4.E: Solutions (Exercises)

Exercises (Definitions)

1. Define solute and solvent.

2. Define saturated, unsaturated, and supersaturated.

3. A solution is prepared by combining 2.09 g of CO₂ and 35.5 g of H₂O. Identify the solute and solvent.

4. A solution is prepared by combining 10.3 g of Hg(ℓ) and 45.0 g of Ag(s). Identify the solute and solvent.

5. Use Table 11.2.1 - Solubilities of Some Ionic Compounds, to decide if a solution containing 45.0 g of NaCl per 100 g of H₂O is unsaturated, saturated, or supersaturated.
6. Use Table 11.2.1 - Solubilities of Some Ionic Compounds, to decide if a solution containing 0.000092 g of AgCl per 100 g of H₂O is unsaturated, saturated, or supersaturated.
7. Would the solution in Exercise 5 be described as dilute or concentrated? Explain your answer.

8. Would the solution in Exercise 6 be described as dilute or concentrated? Explain your answer.

9. Identify a solute from Table 11.2.1 - Solubilities of Some Ionic Compounds, whose saturated solution can be described as dilute.
10. Identify a solute from Table 11.2.1 - Solubilities of Some Ionic Compounds, whose saturated solution can be described as concentrated.

11. Which solvent is Br₂ more likely soluble in—CH₃OH or C₆H₆?

12. Which solvent is NaOH more likely soluble in—CH₃OH or C₆H₆?

13. Compounds with the formula C_nH_{2n + 1}OH are soluble in H₂O when n is small but not when n is large. Suggest an explanation for this phenomenon.

14. Glucose has the following structure:

What parts of the molecule indicate that this substance is soluble in water?

 

Answers

1.   The solvent is the majority component of a solution, whereas the solute is the minority component of a solution.

3.   solute: CO₂; solvent: H₂O

5.   supersaturated

7.   concentrated because there is a lot of solute

9.   AgCl or CaCO₃

11. C₆H₆

13. The nonpolar end dominates intermolecular forces when n is large.

Exercises (Quantitative Units of Concentration)

1. Differentiate between molarity and molality.

2. Differentiate between mass percentage and parts per thousand.

3. What is the molarity of a solution made by dissolving \(13.4 \mathrm{~g}\) of \(\mathrm{NaNO}_3\) in 345 \(\mathrm{mL}\) of solution?

4. What is the molarity of a solution made by dissolving \(332 \mathrm{~g}\) of \(\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6\) in 4.66 L of solution?

5. How many moles of \(\mathrm{MgCl}_2\) are present in \(0.0331 \mathrm{~L}\) of a \(2.55 \mathrm{M}\) solution?

6. How many moles of \(\mathrm{NH}_4 \mathrm{Br}\) are present in \(88.9 \mathrm{~mL}\) of a \(0.228 \mathrm{M}\) solution?

7. What volume of \(0.556 \mathrm{M} \mathrm{NaCl}\) is needed to obtain \(0.882 \mathrm{~mol}\) of \(\mathrm{NaCl}\) ?

8. What volume of \(3.99 \mathrm{M} \mathrm{H}_2 \mathrm{SO}_4\) is needed to obtain \(4.61 \mathrm{~mol}\) of \(\mathrm{H}_2 \mathrm{SO}_4\) ?

9. What volume of \(0.333 \mathrm{M} \mathrm{Al}\left(\mathrm{NO}_3\right)_3\) is needed to obtain \(26.7 \mathrm{~g}\) of \(\mathrm{Al}\left(\mathrm{NO}_3\right)_3\) ?

10. What volume of \(1.772 \mathrm{M} \mathrm{BaCl}_2\) is needed to obtain \(123 \mathrm{~g}\) of \(\mathrm{BaCl}_2\) ?

11. What are the individual ion concentrations and the total ion concentration in \(0.66 \mathrm{M} \mathrm{Mg}\left(\mathrm{NO}_3\right)_2\) ?

