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# 13: Solutions

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## 13.1: Units of Concentration

### Review of Molarity

Exercise $$\PageIndex{1.1}$$

Calculate the molarity of a solution containing 15.2g H3AsO4 in 600mL of water. The molecular weight of H3AsO4 is 141.94g/mol.

Answer

$15.2g H_{3}AsO_{4}*\left ( \frac{1 mol}{141.94g H_{3}AsO_{4}} \right )*\left ( \frac{1}{600mL} \right )*\left ( \frac{1000mL}{1L} \right )=0.178M$

Exercise $$\PageIndex{1.2}$$

Given the molecular weight of H3AsO4 is 141.94g/mol, calculate the mass of H3AsO4 required to prepare a 0.75M solution in 400mL of water.

Answer

$400mL*\left ( \frac{1L}{1000mL} \right )*\left ( \frac{0.75mol}{1L} \right )*\left ( \frac{141.94gH_{3}AsO_{4}}{1mol} \right )=42.6gH_{3}AsO_{4}$

Exercise $$\PageIndex{1.3}$$

What volume of water must be added to 47 grams of KBr to make a 2.6M solution? The molecular weight of KBr is 119g/mol.

Answer

$47gKBr*\left ( \frac{1molKBr}{119gKBr} \right )*\left ( \frac{1L}{2.6molKBr} \right )*\left ( \frac{1000mL}{1L} \right )=152mL$

Exercise $$\PageIndex{1.4}$$

How many grams of KBr are required to make 50mL of a 1.2M solution in water? The molecular weight of KBr is 119g/mol.

Answer

$50mL*\left ( \frac{1L}{1000mL} \right )*\left ( \frac{1.2molKBr}{1L} \right )*\left ( \frac{119gKBr}{1molKBr} \right )=7.14gKBr$

Exercise $$\PageIndex{1.5}$$

Calculate the molarity of a solution containing 13.41g of AgCl2 in 250mL of water. The molecular weight of AgCl2 is 178.8g/mol.

Answer

$13.41gAgCl_{2}*\left ( \frac{1molAgCl_{2}}{178.8gAgCl_{2}} \right )*\left ( \frac{1}{250mL} \right )*\left ( \frac{1000mL}{1L} \right )=0.300M$

Exercise $$\PageIndex{1.6}$$

What is the molarity of a Cl- in a solution prepared by dissolving 23.7g of CaCl2 in 375g of water and a density of 1.05g/mL?

Answer

$\left ( \frac{23.7g\,CaCl_{2}}{1} \right )*\left ( \frac{1mol}{110.98g\,CaCl_{2}} \right )*\left ( \frac{1}{375mL} \right )*\left ( \frac{1000mL}{1L} \right )=0.5695M\,CaCl_{2}$

For each CaCl2 dissolved two Cl- ions created so,

$0.5695M*2=1.14M\,Cl^{-}$

### Molality

Exercise $$\PageIndex{1.7}$$

What is the definition of molality?

Answer

moles of solute/kg of solvent

Exercise $$\PageIndex{1.8}$$

Calculate the molality of a solution containing 112g CH3OH in 134mL of water. The density of water is 1.0g/mL and the molecular weight of CH3OH is 32.0g/mol.

Answer

$112gCH_{3}OH*\left ( \frac{1molCH_{3}OH}{32.0gCH_{3}OH} \right )*\left ( \frac{1}{134mL} \right )*\left ( \frac{1mL}{1g} \right )*\left ( \frac{1000g}{1kg} \right )=26.1m$

Exercise $$\PageIndex{1.9}$$

Calculate the molality of all the ions by adding 1.4g NaCl to 75mL of water.

Answer

$1.4gNaCl*\left ( \frac{1mol_{NaCl}}{58.44gNaCl} \right )*\left ( \frac{2mol_{ion}}{1mol_{NaCl}} \right )*\left ( \frac{1}{75mL} \right )*\left ( \frac{1mL}{1g} \right )*\left ( \frac{1000g}{1kg} \right )=0.64m$

Exercise $$\PageIndex{1.10}$$

Calculate the molality of the Br- ion by adding 2.2g MgBr2 to 100mL of water. The molecular weight of MgBr2 is 184.1g/mol.

Answer

$2.2gMgBr_{2}*\left ( \frac{1molMgBr_{2}}{184.1gMgBr_{2}} \right )*\left ( \frac{2molBr^{-}}{1molMgBr_{2}} \right )*\left ( \frac{1}{100mL} \right )*\left ( \frac{1mL}{1g} \right )*\left ( \frac{1000g}{1kg} \right )=0.24m$

Exercise $$\PageIndex{1.11}$$

What volume of water in mL would be required to prepare a 32.6m solution from 78g of CaCl2?

Answer

$78gCaCl_{2}*\left ( \frac{1molCaCl_{2}}{110.98gCaCl_{2}} \right )*\left ( \frac{1kg}{32.6molCaCl_{2}} \right )*\left ( \frac{1000g}{1kg} \right )*\left ( \frac{1mL}{1g} \right )=21.6mL$

Exercise $$\PageIndex{1.12}$$

What mass of KBr should be added to 120mL of water to create a 1.8M solution? The molecular weight of KBr is 119g/mol.

Answer

$120mL*\left ( \frac{1g}{1mL} \right )*\left ( \frac{1000g}{1kg} \right )*\left ( \frac{1.8molKBr}{1kg} \right )*\left ( \frac{119gKBr}{1molKBr} \right )=25.7gKBr$

### Mole and Mass Fractions

Exercise $$\PageIndex{1.13}$$

Calculate the mole fraction of methane in a 10.0L flask containing 0.367 moles of methane, 0.221 moles hydrogen, and 0.782 moles carbon dioxide.

