A 0.649 m aqueous solution of a monoprotic acid (HA) freezes at -2.34°C. Find the pKa of this monoprotic acid. Kf of water = 1.86 °C/m

dT = i*Kf*m

i = 2.34/1.86*0.649
i = 1.938 so it's not quite 2.0 which means it's 93.8% ionized.
........HA ==> H^+ + A^-
I....0.649.....0.....0
C......-x......x.....x
E....0.649-x...x.....x

You know x = 0.938*0.649 = 0.609 = (H^+). Plug those numbers into Ka expression and solve for Ka, then convert to pKa.

Ka = [H+][A-] / [HA]

2.34 / 1.86 = 1.26 M

2 x + (.649 - x) = 1.26

Ka = x^2 / (.649 - x)

pKa = -log(Ka)

To find the pKa of the monoprotic acid (HA), we first need to find the freezing point depression caused by the solute.

The freezing point depression (ΔTf) is given by the formula:

ΔTf = Kf * molality

Where:
Kf is the freezing point depression constant of water (given as 1.86 °C/m)
molality is the molal concentration of the solute (in moles/kg solvent)

The molality (m) can be calculated as:

m = moles of solute / kg of solvent

Since we are given the concentration of the solution in molarity (M), we can calculate the moles of solute by multiplying the concentration with the volume of the solution in liters.

Let's assume the kg of solvent is 1 kg (1000 g) for simplicity.

First, convert the molarity to molality:

Molarity (M) = moles of solute / volume of solution (in liters)

moles of solute = Molarity * volume of solution (L)

Since we have 0.649 m solution, the moles of solute can be calculated as:

moles of solute = 0.649 mol/L * volume of solution (L)

Now, let's calculate the ΔTf:

ΔTf = Kf * molality

ΔTf = 1.86 °C/m * moles of solute/1 kg

Since we assumed 1 kg of solvent, moles of solute = moles of solute/1 kg

Now, we know that the freezing point depression (ΔTf) is given as -2.34 °C. So we can write the equation as:

-2.34 °C = 1.86 °C/m * moles of solute/1 kg

Simplifying the equation:

moles of solute/1 kg = -2.34 °C / 1.86 °C/m

moles of solute = -2.34 °C / 1.86 °C/m * 1 kg

moles of solute = -1.258 mol

Now, we need to calculate the concentration of the solute (HA) in mol/L:

Concentration (M) = moles of solute / volume of solution (L)

0.649 mol/L = -1.258 mol / volume of solution (L)

Rearranging the equation to find the volume of solution:

volume of solution (L) = -1.258 mol / 0.649 mol/L

volume of solution (L) = -1.94 L

Since the volume of the solution cannot be negative, there seems to be an error in the calculation. Please double-check your data to ensure the correct values are used.

To find the pKa of the monoprotic acid (HA), we can use the equation relating freezing point depression to the concentration of the solute:

ΔT = Kf * m

Where:
ΔT is the change in freezing point (in °C)
Kf is the freezing point depression constant for water (given as 1.86 °C/m)
m is the molality of the solute (moles of solute per kg of solvent)

In this case, we are given the freezing point depression (ΔT) as -2.34°C and the concentration (m) as 0.649 m. However, we need to convert the molality into moles of solute per liter of solution (M).

To do this, we use the formula:

M = m * MW

Where:
M is the molarity of the solution (moles of solute per liter of solution)
m is the molality of the solute (moles of solute per kg of solvent)
MW is the molecular weight of the solute (in g/mol)

Since HA is a monoprotic acid, its molecular weight (MW) is equal to its molar mass. We'll assume the molar mass of HA is known or provided.

Once we have the molarity (M) of the solution, we can use the Henderson-Hasselbalch equation to relate the pKa of the acid and its concentration:

pKa = -log10([A-]/[HA])

Where:
pKa is the acid dissociation constant
[A-] is the concentration of the conjugate base
[HA] is the concentration of the acid

Given that we have a monoprotic acid, [HA] is equivalent to the molarity of the acid (M) we calculated from the molality (m). [A-] can be assumed to be negligibly small compared to [HA], so the equation can be simplified to:

pKa ≈ -log10(M)

Now, let's plug in the given values and calculate the pKa.

Step 1: Convert molality to molarity
M = m * MW
M = 0.649 mol/kg * MW

Step 2: Use the Henderson-Hasselbalch equation
pKa ≈ -log10(M)

By substituting the value of M that we calculated from the molality, we can find the pKa.