13.E: Homework Chapter 13
 Page ID
 202225
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{\!\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\ #1 \}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\ #1 \}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{\!\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{\!\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left#1\right}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Solutions, Solvents, and Solutes:
1. Define the following terms.
a.) Solution:
b.) Solvent:
c.) Solute:
2. Is it possible to combine any two substances to create a solution? Explain.
3. If you were to mix a polar and a nonpolar substance together in a beaker, what will happen? Is this a solution?
4. What is the difference between a saturated solution and a concentrated solution?
5. One brand of ethyl alcohol is 95% ethyl alcohol, and the remaining 5% of the solution is water. What is the solvent and what is the solute of this solution?
6. A bottle of apple juice is 80% apple juice, and the remaining 20% of the solution is water. What is the solvent and what is the solute of this solution?
7. A stock solution of 1.0 M sodium hydroxide is diluted with water. If the solution is 5% sodium hydroxide and 95% water, what is the solvent and what is the solute of this solution?
8. For the following substances, identify the solute:
a.) salt water
b.) sweet tea
c.) soda
9. From the following solvents, which would be the best at removing grease from an object? **Hint: grease is nonpolar**
a.) NH_{3}
b.) H_{2}O
c.) CH_{3}CH_{2}CH_{2}CH_{3 }
d.) CH_{3}OCH_{3}
10. Solutions do not necessarily have to be a liquid; which of the following choices would be the solvent in air?
a.) O_{2}
b.) N_{2 }
c.) CO_{2}
d.) CO
11. How many grams of KNO_{3} are in a 165 g solution containing 15.3% (by mass) of the solute (KNO_{3})?
12. How many moles of H_{2}O are in a 178 g solution containing 46.2% (by mass) water?
13. How many grams of CO_{2 }are in 65.5 mL of soda if 30.4% (by mass) of the solution is CO_{2}?
**Helpful conversion factor: (1.00 mL/1.00 g) **
14. Using the information in the previous problem, how many molecules of CO_{2} are present in the soda?
15. How many moles of aluminum are present in a 153 g solution if 36.7% (by mass) of the solution is aluminum? Is aluminum the solvent or solute in this particular solution?
16. How many grams of aluminum are present in a 436 g solution if 57.2% (by mass) of the solution is aluminum? Is aluminum the solvent or solute in this particular solution?
17. A solution contains 20 g of NaCl per 100 g of water at 25 degrees Celsius. Is the solution saturated, unsaturated, or supersaturated? The solubility curve graph below may be helpful.
18. A solution contains 110 g of KNO_{3} per 100 g of water at 50 degrees Celsius. Is the solution saturated, unsaturated, or supersaturated? The graph in the previous problem may be helpful.
Mass Percent Calculations:
19. What is the mass percent of a solution prepared by dissolving 23.4 g of a solid into 45.7g of water?
20. What is the mass percent of a solution prepared by dissolving 54.6g of solid sodium chloride into 85.4g of water?
21. Calculate the mass percent for each of the following:
a.) 32.5g sugar in 687g H_{2}O
b.) 58.3g NaCl in 476g H_{2}O
c.) 67.9g of a solid in 679g H_{2}O
22. Fill in the table below by calculating what is missing.

Mass Solute 
Mass Solvent 
Mass Solution 
Mass % 
a.) 
56.8g 
583g 


b.) 

67.5g 

4.35% 
c.) 
6.89g 

96.3g 

23. If the mass percent of a solution is 5.68%, and the mass of the solute is 6.43g, then what is the mass of the solvent?
24. If the mass of the solute is 8.54g and the mass of the solvent is 53.9g, what is the mass percent?
25. What is the mass percent of the solution in which 8.3g of a solid is dissolved in 453g of water?
26. The mass of a solution is 543g. The mass of the solute is 54.2g. Calculate the mass percent of the solution.
27. The mass of a solution is 687g. The mass of the solvent is 483g. Calculate the mass percent of the solution.
28. Calculate the mass percent of the solution if 5.03g of NaCl are dissolved in 14.56g of water.
29. Calculate the mass percent of the solution if 17.8g of sugar are dissolved in 275g of water.
30. Calculate the mass percent of a solution in which the mass of the solute is 4.02g and the mass of the solution is 67.4g.
Molarity Calculations:
31. Find the molarity for the following solutions:
a.) 2.35 mol Ca(OH)_{2} in 30.2 L of solution.
b.) 4.78 mol NaOH in 45.2 L of solution.
c.) 1.58 mol HCl in 30.3 L of solution.
d.) 5.03 mol LiOH in 10.2 L of solution.
32. Find the molarity for the following solutions:
a.) 54.3 g of Ca(s) in 104.8 mL of solution.
b.) 1.87 g Cu(s) in 15.8 L of solution.
c.) 0.0346 mol K(s) in 6.95 L of solution.
d.) 0.487 mol Mg(s) in 14.8 L of solution.
33. How many grams of KCl is needed to create 0.00342 L of a 1.0 M KCl solution?
34. How many grams of KNO_{3} is needed to create 0.0258 L of a 2.0 M KNO_{3} solution?
35. The mass of HCl in the HCl solution is 54.8 g. Find the molarity of the 2.00 L solution.
36. Complete the following calculations for the missing parts of the table below.