Answer

\text {Mole fraction }=\mathrm{X}_{\mathrm{A}}=\frac{\text { moles } \mathrm{A}}{\text { total number of moles }}

\text { Mole fraction }=\mathrm{X}_{\text {methane}}=\frac{\text { moles methane }}{\text { moles methane }+\text { moles hydrogen }+\text { moles carbon dioxide }}

\text { Mole fraction }=\mathrm{X}_{\text {methane}}=\frac{\text { 0.367 moles methane }}{\text { 0.367 moles methane }+\text { 0.221 moles hydrogen }+\text { 0.782 moles carbon dioxide }}

\text { Mole fraction }=\mathrm{X}_{\text {methane}}=\frac{0.367}{1.37}=0.268

Exercise $$\PageIndex{1.14}$$

If the mole fraction for nitrogen in a gaseous mixture were 0.565 and the total number of moles present were 2.49 moles, how many moles of nitrogen are present?

Answer

\text {Mole fraction }=\mathrm{X}_{\mathrm{A}}=\frac{\text { moles } \mathrm{A}}{\text { total number of moles }}

\text {Mole fraction }=\mathrm{X}_{\text {nitogen }}=\frac{\text { moles nitrogen }}{\text { total number of moles }}

\text {Mole fraction }=0.565=\frac{\text { moles nitrogen }}{\text { 2.49 total moles }}

\text {moles nitrogen }=\text {0.565}*\text {2.49 total moles}

\text {moles nitrogen }=\text {1.41 moles nitrogen}

Exercise $$\PageIndex{1.15}$$

Calculate the Mass percent if 7.50g CaCl2 were placed in 500mL of water. The density of water is 1.0g/mL.

Answer

\text {Mass fraction}=\frac{\text {mass solute}}{\text {total mass}}

\text { Mass Fraction }=\frac{\text { mass } \mathrm{CaCl}_{2}}{\text { mass } \mathrm{CaCl}_{2}+\text { mass water }}

\text { Mass Fraction }=\frac{7.50 \mathrm{g} \mathrm{CaCl}_{2}}{7.50 \mathrm{g} \mathrm{CaCl}_{2}+(1.0 \mathrm{g} / \mathrm{mL} \text { water } * 500 \mathrm{mL})}

\text { Mass Fraction }=\frac{7.50 \mathrm{g} \mathrm{CaCl}_{2}}{7.50 \mathrm{g} \mathrm{CaCl}_{2}+500 \mathrm{g} \text { water }}

\text { Mass Fraction }=\frac{7.50 \mathrm{g} \mathrm{CaCl}_{2}}{507.5 \mathrm{g}}

\text { Mass Percent }=0.0148 * 100 \%

\text { Mass Percent }=1.48\%

Exercise $$\PageIndex{1.16}$$

If a scientist needed a NaCl solution that had a mass percent of 2.83%, how many grams of NaCl must be added to 1.00 L of water?

Answer

\text { Mass Percent }=\frac{\text { mass solute }}{\text { mass solute}+\text { mass solvent }} * 100 \%

2.83 \%=\frac{\text { mass } \mathrm{NaCl}}{\text { mass } \mathrm{NaCl}+\text { mass water }} * 100 \%

2.83 \%=\frac{\text { mass } \mathrm{NaCl}}{\text { mass } \mathrm{NaCl}+\left(1.00 \mathrm{L} * 1 \mathrm{g} / \mathrm{mL}^{*} 1000 \mathrm{mL} / \mathrm{L}\right)} * 100 \%

0.0283=\frac{\text { mass } \mathrm{NaCl}}{\text { mass } \mathrm{NaCl}+(1000 \mathrm{g} \text { water })}

0.0283 *[\text { mass } \mathrm{NaCl}+(1000 \mathrm{g} \text { water })]=\mathrm{mass} \mathrm{NaCl}

(0.0283 * \text { mass } \mathrm{NaCl})+(0.0283 * 1000 \mathrm{g} \text { water })=\text { mass } \mathrm{NaCl}

(0.0283 * \text { mass } \mathrm{NaCl})+(28.3 \mathrm{g})=\mathrm{mass} \mathrm{NaCl}

\text { mass } \mathrm{NaCl}-(0.0283 * \text { mass } \mathrm{NaCl})=28.3 \mathrm{g}

(0.9717 * \text { mass } \mathrm{NaCl})=28.3 \mathrm{g}

\frac{(0.9717 * \text { mass } \mathrm{NaCl})}{0.9717}=\frac{28.3 \mathrm{g}}{0.9717}

\text { mass } \mathrm{NaCl}=29.1 \mathrm{g}

Exercise $$\PageIndex{1.17}$$

If 0.589g of KCl is added to a solvent, a mass percent of 0.482 is measured. How many grams of solvent must be present?

Answer

\text { Mass Percent }=\frac{\text { mass solute }}{\text { mass solute}+\text { mass solvent }} * 100 \%

\text { Mass Percent }=48.2 \%=\frac{\text { mass solute }}{\text { mass solute}+\text { mass solvent }} * 100 \%

0.482=\frac{\text { mass } \mathrm{KCl}}{\text { mass } \mathrm{KCl}+\text { mass solvent }}

0.482=\frac{0.589 \mathrm{g} \mathrm{KCl}}{0.589 \mathrm{g} \mathrm{KCl}+\mathrm{mass} \text { solvent }}

0.482 *(0.589 g \mathrm{KCl}+\text { mass solvent })=0.589 \mathrm{g} \mathrm{KCl}

0.284 g+(0.482 * \text { mass solvent })=0.589 \mathrm{g} \mathrm{KCl}

0.305 =0482 * \text { mass solvent }

\text { mass solvent }=0.633 \mathrm{g}

Exercise $$\PageIndex{1.18}$$

What is the mole fraction of NH3 in a solution prepared by dissolving 15.0g NH3 in 250g of water with a resulting density of 0.974g/mL?

Answer

$15.0g\,NH_{3}*\left ( \frac{1mol}{17.031g\,NH_{3}} \right )=0.8807mol\,NH_{3}$

$250g\,H_{2}O*\left ( \frac{1mol}{18.015g\,H_{2}O} \right )=13.8773mol\,H_{2}O$

$X_{NH_{3}}=\frac{moles\,of\,NH_{3}}{total\,moles}=\frac{0.8807mol\,NH_{3}}{(0.8807mol\,NH_{3}+13.8773mol\,H_{2}O)}=0.0597$

Exercise $$\PageIndex{1.19}$$

What is the mole fraction of He in gaseous solution containing 4.0g of He, 6.5g of Ar, and 10.0g of Ne?

