What are the concentrations of benzoic acid and sodium benzoate in a solution that is buffered with a pH of 4.55 and has a freezing point of -2.0 degrees Celsius? (assume complete dissociation and a density of 1.01g/mL for the solution.)
Several steps to this problem. Here is an outline.
1. Use the HH equation and solve for the ratio of base/acid; i.e., sodium benzoate to benzoic acid. Then convert that to percent of each.
2. Use the percents to calculate a van't Hoff factor. That is 2*%base + 1*%acid = total = i
3. Use delta T = iKf*m and solve for m
4. Use density to convert molality to molarity
5. Use the percents to convert to M of each component.
Good luck. Post your work if you get stuck.
To determine the concentrations of benzoic acid and sodium benzoate in the solution, we need to use the Henderson-Hasselbalch equation and the freezing point depression equation.
1. Henderson-Hasselbalch Equation:
The Henderson-Hasselbalch equation relates the pH of a buffer solution to the ratio of the concentrations of the acid and its conjugate base. It is given by the equation:
pH = pKa + log([base]/[acid])
In this case, benzoic acid (C6H5COOH) acts as the acid, and sodium benzoate (C6H5COONa) acts as the conjugate base. The pKa of benzoic acid is 4.20.
2. Freezing Point Depression Equation:
The freezing point depression (∆Tf) of a solution is related to the molality (m) of the solute. For a non-electrolyte, the equation is:
∆Tf = Kf * m
Where Kf is the molal freezing point depression constant, and m is the molality of the solute in the solution.
To solve the problem, we need to follow these steps:
Step 1: Calculate the molality (m):
We can use the density of the solution to calculate the moles of solute (benzoic acid + sodium benzoate) per kilogram of solvent (water).
Assuming a density of 1.01 g/mL, we convert it to kg/L by dividing by 1000:
density = 1.01 g/mL = 1.01 g/cm^3 = 1.01 kg/L
Step 2: Calculate the freezing point depression (∆Tf):
The freezing point depression (∆Tf) can be calculated using the formula:
∆Tf = Kf * m
Assuming a freezing point depression constant (Kf) of water as 1.86 °C/kg·molal, we can calculate ∆Tf.
Step 3: Substitute the values in the Henderson-Hasselbalch equation:
Using the given pH of 4.55 and the pKa of benzoic acid as 4.20, we can substitute those values into the Henderson-Hasselbalch equation:
4.55 = 4.20 + log([base]/[acid])
Step 4: Solve for the ratio of [base]/[acid]:
Rearrange the Henderson-Hasselbalch equation to solve for the ratio [base]/[acid]:
[base]/[acid] = 10^(pH - pKa)
Step 5: Calculate the concentrations of benzoic acid and sodium benzoate:
Using the obtained ratio [base]/[acid], we can calculate the concentrations of benzoic acid ([acid]) and sodium benzoate ([base]).
Please note that a few extra pieces of information are needed, such as the molality or moles of solute, to determine the exact concentrations of benzoic acid and sodium benzoate.