To determine a pH range for which a buffer system containing benzoic acid would be appropriate, you need to consider the pKa of benzoic acid. The pKa is a measure of the acid's tendency to lose a proton and become its conjugate base.
In this case, benzoic acid (C6H5COOH) dissociates into its conjugate base, called benzoate (C6H5COO-), and a proton (H+). The pKa of benzoic acid is 4.20.
For a buffer solution to function effectively, the pH of the solution should be within approximately ±1 unit of the pKa value. In this case, a suitable pH range for the buffer system containing benzoic acid would be around 3.20 to 5.20.
Now, let's devise a recipe for preparing a 1.0 L buffer solution with a pH of 4.48 and a total of 0.150 mol of buffer components (acid plus conjugate base):
Step 1: Calculate the ratio of benzoic acid to sodium benzoate required to achieve the desired pH.
Since the Henderson-Hasselbalch equation for a buffer system is pH = pKa + log([conjugate base]/[acid]), we can rearrange the equation to solve for the ratio:
[conjugate base]/[acid] = 10^(pH - pKa)
Plugging in the values, [conjugate base]/[acid] = 10^(4.48 - 4.20) = 2.5119.
Step 2: Determine the amount of benzoic acid and sodium benzoate needed.
First, calculate the moles of benzoic acid and sodium benzoate required using the total moles of buffer components:
moles of benzoic acid = [acid] = (0.150 mol) / (1 + 2.5119) = 0.05768 mol
moles of sodium benzoate = [conjugate base] = (0.05768 mol) * 2.5119 = 0.145 mols
Step 3: Calculate the masses of benzoic acid and sodium benzoate.
Using the molar masses of benzoic acid (C6H5COOH) and sodium benzoate (C6H5COONa):
mass of benzoic acid = moles of benzoic acid * molar mass of benzoic acid
mass of sodium benzoate = moles of sodium benzoate * molar mass of sodium benzoate
Step 4: Dissolve and mix the calculated masses of benzoic acid and sodium benzoate in distilled water to make a 1.0 L solution.
Make sure to calculate the volume of water needed accurately, as you need a total volume of 1.0 L.
That's it! You have now prepared a 1.0 L buffer solution that contains a total of 0.150 mol of buffer components and has a pH of 4.48, using benzoic acid and sodium benzoate as the buffer components.