Answer

$4.0g\,He*\frac{1mol\,He}{4.0026g\,He}=0.9994mol\,He$

$6.5g\,Ar*\frac{1mol\,Ar}{39.948g\,Ar}=0.1627mol\,Ar$

$10.0g\,Ne*\frac{1mol\,Ne}{20.180g\,Ne}=0.4955mol\,Ne$

$X_{He}=\frac{moles\,of\,He}{total\,moles}=\frac{0.9994mol\,He}{(0.9994mol\,He+0.1627mol\,Ar+0.4955mol\,Ne)}=0.60$

### Parts-per notation

Exercise $$\PageIndex{1.20}$$

Calculate the parts per million of 2.00L of 2.76 * 10-3 M KMnO4.  The molecular weight of KMnO4 is 158g/mol.

Answer

$Part\,per\,million = \frac{mg\,solute}{L\,solution}$

$Part\,per\,million = \frac{mg\,KMnO_{4}}{L\,solution}$

$mg\,KMnO_{4}=2.00\,L*\left ( \frac{2.76*10^{-3}\,mol}{1\,L\,KMnO_{4}}\right )\left ( \frac{158\,g}{1\,mol\,KMnO_{4}} \right )\left ( \frac{1000\,mg}{1\,g} \right )$

$mg\,KMnO_{4}=872\,mg\,KMnO_{4}$

$Parts\,per\,million=\frac{872\,mg\,KMnO_{4}}{2.00\,L\,solution}$

$Part\,per\,million = 436\,ppm$

Exercise $$\PageIndex{1.21}$$

Calculate the parts per million of 2.5L of 7.42 * 10-3M KCl.  The molecular weight of KCl is 74.55 g/mol.

Answer

$Part\,per\,million = \frac{mg\,solute}{L\,solution}$

$Part\,per\,million = \frac{mg\,KCl}{L\,solution}$

$mg\,KCl=2.5\,L*\left ( \frac{7.42*10^{-3}\,mol}{1\,L\,KCl} \right )\left ( \frac{74.55\,g}{1\,mol\,KCl} \right )\left ( \frac{1000\,mg}{1\,g} \right )$

$mg\,KCl=1380\,mg\,KCl$

$Part\,per\,million = \frac{1380\,mg\,KCl}{2.5\,L\,solution}$

$Part\,per\,million = 552\,ppm$

Exercise $$\PageIndex{1.22}$$

Calculate the parts per billion of 6.2L of a 2.77 * 10-6M solution of ZnCl2.  The molecular weight of ZnCl2 is 136.3g/mol.

Answer

$Part\,per\,billion = \frac{\mu g\,solute}{L\,solution}$

$\mu g\,solute=\mu g\,ZnCl_{2}$

$\mu g\,ZnCl_{2}=6.2\,L*\left ( \frac{2.77*10^{-6}\,mol}{1\,L} \right )*\left ( \frac{136.3\,g}{1\,mol} \right )*\left ( \frac{1*10^{6}\,\mu g}{1\,g} \right )$

$\mu g\,ZnCl_{2}=2340.8\,\mu g\,ZnCl_{2}$

$Parts\,per\,billion=\frac{2340.8\,\mu g\,ZnCl_{2}}{6.2\,L\,solution}$

$Parts\,per\,billion=377\,ppb$

Exercise $$\PageIndex{1.23}$$

Calculate the parts per billion of 5.0L of a 2.762 * 10-8M solution of AgBr2.

Answer

$Part\,per\,billion = \frac{\mu g\,solute}{L\,solution}$

$\mu g\,solute=\mu g\,AgBr_{2}$

$\mu g\,AgBr_{2}=5.0\,L*\left ( \frac{2.762*10^{-8}\,mol}{1\,L} \right )\left ( \frac{267.7\,g}{1\,mol} \right )\left ( \frac{1*10^{6}\,\mu g}{1\,g} \right )$

$\mu g\,AgBr_{2}=36.97\, \mu g\,AgBr_{2}$

$Parts\,per\,billion=\frac{36.97\,\mu g\,AgBr_{2}}{5.0\,L\,solution}$

$Parts\,per\,billion=7.39\,ppb$

### Mass Percent and Molarity

Exercise $$\PageIndex{1.24}$$

Which of the following is correct about a solution containing 28% phosphoric acid by mass?

1. The density of this solution is 2.8g/mL
2. 100g of this solution contains 28g of phosphoric acid
3. 1 mL of this solution contains 28g of phosphoric acid
4. 1 L of this solution has a mass of 28g
5. 1 L of this solution contains 28mL of phosphoric acid
Answer

b. 100g of this solution contains 28g of phosphoric acid

Exercise $$\PageIndex{1.25}$$

What is the concentration of chloride ion (mass %) in a solution that contains 35.0ppm chloride?

Answer

$\frac{35.0ppm}{10^{6}}*100=0.0035\%$

Exercise $$\PageIndex{1.26}$$

What is the concentration of CaCl2 (mass %), if a solution is prepared by dissolving 23.7g of CaCl2 in 375g of water with a density of 1.05g/mL?

Answer

$\%\,by\,mass=\frac{mass\,of\,solute}{total\,mass\,of\,solution}*100$

$\%\,by\,mass=\frac{23.7g}{23.7g\,+\,375g}*100=5.94\%$

Exercise $$\PageIndex{1.27}$$

Urea has a molar mass of 60.0g/mol. If 16g of urea is dissolved in 39g of water, what is the resulting concentration in mass percent?

Answer

$\%\,by\,mass=\frac{mass\,of\,solute}{total\,mass\,of\,solution}*100$

$\%\,by\,mass=\frac{16g}{16g\,+\,39g}*100=29\%$

Exercise $$\PageIndex{1.28}$$

An organic solution is 72% water.  If the density of the organic material is 1.3 g/mL and the molecular weight is 64 g/mol, calculate the molarity of the solution.

