak acid (HA) and its conjugate base, acetate ion (CH3COO-), is the base (A-).
First, let's determine the pKa of acetic acid. The pKa of acetic acid is given as 4.75.
Next, we need to calculate the ratio [A-]/[HA] at pH 4.50 using the Henderson-Hasselbalch equation:
4.50 = 4.75 + log([A-]/[HA])
Rearranging the equation gives:
log([A-]/[HA]) = 4.50 - 4.75
log([A-]/[HA]) = -0.25
Taking the antilog of both sides:
[A-]/[HA] = 10^(-0.25)
Now, we can calculate the concentration of acetate ion ([A-]) in the buffer solution. Since the concentration of acetic acid ([HA]) is given as 0.55 M, we can write:
[A-] = 10^(-0.25) * [HA]
[A-] = 10^(-0.25) * 0.55 M
Now, we need to calculate the moles of acetate ion in the solution:
moles of acetate ion = [A-] * volume of solution
moles of acetate ion = 10^(-0.25) * 0.55 M * 2.50 L
Finally, to find the mass of solid sodium acetate, we need to convert moles to grams using the molar mass of sodium acetate (the sum of the atomic masses of the constituent elements Na, C, H, and O).
Once the molar mass is obtained, multiply it by the number of moles calculated above to get the mass of solid sodium acetate required.
Note: The molar mass of sodium acetate is 82.03 g/mol.
Therefore, the mass of solid sodium acetate required to make the buffer solution is:
mass = moles of acetate ion * molar mass of sodium acetate
Where:
- moles of acetate ion = 10^(-0.25) * 0.55 M * 2.50 L
- molar mass of sodium acetate = 82.03 g/mol