You have 875 mL of an 0.53 M acetic acid solution. What volume (V) of 1.30 M NaOH solution must you add in order to prepare an acetate buffer of pH = 4.94? (The pKa of acetic acid is 4.76.)
To solve this problem, first, we need to understand the concept of a buffer solution. A buffer solution is a solution that resists changes in pH when small amounts of acid or base are added to it. It is composed of a weak acid and its conjugate base or a weak base and its conjugate acid.
In this case, we want to prepare an acetate buffer, which consists of acetic acid (CH3COOH) and its conjugate base, acetate ion (CH3COO-). The pH of the buffer solution depends on the ratio of the concentrations of the acid and the conjugate base.
Now let's solve the problem step by step:
Step 1: Calculate the initial concentrations of acetic acid and acetate ion.
Given:
Volume of acetic acid solution (Va) = 875 mL = 0.875 L
Molarity of acetic acid solution (Ma) = 0.53 M
Using the formula for concentration, we can calculate the initial moles of acetic acid:
Na = Ma * Va
Na = 0.53 M * 0.875 L
Step 2: Calculate the required moles of conjugate base (acetate ion).
The moles of acetic acid should be equal to the moles of acetate ion to achieve a buffer solution. Since the pKa of acetic acid is given as 4.76, we can use the Henderson-Hasselbalch equation:
pH = pKa + log10([Acetate ion]/[Acetic acid])
Substituting the given values:
4.94 = 4.76 + log10([Acetate ion]/[Acetic acid])
Now solving for the ratio of [Acetate ion]/[Acetic acid].
Step 3: Calculate the required volume of 1.30 M NaOH solution to be added.
Given:
Molarity of NaOH solution (Mb) = 1.30 M
Volume of NaOH solution (Vb) = ?
Using the formula for concentration, we can calculate the required moles of NaOH:
Nb = Mb * Vb
Step 4: Equate the moles of acetic acid and acetate ion.
Since the moles of acetic acid and acetate ion in the buffer solution should be equal, we can set up an equation:
Na = Nb
By substituting the calculated values from previous steps, we can solve for Vb:
0.53 M * 0.875 L = 1.30 M * Vb
Solving this equation gives us the required volume of NaOH solution (Vb) to be added.
Step 5: Solve for Vb.
By rearranging the equation from step 4, we can solve for Vb:
Vb = (0.53 M * 0.875 L) / 1.30 M
Calculating this equation will give you the volume (V) of 1.30 M NaOH solution that must be added to prepare the acetate buffer of pH = 4.94.