Answer

$\%\,water+\,\%\,organic\,compound=100\%$

$\%\,organic\,compound=100\%-\%\,water$

$\%\,organic\,compound=100\%-72\%$

$\%\,organic\,compound=28\%$

$Molarity=\frac{moles\,organic\,compound}{L\,solution}$

$Molarity=\left ( \frac{28mL\,organic\,compound}{100mL\,solution} \right )*\left ( \frac{1.3g\,organic\,compound}{1mL\,organic\,compound} \right )*\left ( \frac{1mol\,organic\,compound}{65g\,organic\,compound} \right )*\left ( \frac{1000mL}{L} \right )$

$Molarity=\frac{5.7\,moles\,organic\,solution}{L\,solution}$

$Molarity=5.7M$

Exercise $$\PageIndex{1.29}$$

Commercial vinegar has been analytically determined to be 10.2% acetic acid (CH3COOH) by mass.  The molecular mass of acetic acid is 60 g/mol.  The density of vinegar is 1.01g/mL.  Calculate the molarity of acetic acid in 50 mL of vinegar.

Answer

$Molarity=\frac{moles\,CH_{3}COOH}{L\,solution}$

$Molarity=\left ( \frac{10.2g\,CH_{3}COOH}{100g\,solution} \right )*\left ( \frac{1.01g\,solution}{1mL\,solution} \right )*\left ( \frac{1mol\,CH_{3}COOH}{60g\,CH_{3}COOH} \right )*\left ( \frac{1000mL}{L} \right )$

$Molarity=1.717M$

Exercise $$\PageIndex{1.30}$$

What is the molarity of a solution that is 3.6% by mass NaOH.  The molecular mass of NaOH is 40 g/mol, and the density of the solution is 1.0g/mL.

Answer

$Molarity=\frac{moles\,NaOH}{L\,solution}$

$Molarity=\left ( \frac{3.6g\,NaOH}{100g\,solution} \right )*\left ( \frac{1.00g\,solution}{1mL\,solution} \right )*\left ( \frac{1mol\,NaOH}{40g\,NaOH} \right )*\left ( \frac{1000mL}{L} \right )$

$Molarity=0.900M$

Exercise $$\PageIndex{1.31}$$

A 2.7M solution is found to be composed of 8.3% by mass of an unknown organic compound.  The density of the solution was experimentally determined to be 1.5g/mL.  In order for a scientist to identify the compound, he must know the molecular mass.  Calculate the molecular mass of the unknown compound.

Answer

$Molecular\,weight=\frac{grams}{mole}unknown$

$Molecular\,weight=\left ( \frac{8.3g\,unknown}{100g\,solution} \right )*\left ( \frac{1.5g\,solution}{1mL\,solution} \right )*\left ( \frac{1000mL}{L} \right )*\left ( \frac{1L\,solution}{2.7\,moles\,unknown} \right )$

$Molecular\,weight=46g/mol$

Exercise $$\PageIndex{1.32}$$

Calculate the molar concentration of a solution containing 11.8g MgBr2 dissolved in 100mL of water.  The density of the solution is 1.2g/mL, and the molecular mass of MgBr2 is 184g/mol.

Answer

$Molarity=\frac{moles\,MgBr_{2}}{L\,solution}$

$moles\,MgBr_{2}=\frac{mass\,MgBr_{2}}{molar\,mass\,MgBr_{2}}$

$moles\,MgBr_{2}=11.8g\,MgBr_{2}*\left ( \frac{1mol\,MgBr_{2}}{184g\,MgBr_{2}} \right )=0.0641mol\,MgBr_{2}$

$volume=0.118kg*\left ( \frac{L}{1.2kg} \right )=0.0983L$

$Molarity=\frac{0.0641mol\,MgBr_{2}}{0.0983L}=0.652M$

## 13.3: Pressure and Temperature Effects on Solubility

### Henry's Law

Exercise $$\PageIndex{3.1}$$

With a solute of methane gas (CH4), what is the lowest Henry’s Law constant (k) that can be obtained with _____ as the solvent and _____ K as the temperature?

1. C5H12, 301
2. C6H6, 322
3. C6H6, 349
4. H2O, 301
5. H2O, 349
Answer

e. H2O, 349

Exercise $$\PageIndex{3.2}$$

The solubility of nitrogen in blood is 5.4x10-4M at 37°C and 0.8atm.  When a deep-sea diver breathes the compressed air from a tank at a partial pressure of 1.6atm, what would be the solubility of nitrogen if the temperature remains constant?

Answer

$S=kP$

$\frac{S_{1}}{S_{2}}=\frac{kP_{1}}{kP_{2}}$

$S_{1}=S_{2}\frac{P_{1}}{P_{2}}$

$S_{1}=5.4*10^{-4}M\left ( \frac{1.6atm}{0.8atm} \right )$

$S_{1}=1.08*10^{-3}M$

Exercise $$\PageIndex{3.3}$$

What is the Henry’s law Constant k in Q 13.3.2?

Answer

$S=kP$

$\frac{S}{P}=k=\frac{5.4*10^{-4}M}{0.8atm}=6.75*10^{-4}M/atm$

Exercise $$\PageIndex{3.4}$$

The solubility of CO2 in water is 0.035M at 25°C and 1 atm.  What is the Henry’s law Constant k?

Answer

$S=kP$

$\frac{S}{P}=k=\frac{0.035M}{1atm}=0.035M/atm$

Exercise $$\PageIndex{3.5}$$

What would be the solubility of CO2 in water at 0.04atm?  (Use the information from Q 13.3.4)

Answer

$S=kP$

$\frac{S_{1}}{S_{2}}=\frac{kP_{1}}{kP_{2}}$

$S_{1}=S_{2}\frac{P_{1}}{P_{2}}$

$S_{1}=0.035M\left ( \frac{0.04atm}{1atm} \right )$

$S_{1}=1.4*10^{-3}M$

Exercise $$\PageIndex{3.6}$$

The solubility of oxygen in water at 0°C and 1 atm is 0.07g/L, what is the Henry’s law Constant k?

