Measured freezing point depression point of a 0.1m aq. Acetic acid solution is 0.19oC. The acid dissociation constant at this concentration will be (in the multiple of 10–5):Correct answer is '4'. Can you explain this answer?

Question

Measured freezing point depression point of a 0.1m aq. Acetic acid solution is 0.19oC. The acid dissociation constant at this concentration will be (in the multiple of 10&ndash;5):Correct answer is '4'. Can you explain this answer?

Answer

Answer

To determine the acid dissociation constant (Ka) at a given concentration, we can use the formula:

ΔTf = Kf * m

where ΔTf is the freezing point depression, Kf is the cryoscopic constant (which is a constant for the solvent), and m is the molality of the solution.

In this case, we are given the freezing point depression (ΔTf) as 0.19°C and the molality (m) as 0.1 mol/kg.

Now, we need to find the cryoscopic constant (Kf) for the solvent, which is water in this case. The cryoscopic constant for water is 1.86 °C/m.

Substituting the given values into the formula:

0.19°C = 1.86 °C/m * 0.1 mol/kg

Now, we can rearrange the equation to solve for the acid dissociation constant (Ka):

Ka = ΔTf / (Kf * m)
= 0.19°C / (1.86 °C/m * 0.1 mol/kg)
= 0.19 / (1.86 * 0.1)
= 0.19 / 0.186
≈ 1.02

Therefore, the acid dissociation constant at this concentration is approximately 1.02.

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