Solute: 
Mass of Solute (g): 
Mole of Solute: 
Volume of Solution (L): 
Molarity: 
a.) 
NaOH 
0.589 g 

14.5 L 

b.) 
H_{2}SO_{4} 

0.880 mol 
25.5 L 

c.) 
Fe_{2}O_{3} 
9.20 g 


1.50 M 
d.) 
HBr 

0.539 mol 

2.18 M 
37. Find the molarity for the solution with 0.528 g of Carbon in 1.28 L.
38. Find the molarity for the following solutions:
a.) 0.406 mol Ni(s) in a 1.25 L solution.
b.) 1.58 mol C(s) in a 0.0389 L solution.
c.) 9.40 mol Ti(s) in a 14.6 L solution.
d.) 8.00 mol Mg(s) in a 25.0 L solution.
39. Find the molarity for the solution with 4.50 g Na(s) in 25.50 mL.
Dilution Calculations:
40. If you have 15.0 L of a solution with a concentration of 1.50 M, and you dilute the solution with water and now have 65.0 L of solution, what is the new concentration?
41. What will be the final concentration of a solution if you dilute 55.0 mL of 10.0 M HCl to create a final volume of 78.0 mL?
42. What will the final volume of a solution be if you started with 12.0 L of a 1.50 M NaOH and ended with a 0.311 M NaOH solution?
43. What was the original volume of a solution if the starting concentration was 2.00 M, and the final volume is 50.0 mL and the final concentration is 0.500 M?
44. How would you make 5.00 L of a 1.00 M HCl solution from a 12.0 M HCl stock solution? You do not need to provide calculations for this problem (although they may be helpful); just explain what you would need to do.
45. How would you make 15.0 mL of a 2.00 M NaOH solution from a 10.0 M NaOH stock solution? You do not need to provide calculations for this problem (although they may be helpful); just explain what you would need to do.
46. How would you make 10.0 mL of a 3.00 M NH_{4}OH solution from a 12.0 M NH_{4}OH stock solution? You do not need to provide calculations for this problem (although they may be helpful); just explain what you would need to do.
47. Determine the volume of 1.00 M NaOH required to neutralize each sample below. The following neutralization reaction may be helpful to know.
NaOH(aq) + HCl(aq) → H_{2}O(l) + NaCl(aq)
a.) 18.0 mL of 1.00 M HCl
b.) 28.0 mL of 0.500 M HCl
c.) 15.0 mL of 3.50 M HCl
d.) 20.0 mL of 2.00 M HCl
48. Determine the final concentration of a solution if it started out as being 9.80 mL of a 10.0 M NaOH solution and was diluted with water to 20.0mL.
49. Determine the final volume of a solution if it started out as being 8.50 L of a 12.0 M HCl solution, and its final concentration is 5.50 M.
50. Determine the initial concentration of a solution that was 15.0 mL, and ended up having a final concentration of 15.0 M and a final volume of 50.0 mL.
51. Determine the final volume of a solution that was originally 25.0 mL of 5.00 M HCl and ended up with a final concentration of 1.00 M HCl.
52. Determine the final concentration for each of the scenarios below. The initial concentration was 5.00 M.
a.) initial volume: 5.00 mL; final volume: 15.0 mL
b.) initial volume: 10.0mL; final volume: 25.0 mL
c.) initial volume: 3.00 L; final volume: 520. mL
d.) initial volume: 8.00 mL; final volume: 16.0 mL
53. Determine the initial concentrations for each of the following scenarios below. The final concentration is 3.00 M.
a.) initial volume: 12.0 mL; final volume: 20.0 mL
b.) initial volume: 5.00 mL; final volume: 10.0 mL
c.) initial volume: 2.00 mL; final volume: 5.0 mL
d.) initial volume: 13.0 mL; final volume: 25.0 mL
54. Determine the final concentration if the original solution had a concentration of 5.00 M, and its initial volume was 15.0 mL, and the final volume is 25.0 mL.
55. Determine the initial concentration if the final solution has a concentration of 1.00 M, and the final volume is 35.0 mL, while the initial volume was 10.0 mL.
56. Determine the final volume that is needed to transform a 15.0 mL solution of 5.00 M into a 2.50 M solution.
57. Determine the final volume that is needed to transform a 10.0 mL solution of 12.0 M HCl into a 5.00 M solution of HCl.
Cumulative/Challenge Problems:
58. If a 50.0 mL sample of 6.00 M KNO_{3} solution is diluted to 2.00 L, what volume of this new solution would contain 25.0 g KNO_{3}?
59. A bottle of a liquid detergent is 90% soap and 10% water. Which ingredient is the solvent and which is the solute?
60. If 55.0 mL of a solution of HCl in water is required to react completely with 1.50 g of aluminum metal, what is the molarity of the HCl solution?
2Al(s)+6HCl(aq)→2AlCl_{3}(aq)+3H_{2}(g)
61. Determine the final concentration of the solution if it originally contained 10.0 mL of 5.00 M HBr, and the final volume of the solution is 30.0 mL
62. Determine the final concentration of the solution if it originally contained 5.00 mL of 8.00 M H_{3}PO_{4} , and the final volume of the solution is 15.0 mL