What should the molar concentrations of benzoic acid and sodium benzoate be in a solution that is buffered at a pH of 4.75 and has a freezing point of -2.0 ∘C? (Assume complete dissociation of sodium benzoate and a density of 1.01 g/mL for the solution.)
To determine the molar concentrations of benzoic acid and sodium benzoate in the solution, we can utilize the Henderson-Hasselbalch equation and the equations related to freezing point depression.
1. Henderson-Hasselbalch Equation:
The Henderson-Hasselbalch equation relates the pH of a buffer solution to the pKa of the acid and the ratio of the concentrations of the acid and its conjugate base. The equation is as follows:
pH = pKa + log([A-]/[HA])
where:
pH = the desired pH of the buffered solution (4.75)
pKa = the dissociation constant of the acid (benzoic acid)
[A-] = concentration of the conjugate base (sodium benzoate)
[HA] = concentration of the acid (benzoic acid)
2. Freezing Point Depression:
The freezing point depression equation relates the freezing point depression (∆Tf) to the molality (m) of a solute in a solvent. The equation is as follows:
∆Tf = Kf * m
where:
∆Tf = freezing point depression (-2.0 ∘C)
Kf = cryoscopic constant for the solvent
m = molality of the solute in the solution
To calculate molality, we need the moles of the solute (benzoic acid and sodium benzoate) and the mass of the solvent (solution). We know that the density of the solution is 1.01 g/mL.
Now, let's break down the steps to find the molar concentrations:
Step 1: Finding pKa
The pKa value for benzoic acid is 4.20. This value is generally available in chemical databases or can be found in reference books.
Step 2: Finding the concentration of [A-] using the Henderson-Hasselbalch equation.
Given:
pH = 4.75
pKa = 4.20
Rearranging the Henderson-Hasselbalch equation, we have:
[A-]/[HA] = 10^(pH - pKa)
[A-]/[HA] = 10^(4.75 - 4.20) = 2.5119
Step 3: Finding the molality using freezing point depression.
Given:
∆Tf = -2.0 ∘C
Kf = cryoscopic constant for the solvent (specific for each solvent)
We need to convert -2.0 ∘C to Kelvin:
∆Tf(K) = -2.0 ∘C + 273.15 = 271.15 K
Using the freezing point depression equation, we have:
∆Tf = Kf * m
We need the cryoscopic constant (Kf) for the solvent to proceed. Since the solvent is not mentioned, we cannot calculate the molality without the Kf value.
Step 4: Finding the molar concentrations
After determining the molality, we can calculate the molar concentrations of benzoic acid and sodium benzoate using the given densities and the molar masses of the compounds.
However, since we lack the Kf value for the solvent and the concentration of the solution, we cannot proceed to calculate the molar concentrations of benzoic acid and sodium benzoate accurately.
Therefore, in this case, the provided information is insufficient to calculate the desired molar concentrations.