SAMPLE PROBLEM 8.1. Solutions of Electrolytes and Nonelectrolytes SOLUTION STUDY CHECK

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SAMPLE PROBLEM 8.1

Solutions of Electrolytes and Nonelectrolytes

Indicate whether solutions of each of the following contain only ions, only molecules, or mostly molecules and a few ions:

a. Na₂SO₄, a strong electrolyte b. CH₃OH, a nonelectrolyte

a. A solution of Na₂SO₄ contains only the ions Na⁺ and SO₄^2–. b. A nonelectrolyte such as CH₃OH dissolves only as molecules.

SOLUTION

STUDY CHECK

Boric acid, H₃BO₃, is a weak electrolyte. Would you expect a boric acid solution to contain only ions, only molecules, or mostly molecules and a few ions?

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SAMPLE PROBLEM 8.2

Electrolyte Concentration

In body fluids, concentrations of electrolytes are often expressed as milliequivalents (mEq) per liter. A typical concentration for Ca²⁺ in the blood is 8.8 mEq/L.

a. How many moles of calcium ion are in 0.50 L of blood?

b. If chloride ion is the only other ion present, what is its concentration in mEq/L?

STUDY CHECK

A Ringer’s solution for intravenous fluid replacement contains 155 mEq Cl^– per liter of solution. If a patient receives 1250 mL of Ringer’s solution, how many moles of chloride were given?

a. Using the volume and the electrolyte concentration (in mEq/L), we can find the number of equivalents in 0.50 L of blood:

SOLUTION

We can then convert equivalents to moles (for Ca²⁺ there are 2 Eq per mole):

b. If the concentration of Ca²⁺ is 8.8 mEq/L, then the concentration of Cl^– must be 8.8 mEq/L to balance the charge.

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SAMPLE PROBLEM 8.3

Saturated Solutions

At 20 ˚C, the solubility of KCl is 34 g/100 g of water. In the laboratory, a student mixes 75 g of KCl with 200. g of water at a temperature of 20 ˚C.

a. How much of the KCl can dissolve?

b. Is the solution saturated or unsaturated?

c. What is the mass of any solid KCl in the bottom of the container?

STUDY CHECK

At 50 ˚C, the solubility of NaNO₃ is 110 g/100 g of water. How many grams of NaNO₃ are needed to make a saturated NaNO₃ solution with 50. g of water at 50 ˚C?

a. KCl has a solubility of 34 g of KCl in 100 g of water. Using solubility as a conversion factor, the maximum amount of KCl that can dissolve in 200. g of water is calculated as follows:

SOLUTION

b. Because 75 g of KCl exceeds the amount that can dissolve in 200. g of water, the KCl solution is saturated.

c. If we add 75 g of KCl to 200. g of water and only 68 g of KCl can dissolve, there is 7 g of solid (undissolved) KCl on the bottom of the container.

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SAMPLE PROBLEM 8.4

Factors Affecting Solubility

Indicate whether the solubility of the solute will increase or decrease in each of the following situations:

a. dissolving sugar using 80 ˚C water instead of 25 ˚C water b. effect on the dissolved O₂ in a lake as it warms

STUDY CHECK

At 10 ˚C, the solubility of KNO₃ is 30 g/100 g H₂O. Would you expect the solubility of KNO₃ to be higher or lower at 40 ˚C? Explain.

a. An increase in the temperature increases the solubility of the sugar.

b. An increase in the temperature decreases the solubility of O₂ gas.

SOLUTION

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SAMPLE PROBLEM 8.5

Formation of an Insoluble Salt

STEP 2 BaSO₄(s) is insoluble.

STUDY CHECK

Predict whether a solid might form in each of the following mixtures of solutions. If so, write the net ionic equation for the reaction.

a. NH₄Cl(aq) + Ca(NO₃)₂(aq) b. Pb(NO₃)₂(aq) + KCl(aq) Solutions of BaCl₂ and K₂SO₄ are mixed and a white solid forms.

a. Write the net ionic equation.

b. What is the white solid that forms?

SOLUTION

a. STEP 1

STEP 3

STEP 4

b. BaSO₄ is the white solid.

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SAMPLE PROBLEM 8.6

Calculating Mass Percent

STEP 2 Plan The mass percent is calculated by using the mass in grams of the solute and solution in the definition of mass percent.

SOLUTION

STEP 1 Given 30.0 g of NaOH and 120.0 g of H₂O Need mass percent (m/m) of NaOH

What is the mass percent of a solution prepared by dissolving 30.0 g of NaOH in 120.0 g of H₂O?

STEP 3 Equalities/Conversion Factors

STEP 4 Set Up Problem The mass of the solute and the solution are obtained from the data:

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SAMPLE PROBLEM 8.6

Calculating Mass Percent (Continued)

STUDY CHECK

What is the mass percent (m/m) of NaCl in a solution made by dissolving 2.0 g of NaCl in 56.0 g of H₂O?

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SAMPLE PROBLEM 8.7

Calculating Percent Concentration

STEP 2 Plan The mass/volume percent is calculated by using the mass in grams of the solute and the volume in mL of the solution in the definition of mass/volume percent.

