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Ch.14 - Solutions
Chapter 14, Problem 112

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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Key Concepts

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

Osmotic Pressure

Osmotic pressure is the pressure required to prevent the flow of solvent into a solution through a semipermeable membrane. It is directly proportional to the concentration of solute particles in the solution, as described by the formula π = iCRT, where π is osmotic pressure, i is the van 't Hoff factor (number of particles the solute dissociates into), C is the molar concentration, R is the ideal gas constant, and T is the temperature in Kelvin.
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Van 't Hoff Factor

The van 't Hoff factor (i) indicates the number of particles into which a solute dissociates in solution. For magnesium citrate, which dissociates into three magnesium ions (Mg²⁺) and two citrate ions (C6H5O7³⁻), the total number of particles is five. This factor is crucial for calculating osmotic pressure, as it affects the effective concentration of solute particles in the solution.
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Molarity and Dilution

Molarity (M) is a measure of concentration defined as the number of moles of solute per liter of solution. To calculate osmotic pressure, one must first determine the molarity of magnesium citrate in the solution. This involves converting the mass of magnesium citrate into moles using its molar mass and then dividing by the volume of the solution in liters. Understanding molarity is essential for accurately applying the osmotic pressure formula.
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Related Practice
Textbook Question

The Safe Drinking Water Act (SDWA) sets a limit for mercury—a toxin to the central nervous system—at 0.0020 ppm by mass. Water suppliers must periodically test their water to ensure that mercury levels do not exceed this limit. Suppose water becomes contaminated with mercury at twice the legal limit (0.0040 ppm). How much of this water would a person have to consume to ingest 50.0 mg of mercury?

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Textbook Question

Water softeners often replace calcium ions in hard water with sodium ions. Since sodium compounds are soluble, the presence of sodium ions in water does not cause the white, scaly residues caused by calcium ions. However, calcium is more beneficial to human health than sodium because calcium is a necessary part of the human diet, while high levels of sodium intake are linked to increases in blood pressure. The U.S. Food and Drug Administration (FDA) recommends that adults ingest less than 2.4 g of sodium per day. How many liters of softened water, containing a sodium concentration of 0.050% sodium by mass, would a person have to consume to exceed the FDA recommendation? (Assume a water density of 1.0 g/mL.)

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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

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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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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