Answer

$S=kP$

$\frac{S}{P}=k=\frac{0.07g/L}{1atm}=0.07g/L*atm$

Exercise $$\PageIndex{3.7}$$

What would be the solubility of oxygen in water at 2.5atm? (Use the information from Q 13.3.6)

Answer

$S=kP$

$\frac{S_{1}}{S_{2}}=\frac{kP_{1}}{kP_{2}}$

$S_{1}=S_{2}\frac{P_{1}}{P_{2}}$

$S_{1}=0.07g/L\left ( \frac{2.5atm}{1atm} \right )$

$S_{1}=0.175g/L$

Exercise $$\PageIndex{3.8}$$

What is the concentration of nitrogen in water when the partial pressure of N2 above the solution is 0.826 atm? Henry’s Law constant for this system is 6.8*10-4 mol/L*atm.

Answer

$S=kP$

$S=kP=\left (6.8*10^{-4}mol/L*atm \right )*\left ( 0.826atm \right )=5.6*10^{-4}M$

Exercise $$\PageIndex{3.9}$$

The solubility of oxygen gas in water at 25°C and 1.0 atm pressure of oxygen is 0.041 g/L. The solubility of oxygen in water at 3.0 atm and 25°C is _____ g/L.

Answer

$S=kP$

$\frac{S_{1}}{S_{2}}=\frac{kP_{1}}{kP_{2}}$

$\frac{S_{1}}{S_{2}}=\frac{P_{1}}{P_{2}}$

$S_{2}=S_{1}*\frac{P_{2}}{P_{1}}=0.041g/L*\frac{3.0atm}{1.0atm}=0.12g/L$

Exercise $$\PageIndex{3.10}$$

The solubility of argon in water is 25°C is 1.6*10-3 mol/L when the pressure of argon above the solution is 1.0 atm. The solubility of argon at a pressure of 2.5 atm is _____ mol/L.

Answer

$S=kP$

$\frac{S_{1}}{S_{2}}=\frac{kP_{1}}{kP_{2}}$

$\frac{S_{1}}{S_{2}}=\frac{P_{1}}{P_{2}}$

$S_{2}=S_{1}*\frac{P_{2}}{P_{1}}=\left ( 1.6*10^{-3}mol/L \right )*\frac{2.5atm}{1.0atm}=4.0*10^{-3}mol/L$

Exercise $$\PageIndex{3.11}$$

The solubility of nitrogen gas in water at 25°C and 0.78 atm is 5.3*10-4 M. What is the partial pressure of nitrogen when its solubility in water (at 25°C) is 1.1*10-3 M?

Answer

$S=kP$

$\frac{S_{1}}{S_{2}}=\frac{kP_{1}}{kP_{2}}$

$\frac{S_{1}}{S_{2}}=\frac{P_{1}}{P_{2}}$

$P_{2}=P_{1}*\frac{S_{2}}{S_{1}}=0.78atm*\frac{1.1*10^{-3}M}{5.3*10^{-4}M}=1.6atm$

## 13.4: Colligative Properties

### Boiling Point

Exercise $$\PageIndex{4.1}$$

The boiling point elevation constant for water is 0.52 C/m. A 1.34 m aqueous solution of compound X had a boiling point of 101.4C. Which of the following could be compound X?

1. Na3PO4
2. KCl
3. CH3CH2OH
4. CaCl2
5. C6H12O6
Answer

b. KCl

Exercise $$\PageIndex{4.2}$$

Ethylene glycol is a common component of anti-freeze.  A solution of ethylene glycol and water has a boiling point of 101.0°C.  What is the molality of the solution?  Kbp of water is 0.5121°C /m

Answer

$\Delta t=K_{bp}m$

The boiling point of pure water is 100°C.

$m=\frac{\Delta t}{K_{bp}}$

$m=\frac{101.0\,^{0}C-100.00\,^{0}C}{0.5121\,^{0}C/m}$

$m=1.95m$

Exercise $$\PageIndex{4.3}$$

How many grams of ethylene glycol (MW=62.068 g/mol) is need to add to 250g of water to increase the boiling point by 1.00°C? Kbp of water is 0.5121°C /m

Answer

$\Delta t=K_{bp}m$

$m=\frac{\Delta t}{K_{bp}}$

$m=\frac{1.0\,^{0}C}{0.5121\,^{0}C/m}$

$m=1.95m$

$molality=\frac{moles\,of\,the\,solute}{mass\,of\,the\,solvent\,in\,kg}$

Assume there is x grams fo ethylene glycol,

$\frac{\frac{x}{62.068}}{\frac{250}{1000}}=1.95m$

solve for x, x=30.3g

Exercise $$\PageIndex{4.4}$$

Determine the boiling point of a 0.80m solution of CaF2

Answer

Kbp of water is 0.5121°C/m

The solution of CaF2 is a mixture of water and CaF2, a strong electrolyte. As each CaF2 creates one Ca+2 and two F- and if we ignore ion pairing (Van't Hoff effect) the total molality is 2.40m.

$\Delta t=K_{bp}m=0.5121*2.40=1.23\,^{0}C$

$T=100.0\,^{0}C+1.23\,^{0}C=101.23\,^{0}C$

Exercise $$\PageIndex{4.5}$$

Methyl Salicylate is used in food flavoring and pharmaceuticals. Adding 1.25g of methyl salicylate (MW=152.14g/mol) to 100g of benzene will raise the boiling point to what temperature?  Kbp of benzene is 2.53°C /m, and the boiling point of pure benzene is 80.10°C.

Answer

$\Delta t=K_{bp}m$

$molality=\frac{moles\,of\,the\,solute}{mass\,of\,the\,solvent\,in\,kg}$

$\Delta t=\frac{\frac{1.25g}{152.14g/mol}}{\frac{100g}{1000}}*2.53\,^{0}C/m=0.21\,^{0}C$

$T=80.10\,^{0}C+0.21\,^{0}C=80.31\,^{0}C$

Exercise $$\PageIndex{4.6}$$

Adding 36.0g of glucose (MW= 180g/mol) to 500.0 g of ethyl alcohol will raise the boiling point to 79.3°C.  Pure ethanol has a boiling point of 78.5°C.  What is the value for Kbp?