12. What are the individual ion concentrations and the total ion concentration in \(1.04 \mathrm{M} \mathrm{Al}_2\left(\mathrm{SO}_4\right)_3\) ?

13. If the \(\mathrm{C}_2 \mathrm{H}_3 \mathrm{O}_2{ }^{-}\)ion concentration in a solution is \(0.554 \mathrm{M}\), what is the concentration of \(\mathrm{Ca}\left(\mathrm{C}_2 \mathrm{H}_3 \mathrm{O}_2\right)_2\) ?

14. If the \(\mathrm{Cl}^{-}\)ion concentration in a solution is \(2.61 \mathrm{M}\), what is the concentration of \(\mathrm{FeCl}_3\) ?

Answers

1. Molarity is moles per liter, whereas molality is moles per kilogram of solvent.

3.   \(0.457 \mathrm{M}\)

5.   \(0.0844 \mathrm{~mol}\)

7.   \(1.59 \mathrm{~L}\)

9.   \(0.376 \mathrm{~L}\)

11. \(\mathrm{Mg}^{2+}=0.66 \mathrm{M} ; \mathrm{NO}_3{ }^{-}=1.32 \mathrm{M}\); total: \(1.98 \mathrm{M}\)

13. \(0.277 \mathrm{M}\)

Exercises (Dilutions and Concentrations )

1. What is the difference between dilution and concentration?
    
2. What quantity remains constant when you dilute a solution?
    
3. A 1.88 M solution of NaCl has an initial volume of 34.5 mL. What is the final concentration of the solution if it is diluted to 134 mL?
    
4. A 0.664 M solution of NaCl has an initial volume of 2.55 L. What is the final concentration of the solution if it is diluted to 3.88 L?
    
5. If 1.00 mL of a 2.25 M H₂SO₄ solution needs to be diluted to 1.00 M, what will be its final volume?
    
6. If 12.00 L of a 6.00 M HNO₃ solution needs to be diluted to 0.750 M, what will be its final volume?
    
7. If 665 mL of a 0.875 M KBr solution are boiled gently to concentrate the solute to 1.45 M, what will be its final volume?
    
8. If 1.00 L of an LiOH solution is boiled down to 164 mL and its initial concentration is 0.00555 M, what is its final concentration?
    
9. How much water must be added to 75.0 mL of 0.332 M FeCl₃(aq) to reduce its concentration to 0.250 M?
    

10. How much water must be added to 1.55 L of 1.65 M Sc(NO₃)₃(aq) to reduce its concentration to 1.00 M?

Answers

1. Dilution is a decrease in a solution’s concentration, whereas concentration is an increase in a solution’s concentration.

3. 0.484 M

5. 2.25 mL

7. 401 mL

9. 24.6 mL

Exercises (Concentrations as Conversion Factors)

1. Using concentration as a conversion factor, how many moles of solute are in 3.44 L of 0.753 M CaCl₂?

2. Using concentration as a conversion factor, how many moles of solute are in 844 mL of 2.09 M MgSO₄?

3. Using concentration as a conversion factor, how many liters are needed to provide 0.822 mol of NaBr from a 0.665 M solution?

4. Using concentration as a conversion factor, how many liters are needed to provide 2.500 mol of (NH₂)₂CO from a 1.087 M solution?

