PROBLEM \(\PageIndex{1}\)
What mass of a concentrated solution of nitric acid (68.0% HNO_{3} by mass) is needed to prepare 400.0 g of a 10.0% solution of HNO_{3} by mass?
 Answer

58.8 g
PROBLEM \(\PageIndex{2}\)
What mass of a 4.00% NaOH solution by mass contains 15.0 g of NaOH?
 Answer

375 g
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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.
 Answer

\(\mathrm{114 \;g}\)
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 Ca^{2+} ions in a water sample with a hardness count of 175 mg CaCO_{3}/L?
 Answer

\(1.75 \times 10^{−3} M\)
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.
 Answer

0.148 M
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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?
 Answer

\(\mathrm{2.38 \times 10^{−4}\: mol}\)
PROBLEM \(\PageIndex{7}\)
What are the mole fractions of H_{3}PO_{4} and water in a solution of 14.5 g of H_{3}PO_{4} in 125 g of water?
 Answer

\(X_\mathrm{H_3PO_4}=0.021\)
\(X_\mathrm{H_2O}=0.979\)
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PROBLEM \(\PageIndex{8}\)
What are the mole fractions of HNO_{3} and water in a concentrated solution of nitric acid (68.0% HNO_{3} by mass)?
 Answer

\(X_\mathrm{HNO_3}=0.378\)
\(X_\mathrm{H_2O}=0.622\)
PROBLEM \(\PageIndex{9}\)
Calculate the mole fraction of each solute and solvent:
 583 g of H_{2}SO_{4} in 1.50 kg of water—the acid solution used in an automobile battery
 0.86 g of NaCl in 1.00 × 10^{2} g of water—a solution of sodium chloride for intravenous injection
 46.85 g of codeine, C_{18}H_{21}NO_{3}, in 125.5 g of ethanol, C_{2}H_{5}OH
 25 g of I_{2} in 125 g of ethanol, C_{2}H_{5}OH
 Answer a

\(X_\mathrm{H_2SO_4}=0.067\)
\(X_\mathrm{H_2O}=0.933\)
 Answer b

\(X_\mathrm{HCl}=0.0026\)
\(X_\mathrm{H_2O}=0.9974\)
 Answer c

\(X_\mathrm{codiene}=0.054\)
\(X_\mathrm{EtOH}=0.946\)
 Answer d

\(X_\mathrm{I_2}=0.035\)
\(X_\mathrm{EtOH}=0.965\)
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PROBLEM \(\PageIndex{10}\)
Calculate the mole fraction of each solute and solvent:
 0.710 kg of sodium carbonate (washing soda), Na_{2}CO_{3}, in 10.0 kg of water—a saturated solution at 0 °C
 125 g of NH_{4}NO_{3} in 275 g of water—a mixture used to make an instant ice pack
 25 g of Cl_{2} in 125 g of dichloromethane, CH_{2}Cl_{2}
 0.372 g of histamine, C_{5}H_{9}N, in 125 g of chloroform, CHCl_{3}
 Answer a

\(X_\mathrm{Na_2CO_3}=0.0119\)
\(X_\mathrm{H_2O}=0.988\)
 Answer b

\(X_\mathrm{NH_4NO_3}=0.09927\)
\(X_\mathrm{H_2O}=0.907\)
 Answer c

\(X_\mathrm{Cl_2}=0.192\)
\(X_\mathrm{CH_2CI_2}=0.808\)
 Answer d

\(X_\mathrm{C_5H_9N}=0.00426\)
\(X_\mathrm{CHCl_3}=0.997\)
PROBLEM \(\PageIndex{11}\)
What is the difference between a 1 M solution and a 1 m solution?
 Answer

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, H_{3}PO_{4}, in a solution of 14.5 g of H_{3}PO_{4} in 125 g of water?
 Answer

1.18 m
PROBLEM \(\PageIndex{13}\)
What is the molality of nitric acid in a concentrated solution of nitric acid (68.0% HNO_{3} by mass)?
 Answer

33.7 m
PROBLEM \(\PageIndex{14}\)
Calculate the molality of each of the following solutions:
 0.710 kg of sodium carbonate (washing soda), Na_{2}CO_{3}, in 10.0 kg of water—a saturated solution at 0°C
 125 g of NH_{4}NO_{3} in 275 g of water—a mixture used to make an instant ice pack
 25 g of Cl_{2} in 125 g of dichloromethane, CH_{2}Cl_{2}
 0.372 g of histamine, C_{5}H_{9}N, in 125 g of chloroform, CHCl_{3}
 Answer

6.70 × 10^{−1} m
 Answer

5.67 m
 Answer

2.8 m
 Answer

0.0358 m
PROBLEM \(\PageIndex{15}\)
A 13.0% solution of K_{2}CO_{3} by mass has a density of 1.09 g/cm^{3}. Calculate the molality of the solution.
 Answer

1.08 m
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