Answer

$\Delta t=K_{bp}m$

$K_{bp}=\frac{\Delta t}{m}=\frac{79.3-78.5}{\frac{\frac{36.0}{180}}{0.500}}=2.0\,^{0}C/m$

### Freezing Point Depression

Exercise $$\PageIndex{4.7}$$

Which of the following liquids have the lowest freezing point?

1. Pure H2O
2. Aq. 0.050 m glucose
3. Aq. 0.030 m NaI
4. Aq. 0.030 m CoI2
5. Aq. 0.030 m AlI3
Answer

e. Aq. 0.030 m AlI3

Exercise $$\PageIndex{4.8}$$

What is the freezing point of an aqueous 2.00m NaCl solution? Kf of water is 1.86°C/m.

Answer

$\Delta t=K_{f}m$

The solution of Nacl is a mixture of water and NaCl, a strong electrolyte. As each NaCl creates one Na+ and one Cl- and if we ignore ion pairing (Van't Hoff effect) the so 2.00m NaCl s 4.00m in all ions.

$\Delta t=K_{f}m=1.86*4.00=7.44\,^{0}C] The freezing point of pure water is 0°C \[t=0-7.44=-7.44\,^{0}C$

Exercise $$\PageIndex{4.9}$$

Determine the freezing point of a solution that is made of 3.60g of glucose C6H12O6 in 20.0g of water. Kf of water is 1.86°C/m.

Answer

$\Delta t=K_{f}m$

$m=\frac{\frac{3.60g}{180g/mol}}{0.0200kg}=1.00m$

The freezing point of pure water is 0°C

$t=0-1.86=-1.86\,^{0}C$

Exercise $$\PageIndex{4.10}$$

Reserpine is a substance that is used as a tranquilizer and sedative. A solution containing 0.20g of reserpine in 5.0g of camphor (Kf = 40.0°C/m) gives a freezing point 2.63°C below the freezing point of pure camphor. Determine the molecular weight of reserpine.

Answer

$\Delta t=K_{f}m$

$m=\frac{\Delta t}{K_{f}}=\frac{2.63}{40.0}=0.06575$

$m=\frac{\frac{0.20g}{Molar\,mass}}{0.050kg}=0.06575$

$Molar\,mass=608.4g/mol$

Exercise $$\PageIndex{4.11}$$

The melting point of pure benzene is 278.70K and Kf 4.90K/m. When 2.10g of an unknown solute is added to 50.0g of benzene, the freezing point of the solution is 277.60K. Determine the molecular weight of the unknown.

Answer

$\Delta t=278.70-277.60=1.10$

$m=\frac{\Delta t}{K_{f}}=\frac{1.10}{4.90}=0.224$

$m=\frac{\frac{2.10g}{Molar\,mass}}{0.0500kg}=0.224$

$Molar\,mass=187.09g/mol$

Exercise $$\PageIndex{14.12}$$

The freezing point of a solution prepared with 3.54g of acetamide (C2H5ON) to 200.0g of naphthalene (C10H8) was 78.2°C.  Pure naphthalene solidified at 80.2°C.  Determine the freezing point constant for naphthalene.

Answer

$\Delta t=80.2-78.2=2.0$

$m=\frac{\frac{3.54g}{59g/mol}}{0.200kg}=0.30$

$K_{f}=\frac{\Delta t}{m}=\frac{2.0}{0.30}=6.7K/m$

Exercise $$\PageIndex{4.13}$$

How many grams of antifreeze (C2H6O2) need be added to 200.0g of water to have a solution that will not freeze at the temperature -10°C?  Kf of water is 1.86°C/m. How many grams of antifreeze (C2H6O2) need be added to 200.0g of water to have a solution that will not freeze at the temperature -10°C?  Kf of water is 1.86°C/m

Answer

$\Delta t=0-(-10.0)=10.0$

$m=\frac{\Delta t}{}K_{f}=\frac{10.0}{1.86}=5.38$

$m=\frac{\frac{mass}{62g/mol}}{0.200kg}=5.38$

$mass=66.7g$

Exercise $$\PageIndex{4.14}$$

Calculate the freezing point (°C) of a solution prepared by dissolving 50.0g of glycerin (C3H8O3, a nonelectrolyte) in 200g of ethanol. Ethanol has a freezing point of -114.6°C and a molal freezing point depression constant of 2.00 °C/m.

Answer

$moles\,solute=50.0g*\frac{1mol}{92.064g}=0.543mol$

$kg\,solvent=200g*\frac{1kg}{1000g}=0.200kg$

$m=\frac{moles\,solute}{kg\,solvent}=\frac{0.543mol}{0.200kg}=2.72m$

$\Delta t=K_{f}m=2.00\,^{0}C/m*2.72m=5.43\,^{0}C$

$\Delta t=T_{f\,solute}-T_{f\,solution}$

$T_{f\,solution}=T_{f\,solute}-\Delta t=-114.6\,^{0}C-5.42\,^{0}C=-120.0\,^{0}C$

### Vapor Pressure and Raoult's Law

Exercise $$\PageIndex{4.15}$$

Which of the following solutes will have the lowest vapor pressure in a 0.100m solution?

1. NaCl
2. KCl4
3. CH3OH
4. Ca(ClO4)2
5. Al(ClO4)3
Answer

e. Al(ClO4)3

Exercise $$\PageIndex{4.16}$$

When _____ negative deviations from Raoult’s Law are encountered.

1. Solute-solute and solvent-solvent interactions are stronger than solute-solvent interactions,
2. Interactions between solute and solvent are very weak,
3. Solute-solute and solvent-solvent interactions have the same strength as solute-solvent interactions,
4. None of these
5. Interactions between solute and solvent are exceptionally strong,
Answer

b. Interactions between solute and solvent are very weak,

Exercise $$\PageIndex{4.17}$$

The vapor pressure of water at room temperature is 23.8 torr.  If 90g of glucose (C6H12O6) were added to 500.0 g of water, what will be the vapor pressure of the solution?

