You are required to make 500 mL of a buffer solution with pH = 5.0 and a total acetate concentration of 0.1000 M. You are supplied with solid sodium actetate
(CH3COONa) and 2.00 M hydrochloric acid. What mass of sodium acetate and what volume of hydrochloric acid would you use? Show all working.
(For CH3COOH, Ka = 1.75 x 10-5)
To make a buffer solution with the desired pH and concentration, we need to calculate how much sodium acetate and hydrochloric acid we need to use. Here's how to do it step by step:
Step 1: Calculate the ratio of conjugate base to weak acid.
The Henderson-Hasselbalch equation relates the pH of a buffer solution to the ratio of the concentration of the conjugate base (acetate, CH3COO-) to the weak acid (acetic acid, CH3COOH). The equation is as follows:
pH = pKa + log([CH3COO-]/[CH3COOH])
Given that the pH is 5.0, and the pKa (dissociation constant) for acetic acid is 1.75 x 10^-5, we can rearrange the equation to solve for the ratio [CH3COO-]/[CH3COOH]:
5.0 = -log(1.75 x 10^-5) + log([CH3COO-]/[CH3COOH])
Expanding this equation, we get:
5.0 = -(-4.76 x 10^(-5)) + log([CH3COO-]/[CH3COOH])
Simplifying further, we have:
5.0 = 4.76 x 10^(-5) + log([CH3COO-]/[CH3COOH])
Now, using the logarithmic identity, we can convert the log function to an exponent:
5.0 = 4.76 x 10^(-5) + log10([CH3COO-]/[CH3COOH])
This can be rewritten as:
5.0 = 4.76 x 10^(-5) + log10([CH3COO-]) - log10([CH3COOH])
To find the ratio [CH3COO-]/[CH3COOH], we need to know the logarithmic values of the concentrations. However, we only have the molar concentration for the total acetate concentration (0.1000 M). To calculate the individual concentrations, we need to know the volume.
Step 2: Calculate the volume of the buffer solution.
The total volume of the buffer solution is given as 500 mL, which is equivalent to 0.5 L.
Step 3: Calculate the moles of acetic acid and sodium acetate.
Next, we need to calculate the moles of acetic acid (CH3COOH) and sodium acetate (CH3COONa) required.
For acetic acid, we can use the formula:
moles = concentration (M) x volume (L)
Since the concentration is unknown, we'll call it x. The volume is given as 0.5 L, so the equation becomes:
moles of acetic acid = x * 0.5
For sodium acetate, we again use the same formula:
moles = concentration (M) x volume (L)
Here, the concentration is known as 0.1000 M and the volume is 0.5 L, so the equation becomes:
moles of sodium acetate = 0.1000 * 0.5
Step 4: Calculate the mass of sodium acetate.
The molar mass of sodium acetate (CH3COONa) is the sum of the atomic masses of its components:
1C + 2H + 3O + 1Na = 23 + 2 + 48 + 12 = 85 g/mol
Since we know the moles of sodium acetate required, we can calculate the mass using the equation:
mass = moles x molar mass
Plug in the values and calculate the mass.
Step 5: Calculate the volume of hydrochloric acid.
The HCl is a strong acid that completely ionizes in water. Therefore, the molar ratio between HCl and the acetate anion is 1:1. This means that the moles of HCl required will be the same as the moles of sodium acetate.
Now, we know the molarity of the HCl solution as 2.00 M, and we can use the equation:
moles = concentration (M) x volume (L)
We can rearrange the equation to solve for the volume:
volume = moles / concentration
Plug in the values and calculate the volume.
By following these steps, you can determine the mass of sodium acetate and the volume of hydrochloric acid needed to make the desired buffer solution.