What mass of sodium benzoate should you add to 150.00 ml of a 0.15M benzoic acid solution to obtain a buffer with a pH of 4.25?
Use the Henderson-Hasselbalch equation. I would substitute 150*0.15 = 22.5 millimoles for acid and x for sodium benzoate. Solve for x = sodium benzoate, change to mols, then n = grams/molar mass and solve for grams.
To determine the mass of sodium benzoate needed to create a buffer solution with a pH of 4.25, we first need to understand the concept of a buffer system.
A buffer is a solution that resists changes in pH when small amounts of acid or base are added to it. It consists of a weak acid and its conjugate base (or a weak base and its conjugate acid). In this case, we have a weak acid, benzoic acid (C6H5COOH), and we need to add sodium benzoate (C6H5COONa), the conjugate base, to create the buffer.
To calculate the mass of sodium benzoate needed, we need some information:
1. The volume of the solution: 150.00 mL
2. The molarity of the benzoic acid solution: 0.15 M
3. The desired pH of the buffer: 4.25
Now, let's walk through the steps to find the mass of sodium benzoate needed:
Step 1: Calculate the concentration of benzoic acid (C6H5COOH) in moles per liter (M):
Given:
Volume of solution (V) = 150.00 mL = 0.15000 L
Molarity of the benzoic acid solution (M1) = 0.15 M
Concentration of benzoic acid (C1) = Molarity (M1)
C1 = M1 = 0.15 M
Step 2: Calculate the concentration of benzoate ions (C6H5COO-) required for the desired pH:
Given:
pH (desired) = 4.25
For a buffer system containing a weak acid and its conjugate base, the Henderson-Hasselbalch equation relates the pH, pKa (acid dissociation constant), and the ratio of concentrations of the weak acid and its conjugate base:
pH = pKa + log10 ([A-] / [HA])
Since we want pH = 4.25, and we know that the weak acid is benzoic acid, which has a pKa of 4.20, we can rearrange the equation and solve for the ratio [A-] / [HA]:
4.25 = 4.20 + log10 ([A-] / [HA])
0.05 = log10 ([A-] / [HA])
Using the definition of logarithms, we can rewrite the equation as:
[A-] / [HA] = 10^0.05
[A-] / [HA] = 1.122
Step 3: Calculate the moles of benzoic acid (C6H5COOH) required to have the desired concentration of benzoate ions (C6H5COO-):
Given:
Volume of solution (V) = 150.00 mL = 0.15000 L
Moles of benzoic acid (moles of HA) = Concentration of benzoic acid (C1) * Volume of solution (V)
moles of HA = C1 * V
Step 4: Calculate the moles of benzoate ions (C6H5COO-) required based on the ratio determined in step 2:
Moles of benzoate ions (moles of A-) = Moles of benzoic acid (moles of HA) * ([A-] / [HA])
moles of A- = moles of HA * ([A-] / [HA])
Step 5: Calculate the mass of sodium benzoate (C6H5COONa) needed based on the moles of benzoate ions:
Molar mass of sodium benzoate (C6H5COONa) = mass / moles
mass = moles of benzoate ions (A-) * Molar mass of sodium benzoate (C6H5COONa)
Finally, plug in the values from the previous steps and calculate the mass of sodium benzoate needed to create the desired buffer solution.