Chapter 1



Chapter 13. Properties of Solutions

13.4 Ways of Expressing Concentration

• All methods involve quantifying the amount of solute per amount of solvent (or solution).

• Concentration may be expressed qualitatively or quantitatively.

• The terms dilute and concentrated are qualitative ways to describe concentration.

• A dilute solution has a relatively small concentration of solute.

• A concentrated solution has a relatively high concentration of solute.

• Quantitative expressions of concentration require specific information regarding such quantities as masses, moles, or liters of the solute, solvent, or solution.

• The most commonly used expressions for concentration are:

• Mass percentage

• Mole fraction

• Molarity

• Molality

Mass percentage, ppm, and ppb

• Mass percentage is one of the simplest ways to express concentration.

• By definition:

• Similarly, parts per million (ppm) can be expressed as the number of mg of solute per kilogram of solution.

• By definition:

• If the density of the solution is 1g/ml, then 1 ppm = 1 mg solute per liter of solution.

• We can extend this again!

• Parts per billion (ppb) can be expressed as the number of µg of solute per kilogram of solution.

• By definition:

• If the density of the solution is 1g/ml, then 1 ppb = 1 µg solute per liter of solution.

Sample Exercise 13.4 (p. 542)

a) A solution is made by dissolving 13.5 g glucose (C6H12O6) in 0.100 kg of water. What is the mass percentage of solute in this solution? (11.9%)

b) A 2.5-g sample of groundwater was found to contain 5.4 μg of Zn2+. What is the concentration of Zn2+ in parts per million? (2.2 ppm)

Practice Exercise 13.4

a) Calculate the mass percentage of NaCl in a solution containing 1.50 g of NaCl in 50.0 g of water. (2.91%)

b) A commercial bleaching solution contains 3.62 mass % sodium hypochlorite, NaOCl. What is the mass of NaOCl in a bottle containing 2500 g of bleaching solution? (90.5 g NaOCl)

Mole Fraction, Molarity, and Molality

• Common expressions of concentration are based on the number of moles of one or more components.

• Recall that mass can be converted to moles using the molar mass.

• Recall:

• Note: Mole fraction has no units.

• Note: Mole fractions range from 0 to 1.

• Recall:

• Note: Molarity will change with a change in temperature (as the solution volume increases or decreases).

• We can define molality (m), yet another concentration unit:

• Molality does not vary with temperature.

• Note: converting between molarity (M) and molality (m) requires density.

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Sample Exercise 13.5 (p. 544)

A solution is made by dissolving 4.35 g glucose (C6H12O6) in 25.0 mL of water. Calculate the molality of glucose in the solution. (0.964 m)

Practice Exercise 13.5

What is the molality of a solution made by dissolving 36.5 g of naphthalene (C10H8) in 425 g of toluene (C7H8)? (0.670 m)

Sample Exercise 13.6 (p. 544)

A solution of hydrochloric acid contains 36% HCl by mass.

a) Calculate the mole fraction of HCl in the solution. (0.22)

b) Calculate the molality of HCl in the solution. (15 m)

Practice Exercise 13.6

A commercial bleach solution contains 3.62 mass % NaOCl in water.

Calculate

a) the mole fraction of NaOCl in the solution and (9.00 x 10-3)

b) the molality of NaOCl in the solution (0.505 m)

Sample Exercise 13.7 (p. 546)

A solution with a density of 0.876 g/mL contains 5.0 g of toluene (C7H8) and 225 g of benzene.

Calculate the molarity of the solution. (0.21 M)

Practice Exercise 13.7

A solution containing equal masses of glycerol (C3H8O3) and water has a density of 1.10 g/mL. Calculate

a) the molality of glycerol; (10.9 m)

b) the mole fraction of glycerol; (0.163)

c) the molarity of glycerol in the solution. (5.97 M)

13.5 Colligative Properties

• Colligative properties depend on number of solute particles.

Colligative properties are physical properties.

• There are four colligative properties to consider:

• Vapor pressure lowering (Raoult's Law).

• Boiling point elevation.

• Freezing point depression.

• Osmotic pressure.

1. Lowering the Vapor Pressure

↑ # particles ( ↓ vapor pressure

e.g. pure H2O vs. H2O + NaCl (salt water)

higher V.P. lower V.P.

Why?

1) Na+ + Cl- particles (nonvolatile solutes) get surrounded by H2O ( fewer “free” H2O particles left to vaporize at surface

2) ↑ IMFs ( harder to get out

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Figure 13.20 Vapor-pressure lowering.

The vapor pressure over a solution formed by a volatile solvent and a nonvolatile solute (b) is lower than that of the solvent alone (a).

The extent of the decrease in the vapor pressure upon addition of the solute depends on the concentration of the solute.

• Raoult’s law quantifies the extent to which a nonvolatile solute lowers the vapor pressure of the solvent.

• If PA is the vapor pressure with solute, PoA is the vapor pressure of the pure solvent, and XA is the mole fraction of A, then

• Ideal solution: one that obeys Raoult’s law.

• Real solutions show approximately ideal behavior when:

• The solute concentration is low.

• The solute and solvent have similarly sized molecules.

• The solute and solvent have similar types of intermolecular attractions.

• Raoult’s law breaks down when the solvent-solvent and solute-solute intermolecular forces are >> or ?@?A?C?T?U???ž?¥?¦?¨?©?HŽIŽrŽtŽ€Ž‚ŽƒŽ†Ž‰ŽŠŽ‹ŽŒŽ Ž¡Ž§Ž©Ž«Ž±?²?ø?û??????????.?úôîåÛÔÛåÊåÊåÀå´åÀåªåÀåîåîåú‹ÛÔÛ„ÛåÀåîåÀåîúîåúå”Û

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i = # particles when CaCl2

dissociates in H2O

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