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8.3: Concentrations of Solutions (Problems)

  • Page ID
    119753
  • 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?

    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 Ca2+ ions in a water sample with a hardness count of 175 mg CaCO3/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 H3PO4 and water in a solution of 14.5 g of H3PO4 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 HNO3 and water in a concentrated solution of nitric acid (68.0% HNO3 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:

    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
    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

    \(X_\mathrm{I_2}=0.035\)

    \(X_\mathrm{EtOH}=0.965\)

    Click here to see a video of the solution

    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
    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, H3PO4, in a solution of 14.5 g of H3PO4 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% HNO3 by mass)?

    Answer

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

    Answer

    1.08 m

     

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