5. What is the mass of solute in 24.5 mL of 0.755 M CoCl₂?

6. What is the mass of solute in 3.81 L of 0.0232 M Zn(NO₃)₂?

7. What volume of solution is needed to provide 9.04 g of NiF₂ from a 0.332 M solution?

8. What volume of solution is needed to provide 0.229 g of CH₂O from a 0.00560 M solution?

9. What volume of 3.44 M HCl will react with 5.33 mol of CaCO₃?

   2HCl + CaCO₃ → CaCl₂ + H₂O + CO₂

10. What volume of 0.779 M NaCl will react with 40.8 mol of Pb(NO₃)₂?

    Pb(NO₃)₂ + 2NaCl → PbCl₂ + 2NaNO₃

11. What volume of 0.905 M H₂SO₄ will react with 26.7 mL of 0.554 M NaOH?

    H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O

12. What volume of 1.000 M Na₂CO₃ will react with 342 mL of 0.733 M H₃PO₄?

    3Na₂CO₃ + 2H₃PO₄ → 2Na₃PO₄ + 3H₂O + 3CO₂

13. It takes 23.77 mL of 0.1505 M HCl to titrate with 15.00 mL of Ca(OH)₂. What is the concentration of Ca(OH)₂? You will need to write the balanced chemical equation first.

14. It takes 97.62 mL of 0.0546 M NaOH to titrate a 25.00 mL sample of H₂SO₄. What is the concentration of H₂SO₄? You will need to write the balanced chemical equation first.

15. It takes 4.667 mL of 0.0997 M HNO₃ to dissolve some solid Cu. What mass of Cu can be dissolved?

    Cu + 4HNO₃(aq) → Cu(NO₃)₂(aq) + 2NO₂ + 2H₂O

16. It takes 49.08 mL of 0.877 M NH₃ to dissolve some solid AgCl. What mass of AgCl can be dissolved?

    AgCl(s) + 4NH₃(aq) → Ag(NH₃)₄Cl(aq)

17. What mass of 3.00% H₂O₂ is needed to produce 66.3 g of O₂(g)?

    2H₂O₂(aq) → 2H₂O(ℓ) + O₂(g)

18. A 0.75% solution of Na₂CO₃ is used to precipitate Ca²⁺ ions from solution. What mass of solution is needed to precipitate 40.7 L of solution with a concentration of 0.0225 M Ca²⁺(aq)?

Na₂CO₃(aq) + Ca²⁺(aq) → CaCO₃(s) + 2Na⁺(aq)

Answers

1.  2.59 mol

3.  1.24 L

5.  2.40 g

7.  0.282 L

9.  3.10 L

11. 8.17 mL

13. 0.1192 M

15. 7.39 mg

17. 4.70 kg

Exercises (Colligative Properties of Solutions)

1. What are the three colligative properties that involve phase changes?

2. Which colligative property does not involve a phase change? Give an example of its importance.

3. If 45.0 g of C₆H₆ and 60.0 g of C₆H₅CH₃ are mixed together, what is the mole fraction of each component?

4. If 125 g of N₂ are mixed with 175 g of O₂, what is the mole fraction of each component?

5. If 36.5 g of NaCl are mixed with 63.5 g of H₂O, what is the mole fraction of each component?

6. An alloy of stainless steel is prepared from 75.4 g of Fe, 12.6 g of Cr, and 10.8 g of C. What is the mole fraction of each component?

7. A solution is made by mixing 12.0 g of C₁₀H₈ in 45.0 g of C₆H₆. If the vapor pressure of pure C₆H₆ is 76.5 torr at a particular temperature, what is the vapor pressure of the solution at the same temperature?

8. A solution is made by mixing 43.9 g of C₆H₁₂C₆ in 100.0 g of H₂O. If the vapor pressure of pure water is 26.5 torr at a particular temperature, what is the vapor pressure of the solution at the same temperature?

9. At 300°C, the vapor pressure of Hg is 32.97 torr. If 0.775 g of Au were dissolved into 3.77 g of Hg, what would be the vapor pressure of the solution?

10. At 300°C, the vapor pressure of Hg is 32.97 torr. What mass of Au would have to be dissolved in 5.00 g of Hg to lower its vapor pressure to 25.00 torr?

