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Ch.13 - Solutions
Chapter 13, Problem 114

When HNO2 is dissolved in water, it partially dissociates according to the equation HNO2 ⇌ H+ + NO2-. A solution is prepared that contains 7.050 g of HNO2 in 1.000 kg of water. Its freezing point is -0.2929 °C. Calculate the fraction of HNO2 that has dissociated.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Dissociation of Acids

Dissociation refers to the process by which an acid separates into its constituent ions in solution. For weak acids like HNO2, this process is not complete, meaning only a fraction of the acid molecules dissociate into hydrogen ions (H+) and nitrite ions (NO2-). Understanding the degree of dissociation is crucial for calculating properties such as freezing point depression.
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Freezing Point Depression

Freezing point depression is a colligative property that describes how the freezing point of a solvent decreases when a solute is added. The extent of this depression depends on the number of solute particles in solution, which can be calculated using the formula ΔTf = i * Kf * m, where 'i' is the van 't Hoff factor, 'Kf' is the freezing point depression constant, and 'm' is the molality of the solution.
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Molality

Molality is a measure of concentration defined as the number of moles of solute per kilogram of solvent. It is expressed in moles per kilogram (mol/kg) and is particularly useful in colligative property calculations because it remains unaffected by temperature changes. In this problem, calculating the molality of the HNO2 solution is essential for determining the extent of freezing point depression and, subsequently, the fraction of dissociated HNO2.
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Related Practice
Textbook Question

An isotonic solution contains 0.90% NaCl mass to volume. Calculate the percent mass to volume for isotonic solutions containing each solute at 25 °C. Assume a van't Hoff factor of 1.9 for all ionic solutes. a. KCl

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Textbook Question

Magnesium citrate, Mg3(C6H5O7)2, belongs to a class of laxatives called hyperosmotics, which cause rapid emptying of the bowel. When a concentrated solution of magnesium citrate is consumed, it passes through the intestines, drawing water and promoting diarrhea, usually within 6 hours. Calculate the osmotic pressure of a magnesium citrate laxative solution containing 28.5 g of magnesium citrate in 235 mL of solution at 37 °C (approximate body temperature). Assume complete dissociation of the ionic compound.

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Open Question
A solution is prepared from 4.5701 g of magnesium chloride and 43.238 g of water. The vapor pressure of water above this solution is 0.3624 atm at 348.0 K. The vapor pressure of pure water at this temperature is 0.3804 atm. What is the value of the van’t Hoff factor (i) for magnesium chloride in this solution?
Textbook Question

A solution of a nonvolatile solute in water has a boiling point of 375.3 K. Calculate the vapor pressure of water above this solution at 338 K. The vapor pressure of pure water at this temperature is 0.2467 atm.

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Textbook Question

The density of a 0.438 M solution of potassium chromate (K2CrO4) at 298 K is 1.063 g/mL. Calculate the vapor pressure of water above the solution. The vapor pressure of pure water at this temperature is 0.0313 atm. (Assume complete dissociation of the solute.)

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Textbook Question

The vapor pressure of carbon tetrachloride, CCl4, is 0.354 atm, and the vapor pressure of chloroform, CHCl3, is 0.526 atm at 316 K. A solution is prepared from equal masses of these two compounds at this temperature. Calculate the mole fraction of the chloroform in the vapor above the solution. If the vapor above the original solution is condensed and isolated into a separate flask, what will the vapor pressure of chloroform be above this new solution?

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