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Chapter 11: Problem 135

Formic acid \(\left(\mathrm{HCO}_{2} \mathrm{H}\right)\) is a monoprotic acid that ionizes only partially in aqueous solutions. A \(0.10-M\) formic acid solution is 4.2\(\%\) ionized. Assuming that the molarity and molality of the solution are the same, calculate the freezing point and the boiling point of 0.10\(M\) formic acid.

Short Answer

Expert verified
The freezing point of the 0.10 M formic acid solution is -0.194 °C, and the boiling point is 100.053 °C.

Step by step solution

01

Calculate the van't Hoff factor

Given that a 0.10 M formic acid solution is 4.2% ionized, we can determine the van't Hoff factor. The van't Hoff factor represents the number of particles produced after ionization. For formic acid, the ionization reaction is: HCO2H (aq) \(\leftrightarrows\) HCO2⁻ (aq) + H⁺ (aq) The van't Hoff factor, i, can be calculated using the following formula: i = 1 + degree of ionization In this case, the degree of ionization is 4.2%, which is equal to 0.042, so, i = 1 + 0.042 = 1.042
02

Calculate the freezing point

Use the freezing point depression formula to determine the new freezing point: ΔTf = i × Kf × m where ΔTf is the freezing point depression, i is the van't Hoff factor, Kf is the freezing point depression constant for water (1.86 °C kg/mol), and m is the molality (equal to molarity, as given in the problem, 0.10 M). ΔTf = 1.042 × 1.86 °C kg/mol × 0.10 mol/kg = 0.194 °C The freezing point of the formic acid solution is the difference between the freezing point of pure water (0 °C) and the freezing point depression: Tf = 0 °C - 0.194 °C = -0.194 °C
03

Calculate the boiling point

Use the boiling point elevation formula to determine the new boiling point: ΔTb = i × Kb × m where ΔTb is the boiling point elevation, i is the van't Hoff factor, Kb is the boiling point elevation constant for water (0.512 °C kg/mol), and m is the molality (equal to molarity, as given in the problem, 0.10 M). ΔTb = 1.042 × 0.512 °C kg/mol × 0.10 mol/kg = 0.053 °C The boiling point of the formic acid solution is the sum of the boiling point of pure water (100 °C) and the boiling point elevation: Tb = 100 °C + 0.053 °C = 100.053 °C In conclusion, the freezing point of the 0.10 M formic acid solution is -0.194 °C, and the boiling point is 100.053 °C.

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