11. If 25.0 g of C₆H₁₂O₆ are dissolved in 100.0 g of H₂O, what is the boiling point of this solution?

12. If 123 g of C₁₀H₁₆O are dissolved in 355 g of C₆H₆, what is the boiling point of this solution?

13. If 1 mol of solid CBr₄ is mixed with 2 mol of CCl₄, what is the boiling point of this solution?

14. A solution of C₂H₂O₄ in CH₃COOH has a boiling point of 123.40°C. What is the molality of the solution?

15. If 123 g of C₁₀H₁₆O are dissolved in 355 g of C₆H₆, what is the freezing point of this solution?

16. If 25.0 g of C₆H₁₂O₆ are dissolved in 100.0 g of H₂O, what is the freezing point of this solution?

17. C₈H₁₇OH is a nonvolatile solid that dissolves in C₆H₁₂. If 7.22 g of C₈H₁₇OH is dissolved in 45.3 g of C₆H₁₂, what is the freezing point of this solution?

18. A solution of C₂H₂O₄ in CH₃COOH has a freezing point of 10.00°C. What is the molality of the solution?

19. If 25.0 g of C₆H₁₂O₆ are dissolved in H₂O to make 0.100 L of solution, what is the osmotic pressure of this solution at 25°C?

20. If 2.33 g of C₂₇H₄₆O are dissolved in liquid CS₂ to make 50.00 mL of solution, what is the osmotic pressure of this solution at 298 K?

21. At 298 K, what concentration of solution is needed to have an osmotic pressure of 1.00 atm?

22. The osmotic pressure of blood is about 7.65 atm at 37°C. What is the approximate concentration of dissolved solutes in blood? (There are many different solutes in blood, so the answer is indeed an approximation.)

Answers

1.   boiling point elevation, freezing point depression, vapor pressure depression

3.   mole fraction C₆H₆: 0.469; mole fraction C₆H₅CH₃: 0.531

5.   mole fraction NaCl: 0.157; mole fraction H₂O: 0.843

7.   65.8 torr

9.   27.26 torr

11. 100.71°C

13. 92.9°C

15. −5.65°C

17. −18.3°C

19. 33.9 atm

21. 0.0409 M

Exercises (Colligative Properties of Ionic Solutes)

1. Explain why we need to consider a van't Hoff factor for ionic solutes but not for molecular solutes.

2. \(\mathrm{NaCl}\) is often used in winter to melt ice on roads and sidewalks, but calcium chloride \(\left(\mathrm{CaCl}_2\right)\) is also used. Which would be better (on a mole-by-mole basis), and why?

3. Calculate the boiling point of an aqueous solution of \(\mathrm{NaNO}_3\) made by mixing \(15.6 \mathrm{~g}\) of \(\mathrm{NaNO}_3\) with \(100.0 \mathrm{~g}\) of \(\mathrm{H}_2 \mathrm{O}\). Assume an ideal van't Hoff factor.

4. Many labs use a cleaning solution of \(\mathrm{KOH}\) dissolved in \(\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}\). If \(34.7 \mathrm{~g}\) of \(\mathrm{KOH}\) were dissolved in \(88.0 \mathrm{~g}\) of \(\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}\), what is the boiling point of this solution? The normal boiling point of \(\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}\) is \(78.4^{\circ} \mathrm{C}\) and its \(\mathrm{Kb}=1.19^{\circ} \mathrm{C} / \mathrm{m}\). Assume an ideal van't Hoff factor. \(1,550 \mathrm{~g}\) of \(\mathrm{H}_2 \mathrm{O}\) ? Assume an ideal van't Hoff factor.

5. What is the freezing point of a solution made by dissolving \(345 \mathrm{~g} \mathrm{of} \mathrm{CaCl}_2\) in \(1,550 \mathrm{~g}\) of \(\mathrm{H}_2 \mathrm{O}\) ? Assume an ideal van't Hoff factor.

6. A classic homemade ice cream can be made by freezing the ice cream mixture using a solution of \(250 \mathrm{~g}\) of \(\mathrm{NaCl}\) dissolved in \(1.25 \mathrm{~kg}\) of ice water. What is the temperature of this ice water? Assume an ideal van't Hoff factor.

