# 7.2.1: Concentrations of Solutions (Problems)

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PROBLEM $$\PageIndex{1}$$

What mass of a concentrated solution of nitric acid (68.0% HNO3 by mass) is needed to prepare 400.0 g of a 10.0% solution of HNO3 by mass?

58.8 g

PROBLEM $$\PageIndex{2}$$

What mass of a 4.00% NaOH solution by mass contains 15.0 g of NaOH?

375 g

PROBLEM $$\PageIndex{3}$$

What mass of solid NaOH (97.0% NaOH by mass) is required to prepare 1.00 L of a 10.0% solution of NaOH by mass? The density of the 10.0% solution is 1.109 g/mL.

$$\mathrm{114 \;g}$$

PROBLEM $$\PageIndex{4}$$

The hardness of water (hardness count) is usually expressed in parts per million (by mass) of $$\ce{CaCO_3}$$, which is equivalent to milligrams of $$\ce{CaCO_3}$$ per liter of water. What is the molar concentration of Ca2+ ions in a water sample with a hardness count of 175 mg CaCO3/L?

$$1.75 \times 10^{−3} M$$

PROBLEM $$\PageIndex{5}$$

A throat spray is 1.40% by mass phenol, $$\ce{C_6H_5OH}$$, in water. If the solution has a density of 0.9956 g/mL, calculate the molarity of the solution.

0.148 M

PROBLEM $$\PageIndex{6}$$

Copper(I) iodide (CuI) is often added to table salt as a dietary source of iodine. How many moles of CuI are contained in 1.00 lb (454 g) of table salt containing 0.0100% CuI by mass?

$$\mathrm{2.38 \times 10^{−4}\: mol}$$

PROBLEM $$\PageIndex{7}$$

What are the mole fractions of H3PO4 and water in a solution of 14.5 g of H3PO4 in 125 g of water?

$$X_\mathrm{H_3PO_4}=0.021$$

$$X_\mathrm{H_2O}=0.979$$

PROBLEM $$\PageIndex{8}$$

What are the mole fractions of HNO3 and water in a concentrated solution of nitric acid (68.0% HNO3 by mass)?

$$X_\mathrm{HNO_3}=0.378$$

$$X_\mathrm{H_2O}=0.622$$

PROBLEM $$\PageIndex{9}$$

Calculate the mole fraction of each solute and solvent:

1. 583 g of H2SO4 in 1.50 kg of water—the acid solution used in an automobile battery
2. 0.86 g of NaCl in 1.00 × 102 g of water—a solution of sodium chloride for intravenous injection
3. 46.85 g of codeine, C18H21NO3, in 125.5 g of ethanol, C2H5OH
4. 25 g of I2 in 125 g of ethanol, C2H5OH

$$X_\mathrm{H_2SO_4}=0.067$$

$$X_\mathrm{H_2O}=0.933$$

$$X_\mathrm{HCl}=0.0026$$

$$X_\mathrm{H_2O}=0.9974$$

$$X_\mathrm{codiene}=0.054$$

$$X_\mathrm{EtOH}=0.946$$

$$X_\mathrm{I_2}=0.035$$

$$X_\mathrm{EtOH}=0.965$$

PROBLEM $$\PageIndex{10}$$

Calculate the mole fraction of each solute and solvent:

1. 0.710 kg of sodium carbonate (washing soda), Na2CO3, in 10.0 kg of water—a saturated solution at 0 °C
2. 125 g of NH4NO3 in 275 g of water—a mixture used to make an instant ice pack
3. 25 g of Cl2 in 125 g of dichloromethane, CH2Cl2
4. 0.372 g of histamine, C5H9N, in 125 g of chloroform, CHCl3

$$X_\mathrm{Na_2CO_3}=0.0119$$

$$X_\mathrm{H_2O}=0.988$$

$$X_\mathrm{NH_4NO_3}=0.09927$$

$$X_\mathrm{H_2O}=0.907$$

$$X_\mathrm{Cl_2}=0.192$$

$$X_\mathrm{CH_2CI_2}=0.808$$

$$X_\mathrm{C_5H_9N}=0.00426$$

$$X_\mathrm{CHCl_3}=0.997$$

PROBLEM $$\PageIndex{11}$$

What is the difference between a 1 M solution and a 1 m solution?

In a 1 M solution, the mole is contained in exactly 1 L of solution. In a 1 m solution, the mole is contained in exactly 1 kg of solvent.

PROBLEM $$\PageIndex{12}$$

What is the molality of phosphoric acid, H3PO4, in a solution of 14.5 g of H3PO4 in 125 g of water?

1.18 m

PROBLEM $$\PageIndex{13}$$

What is the molality of nitric acid in a concentrated solution of nitric acid (68.0% HNO3 by mass)?

33.7 m

PROBLEM $$\PageIndex{14}$$

Calculate the molality of each of the following solutions:

1. 0.710 kg of sodium carbonate (washing soda), Na2CO3, in 10.0 kg of water—a saturated solution at 0°C
2. 125 g of NH4NO3 in 275 g of water—a mixture used to make an instant ice pack
3. 25 g of Cl2 in 125 g of dichloromethane, CH2Cl2
4. 0.372 g of histamine, C5H9N, in 125 g of chloroform, CHCl3

6.70 × 10−1 m

5.67 m

2.8 m

0.0358 m

PROBLEM $$\PageIndex{15}$$

A 13.0% solution of K2CO3 by mass has a density of 1.09 g/cm3. Calculate the molality of the solution.