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Chapter 13: Problem 44

Write the equation relating osmotic pressure to the concentration of a solution. Define all the terms and give their units.

Short Answer

Expert verified
The equation relating osmotic pressure \(\Pi\) to the concentration of a solution is given by the van't Hoff equation, \(\Pi = iCRT\), where \(i\) is the van't Hoff factor, \(C\) is the molar concentration (mol/L), \(R\) is the gas constant (8.314 J/(mol.K)), and \(T\) is the absolute temperature (K). The osmotic pressure (\(\Pi\)) is often measured in Pascals (Pa).

Step by step solution

01

Writing the General Equation

Start by writing the basic van't Hoff equation relating the osmotic pressure to the concentration of a solution: \[ \Pi = iCRT \]
02

Defining the Terms

Define each of the terms:\n\n1. \(\Pi\): This is the osmotic pressure of the solution.\n\n2. \(i\): This is the van't Hoff factor. This factor is the number of particles a solute contributes to the solution. For example, in an ideal solution, glucose (\(i = 1\)) and sodium chloride (\(i = 2\)) since it dissociates into Na and Cl ions.\n\n3. \(C\): This is the molar concentration of the solute in the solution.\n\n4. \(R\): This is the universal gas constant. Its value is 8.314 J/(mol.K) in SI units.\n\n5. \(T\): This is the absolute temperature in Kelvin (K).
03

Providing the Units

Give the units for each term:\n\n1. \(\Pi\): The osmotic pressure is usually measured in Pascals (Pa), but in biological and medical situations, it is often given in atmospheres (atm) or millimeters of Mercury (mmHg).\n\n2. \(i\): The van't Hoff factor is a dimensionless quantity, so it has no units.\n\n3. \(C\): The molar concentration of the solute is typically provided in moles per liter (mol/L).\n\n4. \(R\): The universal gas constant, \(R\), is typically given in Joules per mole-Kelvin (J/(mol.K)).\n\n5. \(T\): The absolute temperature in Kelvin (K).

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Most popular questions from this chapter

Calculate the molality of each of the following aqueous solutions: (a) \(2.50 \mathrm{M} \mathrm{NaCl}\) solution (density of solution \(=1.08 \mathrm{~g} / \mathrm{mL}\) ), (b) 48.2 percent by mass KBr solution.

Calculate the molalities of these aqueous solutions: (a) \(1.22 M\) sugar \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) solution (density of solution \(=1.12 \mathrm{~g} / \mathrm{mL}\) ), (b) \(0.87 \mathrm{M} \mathrm{NaOH}\) solution (density of solution \(=1.04 \mathrm{~g} / \mathrm{mL}),(\mathrm{c})\) \(5.24 \mathrm{M} \mathrm{NaHCO}_{3}\) solution (density of solution \(=\) \(1.19 \mathrm{~g} / \mathrm{mL})\)

Arrange these aqueous solutions in order of decreasing freezing point and explain your reasons: (a) \(0.50 \mathrm{~m}\) \(\mathrm{HCl},\) (b) \(0.50 \mathrm{~m}\) glucose, (c) \(0.50 \mathrm{~m}\) acetic acid.

How does each of the following affect the solubility of an ionic compound: (a) lattice energy, (b) solvent (polar versus nonpolar), (c) enthalpies of hydration of cation and anion?

A solution of \(2.50 \mathrm{~g}\) of a compound of empirical formula \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{P}\) in \(25.0 \mathrm{~g}\) of benzene is observed to freeze at \(4.3^{\circ} \mathrm{C}\). Calculate the molar mass of the solute and its molecular formula.
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