Answer

$P_{solvent}=X_{solvent}*P^{0}_{solvent}$

$90g\,C_{6}H_{12}O_{6}*\left ( \frac{1mol\,C_{6}H_{12}O_{6}}{180g\,C_{6}H_{12}O_{6}} \right )=0.5mol\,C_{6}H_{12}O_{6}$

$500g\,H_{2}O*\left ( \frac{1mol\,H_{2}O}{18g\,H_{2}O} \right )=27.8mol\,\,H_{2}O$

$X=\frac{27.8mol\,H_{2}O}{27.8mol\,H_{2}O+0.5mol\,C_{6}H_{12}O_{6}}=0.98$

$P=0.98*23.8=23.3torr$

Exercise $$\PageIndex{4.18}$$

What would be the vapor pressure when 32.0g of naphthalene(C10H8) are dissolved in 1000g of benzene (C6H6) at 250C?  The vapor pressure of benzene at 250C is 110 torr.

Answer

$P_{solvent}=X_{solvent}*P^{0}_{solvent}$

The molar mass of naphthalene is 128g/mol, and he benzene is 78g/mol.

$P=\frac{\frac{1000}{78}}{\frac{1000}{78}+\frac{32}{128}}*110torr=107.9torr$

Exercise $$\PageIndex{4.19}$$

The vapor pressure of water at 30.00C is 31.8 torr.  How many moles of glucose C6H12O6  need to be added into 150.0 g of water to lower the vapor pressure to 29.0 torr?

Answer

$P_{solvent}=X_{solvent}*P^{0}_{solvent}$

$X_{solvent}=\frac{P_{solvent}}{P^{0}_{solvent}}=\frac{29.0}{31.8}=0.91$

$\frac{150.0g}{18g/mol}=8.3moles\,of\,water$

$X_{solvent}=\frac{8.3}{8.3+moles\,of\,glucose}=0.91$

$moles\,of\,glucose:\,0.8moles$

Exercise $$\PageIndex{4.20}$$

When 90.0 g of the solid were added to 50.0g of water, the vapor pressure of the solution dropped from 17.4 torr to 12.4 torr.  Determine the molecular mass of the compound.

Method 1

$P_{solvent}=X_{solvent}*P^{0}_{solvent}$

$X_{solvent}=\frac{P_{solvent}}{P^{0}_{solvent}}=\frac{12.4}{17.4}=\frac{\frac{50.0}{18}}{\frac{50.0}{18}+\frac{90.0}{MW}}$

solve for MW,

$MW=80.4g/mol$

Method 2

$\Delta P=-X_{solute}*P^{0}_{solvent}$

$\Delta P=12.4-17.4=-5.0torr$

$X_{solvent}=-\frac{\Delta P}{P^{0}_{solvent}}=-\frac{-5.0}{17.4}=0.287$

$X_{solvent}=\frac{\frac{90.0}{MW}}{\frac{90.0}{MW}+\frac{50.0}{18}}=0.287$

solve for MW,

$MW=80.4g/mol$

Exercise $$\PageIndex{4.21}$$

What is the vapor pressure of a 10% aqueous solution of sucrose (C12H22O11) at 200C?  The vapor pressure of water at 200C is 17.5 torr.

Answer

Assume the solution is 100.0g. Then, 10% of the solution implies that the solution contains 10.0g of the solute (sucrose MW=342g/mol), and 90.0g of water.

$\frac{10.0g}{342g/mol}=0.029mol\,sucrose$

$\frac{90.0}{18g/mol}=5.0g$

$X=\frac{5.0}{5.0+0.029}=0.994$

$P_{solvent}=X_{solvent}*P^{0}_{solvent}$

$P=0.994*17.5=17.4torr$

Exercise $$\PageIndex{4.22}$$

Pure ethanol has a vapor pressure of 349 torr at 60°C. Using Raoult’s Law predict the vapor pressure of 10.0 mmol naphthalene (nonvolatile) dissolving in 90.0 mmol of ethanol.

Answer

$X=\frac{moles\,ethanol}{total\,moles}=\frac{90.0mmol}{90.0mmol+10.0mmol}=0.90$

$P=X*P^{0}=0.90*349torr=314torr$

Exercise $$\PageIndex{4.23}$$

Calculate the vapor pressure of water above a solution prepared by dissolving 18g of glucose (a nonelectrolyte, MW=180g/mol) in 95g of water? Pure water has a vapor pressure of 23.8 torr at 25°C.

Answer

$18g\,glucose*\frac{1mol}{180g\,glucose}=0.1mol\,glucose$

$95g\,water*\frac{1mol}{18g\,water}=5.28mol\,water$

$X=\frac{moles\,water}{total\,moles}=\frac{5.28mol}{5.28mol+0.1mol}=0.981$

$P=X*P^{0}=0.981*23.8torr=23.4torr$

### Osmotic Pressure

Exercise $$\PageIndex{4.24}$$

What is the osmotic pressure of a solution made by adding 9.0g of glucose, C6H12O6, to enough water to make 250ml solution at 25°C?

Answer

$$\pi =MRT$$, where R = 0.08206 L/K*mol

$M=\frac{\frac{9.0g}{180g/mol}}{0.250L}=0.2M$

$\pi =0.2*0.08206*(273.15+25)=4.89atm$

Exercise $$\PageIndex{4.25}$$

The osmotic pressure of blood is 7.5atm at 37°C.  How much glucose should be used per liter to make an intravenous injection that has the same osmotic pressure as blood?

Answer

$$\pi =MRT$$, where R = 0.08206 L/K*mol

$M=\frac{\pi }{RT}=\frac{7.5}{0.08206*310.15}=0.295M$

$0.95mol/L*180g/mol=53.04g$

Exercise $$\PageIndex{4.26}$$

What is the osmotic pressure of 0.0015g of NaCl at 25°C?

Answer

$$\pi =MRT$$, where R = 0.08206 L/K*mol

The solution of NaCl is a mixture of water and NaCl, a strong electrolyte. As each NaCl creates on Na+ and one Cl- and if we ignore ion pairing (Van't Hoff effect) the 0.0015M NaCl is 0.0030M in all ions.