7. Seawater can be approximated as a \(3.5 \% \mathrm{NaCl}\) solution by mass; that is, \(3.5 \mathrm{~g}\) of \(\mathrm{NaCl}\) are combined with \(96.5 \mathrm{~g} \mathrm{H}_2 \mathrm{O}\). What is the osmotic pressure of seawater? Assume an ideal van't Hoff factor.

8. The osmotic pressure of blood is \(7.65 \mathrm{~atm}\) at \(37^{\circ} \mathrm{C}\). If blood were considered a solution of \(\mathrm{NaCl}\), what is the molar concentration of \(\mathrm{NaCl}\) in blood? Assume an ideal van't Hoff factor.

9. What is the vapor pressure of an aqueous solution of \(36.4 \mathrm{~g}\) of \(\mathrm{KBr}\) in \(199.5 \mathrm{~g}\) of \(\mathrm{H}_2 \mathrm{O}\) if the vapor pressure of \(\mathrm{H}_2 \mathrm{O}\) at the same temperature is 32.55 torr? What other solute(s) would give a solution with the same vapor pressure? Assume an ideal van't Hoff factor.

10. Assuming an ideal van't Hoff factor, what mole fraction is required for a solution of \(\mathrm{Mg}\left(\mathrm{NO}_3\right)_2\) to have a vapor pressure of 20.00 torr at \(25.0^{\circ} \mathrm{C}\) ? The vapor pressure of the solvent is 23.61 torr at this temperature.

Answers

1. Ionic solutes separate into more than one particle when they dissolve, whereas molecular solutes do not.

3. \(101.9^{\circ} \mathrm{C}\)

5. \(-7.5^{\circ} \mathrm{C}\)

7. \(30.3 \mathrm{~atm}\)

9. 30.86 torr; any two-ion salt should have the same effect.

Additional Exercises

1. One brand of ethyl alcohol (Everclear) is \(95 \%\) ethyl alcohol, with the remaining \(5 \%\) being water. What is the solvent and what is the solute of this solution?

2. Give an example of each type of solution from your own experience.

a. A solution composed of a gas solute in a liquid solvent.
b. A solution composed of a solid solute in a liquid solvent.
c. A solution composed of a liquid solute in a liquid solvent.
d. A solution composed of a solid solute in a solid solvent. (Hint: usually such solutions are made as liquids and then solidified.)

3. Differentiate between the terms saturated and concentrated.

4. Differentiate between the terms unsaturated and dilute.

5. What mass of \(\mathrm{FeCl}_2\) is present in \(445 \mathrm{~mL}\) of \(0.0812 \mathrm{M} \mathrm{FeCl}_2\) solution?

6. What mass of \(\mathrm{SO}_2\) is present in \(26.8 \mathrm{~L}\) of \(1.22 \mathrm{M} \mathrm{SO}_2\) solution?

7. What volume of \(0.225 \mathrm{M} \mathrm{Ca}(\mathrm{OH})_2\) solution is needed to deliver \(100.0 \mathrm{~g}\) of \(\mathrm{Ca}(\mathrm{OH})_2\) ?

8. What volume of \(12.0 \mathrm{M} \mathrm{HCl}\) solution is needed to obtain exactly \(1.000 \mathrm{~kg}\) of \(\mathrm{HCl}\) ?

9. The World Health Organization recommends that the maximum fluoride ion concentration in drinking water is \(1.0 \mathrm{ppm}\). Assuming water has the maximum concentration, if an average person drinks \(1,920 \mathrm{~mL}\) of water per day, how many milligrams of fluoride ion are being ingested?

10. For sanitary reasons, water in pools should be chlorinated to a maximum level of \(3.0 \mathrm{ppm}\). In a typical 5,000 gal pool that contains \(21,200 \mathrm{~kg}\) of water, what mass of chlorine must be added to obtain this concentration?

