3.7.2.0: Concentrations of Solutions (Problems)
- Page ID
- 210735
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)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:
- 583 g of H2SO4 in 1.50 kg of water—the acid solution used in an automobile battery
- 0.86 g of NaCl in 1.00 × 102 g of water—a solution of sodium chloride for intravenous injection
- 46.85 g of codeine, C18H21NO3, in 125.5 g of ethanol, C2H5OH
- 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
-
\(X_\mathrm{I_2}=0.035\)
\(X_\mathrm{EtOH}=0.965\)
PROBLEM \(\PageIndex{10}\)
Calculate the mole fraction of each solute and solvent:
- 0.710 kg of sodium carbonate (washing soda), Na2CO3, in 10.0 kg of water—a saturated solution at 0 °C
- 125 g of NH4NO3 in 275 g of water—a mixture used to make an instant ice pack
- 25 g of Cl2 in 125 g of dichloromethane, CH2Cl2
- 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:
- 0.710 kg of sodium carbonate (washing soda), Na2CO3, in 10.0 kg of water—a saturated solution at 0°C
- 125 g of NH4NO3 in 275 g of water—a mixture used to make an instant ice pack
- 25 g of Cl2 in 125 g of dichloromethane, CH2Cl2
- 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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Contributors and Attributions
Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/85abf193-2bd...a7ac8df6@9.110).
- Adelaide Clark, Oregon Institute of Technology
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