SOLUTION

STEP 1 Given 5.0 g of KI and 250 mL of solution Need mass/volume percent (m/v) of KI

A student prepared a solution by dissolving 5.0 g of KI in enough water to give a final volume of 250 mL. What is the mass/volume percent (m/v) of the KI solution?

STEP 3 Equalities/Conversion Factors Write the mass/volume percent expression.

STEP 4 Set Up Problem Substitute solute and solution quantities into the mass/volume percent expression.

STUDY CHECK

What is the mass/volume percent (m/v) of Br₂ in a solution prepared by dissolving 12 g of bromine (Br₂) in enough carbon tetrachloride to make 250 mL of solution?

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A topical antibiotic is 1.0% (m/v) Clindamycin. How many grams of Clindamycin are in 60. mL of the 1.0% (m /v) solution?

SAMPLE PROBLEM 8.8

Using Mass/Volume Percent to Find Mass of Solute

SOLUTION

STEP 1 Given 1.0% (m/v) Clindamycin Need grams of Clindamycin STEP 2 Plan

STEP 3 Equalities/Conversion Factors The percent (m/v) indicates the grams of a solute in every 100 mL of a solution. The 1.0% (m/v) can be

written as two conversion factors:

STEP 4 Set Up Problem The volume of the solution is converted to mass of solute using the conversion factor:

STUDY CHECK

Calculate the grams of KCl in 225 g of an 8.00% (m/m) KCl solution.

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SAMPLE PROBLEM 8.9

Calculating Molarity

SOLUTION

STEP 1 Given 60.0 g of NaOH in 0.250 L of solution Need molarity (moles/L)

What is the molarity (M) of 60.0 g of NaOH in 0.250 L of solution?

STEP 2 Plan The calculation of molarity requires the moles of NaOH and the volume of the solution in liters.

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SAMPLE PROBLEM 8.9

Calculating Molarity (Continued)

SOLUTION

What is the molarity (M) of 60.0 g of NaOH in 0.250 L of solution?

STEP 4 Set Up Problem

The molarity is calculated by dividing the moles of NaOH by the volume in liters.

STUDY CHECK

What is the molarity of a solution that contains 75.0 g of KNO₃ dissolved in 0.350 L of solution?

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How many liters of a 2.00 M NaCl solution are needed to provide 67.3 g of NaCl?

SAMPLE PROBLEM 8.10

Using Molarity to Find Volume

SOLUTION

STEP 1 Given 67.3 g of NaCl from a 2.00 M NaCl solution Need liters of NaCl solution

STEP 2 Plan The volume of the NaCl solution is calculated using the moles of NaCl and molarity of the NaCl solution:

The molarity of any solution can be written as two conversion factors:

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How many liters of a 2.00 M NaCl solution are needed to provide 67.3 g of NaCl?

SAMPLE PROBLEM 8.10

Using Molarity to Find Volume (Continued)

SOLUTION

STUDY CHECK

How many moles of HCl are present in 750 mL of a 6.0 M HCl solution?

STEP 4 Set Up Problem

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SAMPLE PROBLEM 8.11

Molarity of a Diluted Solution

STEP 2 Plan The unknown molarity can be calculated by solving the dilution expression for M₂:

What is the molarity of a solution prepared when 75.0 mL of a 4.00 M KCl solution is diluted to a volume of 0.500 L?

SOLUTION

STEP 1 Give Data in a Table We make a table of the molar concentrations and volumes of the initial and diluted solutions. For the calculation, units must be the same.

STEP 3 Set Up Problem The values from the table are placed into the dilution expression:

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SAMPLE PROBLEM 8.12

Volume of a Solution in a Reaction

SOLUTION

STEP 1 Given 5.32 g of Zn and a 1.50 M HCl solution Need liters of HCl solution

Zinc reacts with HCl to produce ZnCl₂ and hydrogen gas H₂:

How many liters of a 1.50 M HCl solution completely react with 5.32 g of zinc?

STEP 2 Plan We start the problem with the grams of Zn given and use its molar mass to calculate moles. Then we can use the mole–mole factor from the equation and the molarity of the HCl as conversion factors:

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SAMPLE PROBLEM 8.12

Volume of a Solution in a Reaction (Continued)

SOLUTION

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SAMPLE PROBLEM 8.12

Volume of a Solution in a Reaction (Continued)

SOLUTION

STUDY CHECK

Using the reaction in Sample Problem 8.12, how many grams of zinc can react with 225 mL of 0.200 M HCl solution?

STEP 4 Set Up Problem We can write the problem setup as seen in our plan:

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SAMPLE PROBLEM 8.13

Isotonic, Hypotonic, and Hypertonic Solutions

Describe each of the following solutions as isotonic, hypotonic, or hypertonic. Indicate whether a red blood cell placed in each solution will undergo hemolysis, crenation, or no change.

a. a 5.0% (m/v) glucose solution b. a 0.2% (m/v) NaCl solution

a. A 5.0% (m/v) glucose solution is isotonic. A red blood cell will not undergo any change.

b. A 0.2% (m/v) NaCl solution is hypotonic. A red blood cell will undergo hemolysis.

SOLUTION

STUDY CHECK

What is the effect of a 10% (m/v) glucose solution on a red blood cell?