11. Given its notoriety, you might think that uranium is very rare, but it is present at about 2-4 ppm of the earth's crust, which is more abundant than silver or mercury. If the earth's crust is estimated to have a mass of \(8.50 \times 10^{20} \mathrm{~kg}\), what range of mass is thought to be uranium in the crust?

12. Chromium is thought to be an ultratrace element, with about \(8.9 \mathrm{ng}\) present in a human body. If the average body mass is \(75.0 \mathrm{~kg}\), what is the concentration of chromium in the body in pptr?

13. What mass of \(3.00 \% \mathrm{H}_2 \mathrm{O}_2\) solution is needed to produce \(35.7 \mathrm{~g}\) of \(\mathrm{O}_2(\mathrm{~g})\) at \(295 \mathrm{~K}\) at \(1.05 \mathrm{~atm}\) pressure?

\[
2 \mathrm{H}_2 \mathrm{O}_2(\mathrm{aq}) \rightarrow 2 \mathrm{H}_2 \mathrm{O}(\ell)+\mathrm{O}_2(\mathrm{~g})
\]

14. What volume of pool water is needed to generate \(1.000 \mathrm{~L} \mathrm{of}_{\mathrm{Cl}}^2(\mathrm{~g})\) at standard temperature and pressure if the pool contains \(4.0 \mathrm{ppm} \mathrm{HOCl}\) and the water is slightly acidic? The chemical reaction is as follows:
\[
\mathrm{HOCl}(\mathrm{aq})+\mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{H}_2 \mathrm{O}(\ell)+\mathrm{Cl}_2(\mathrm{~g})
\]

Assume the pool water has a density of \(1.00 \mathrm{~g} / \mathrm{mL}\).

15. A \(0.500 \mathrm{~m}\) solution of \(\mathrm{MgCl}_2\) has a freezing point of \(-2.60^{\circ} \mathrm{C}\). What is the true van't Hoff factor of this ionic compound? Why is it less than the ideal value?

16. The osmotic pressure of a \(0.050 \mathrm{M} \mathrm{LiCl}\) solution at \(25.0^{\circ} \mathrm{C}\) is \(2.26 \mathrm{~atm}\). What is the true van't Hoff factor of this ionic compound? Why is it less than the ideal value?

17. Order these solutions in order of increasing boiling point, assuming an ideal van't Hoff factor for each: \(0.10 \mathrm{~m} \mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6, 0.06 \mathrm{~m} \mathrm{NaCl}, 0.4 \mathrm{~m} \mathrm{Au}\left(\mathrm{NO}_3\right)_3\), and \(0.4 \mathrm{~m} \mathrm{Al}_2\left(\mathrm{SO}_4\right)_3\).

18. Order these solutions in order of decreasing osmotic pressure, assuming an ideal van't Hoff factor: \(0.1 \mathrm{M} \mathrm{HCl}, 0.1 \mathrm{M} \mathrm{CaCl}_2, 0.05 \mathrm{M} \mathrm{MgBr}_2\), and \(0.07 \mathrm{M}\) \(\mathrm{Ga}\left(\mathrm{C}_2 \mathrm{H}_3 \mathrm{O}_2\right)_3\)

Answers

1. solvent: ethyl alcohol; solute: water

3. Saturated means all the possible solute that can dissolve is dissolved, whereas concentrated implies that a lot of solute is dissolved.

5. \(4.58 \mathrm{~g}\)

7. \(6.00 \mathrm{~L}\)

9. \(1.92 \mathrm{mg}\)

11. \(1.7 \times 10^{15}\) to \(3.4 \times 10^{15} \mathrm{~kg}\)

13. \(2,530 \mathrm{~g}\)

15. 2.80 ; it is less than 3 because not all ions behave as independent particles.

17. \(0.10 m \mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6<0.06 m \mathrm{NaCl}<0.4 m \mathrm{Au}\left(\mathrm{NO}_3\right)_3<0.4 m \mathrm{Al}_2\left(\mathrm{SO}_4\right)_3\)