$\pi =0.0030*0.08206*298.15=0.074atm$

Exercise $$\PageIndex{4.27}$$

What is the minimum pressure required to desalinate 1.0M NaCl solution at 25°C?

Answer

$$\pi =MRT$$, where R = 0.08206 L/K*mol

The solution of NaCl is a mixture of water and NaCl, a strong electrolyte. As each NaCl creates on Na+ and one Cl- and if we ignore ion pairing (Van't Hoff effect) the 1.0M NaCl is 2.0M in all ions.

$\pi =2.0*0.08206*298.15=49atm$

The reverse osmotic pressure has to be twice as much to desalinate the salt solution. Therefore, the answer will be 98 atm.

Exercise $$\PageIndex{4.28}$$

What is the osmotic pressure of a 0.25M urea solution that is isotonic with seawater at 4°C?

Answer

$$\pi =MRT$$, where R = 0.08206 L/K*mol

$\pi =0.25*0.08206*277.15=5.7atm$

Exercise $$\PageIndex{4.29}$$

The osmotic pressure of a tryptophan solution is 103.5torr at 25°C.  If the solution has a density of 1.136g/L, what is the molar mass of the amino acid?

Answer

$$\pi =MRT$$, where R = 0.08206 L/K*mol

$103.5torr*\frac{1atm}{760torr}=0.136atm$

$M=\frac{\pi }{RT}=\frac{0.136}{0.08206*298.15}=0.0056M$

$\frac{\frac{1.136g}{molar\,mass}}{1L}=0.0056M$

$molar\,mass=204g/mol$

Exercise $$\PageIndex{4.30}$$

Using a solution prepared by dissolving 0.60g of nicotine (a nonelectrolyte) in water to make 12mL of solution has an osmotic pressure of 7.55atm at 25C. What is the molecular weight of nicotine in g/mol?

Answer

$$\pi =MRT$$, where R = 0.08206 L/K*mol

$M=\frac{\pi }{RT}=\frac{7.55atm}{0.08206*(25+273.15)}=0.309M$

$12mL*\frac{1L}{1000mL}\frac{0.309mol}{1L}=3.70*10^{-3}mol$

$3.70*10^{-3}mol=\frac{0.60g}{molar\,mass}$

$molar\,mass=162g/mol$

## General Questions

Exercise $$\PageIndex{1}$$

Of the following, _____ is the only unit that varies with temperature.

1. Mole fraction
2. Molarity
3. Molality
4. Mass percent
5. All of these
Answer

b. Molarity

Exercise $$\PageIndex{2}$$

_____ is the process of solute particles being surrounded by solvent particles.

1. Agglomeration
2. Agglutination
3. Passivation
4. Salutation
5. Solvation
Answer

e. Solvation

Exercise $$\PageIndex{3}$$

_____ prevents the dissolution of water in octane (C8H18).

1. Dipole-dipole attraction between octane molecules
2. Hydrogen bonding between molecules
3. Ion-dipole attraction between water and octane molecules
4. London dispersion forces between octane molecules
5. Repulsion between like-charged water and octane molecules
Answer

b. Hydrogen bonding between molecules

Exercise $$\PageIndex{4}$$

Which of the following cannot constitute a solution?

1. Gaseous solvent, gaseous solute
2. Gaseous solvent, solid solute
3. Liquid solvent, gaseous solute
4. Solid solvent, gaseous solute
5. Solid solvent, liquid solute
Answer

b. Gaseous solvent, solid solute

Exercise $$\PageIndex{5}$$

Like dissolves like” refers to the fact that _____.

1. Condensed phases can only dissolve other condensed phases
2. Gases can only dissolve other gases
3. Polar solvents dissolve nonpolar solutes and vice versa
4. Polar solvents dissolve polar solutes and nonpolar solvents dissolve nonpolar solutes
5. Solvents can only dissolve solutes of similar molar mass
Answer

d. Polar solvents dissolve polar solutes and nonpolar solvents dissolve nonpolar solutes

Exercise $$\PageIndex{6}$$

A saturated solution _____.

1. cannot be attained
2. contains as much solvent as it can hold
3. contains dissolved solute in equilibrium with undissolved solid
4. contains no double bonds
5. will rapidly precipitate if a seed crystal is added
Answer

c. contains dissolved solute in equilibrium with undissolved solid

Exercise $$\PageIndex{7}$$

Which of the following should be immiscible with carbon tetrachloride, CCl4?

1. Br2
2. C3H8
3. C6H14
4. CH3CH2OH
5. CHCl3
Answer

d. CH3CH2OH

Exercise $$\PageIndex{8}$$

Of the following, _____ will be the most soluble in CCl4.

1. C10H22
2. CH3CH2OH
3. H2O
4. NaCl
5. NH3
Answer

a. C10H22

Exercise $$\PageIndex{9}$$

_____ is more likely to dissolve in CH3OH.

1. CCl4
2. CH3CH2OH
3. H2
4. Kr
5. N2
Answer

b. CH3CH2OH

Exercise $$\PageIndex{10}$$

Of the following, _____ is more likely to dissolve in benzene (C6H6)?

1. CCl4
2. CH3CH3OH
3. HBr
4. NaCl
5. NH3
Answer

a. CCl4

Exercise $$\PageIndex{11}$$

Which of the following alcohols is the most soluble in water?

1. CH3OH
2. CH3CH2OH
3. CH3CH2CH2OH
4. CH3CH2CH2CH2OH
5. CH3CH2CH2CH2CH2OH
Answer

a. CH3OH

Exercise $$\PageIndex{12}$$

Which of the following alcohols is the most soluble in hexane (C6H14)?

1. CH3OH
2. CH3CH2OH
3. CH3CH2CH2OH
4. CH3CH2CH2CH2OH
5. CH3CH2CH2CH2CH2OH
Answer

e. CH3CH2CH2CH2CH2OH

Exercise $$\PageIndex{13}$$

_____ is a solution with a concentration higher that the solubility.

1. Unsaturated solution
2. Supersaturated solution
3. Supercritical solution
4. Saturated solution
5. Not possible solution
Answer

b. Supersaturated solution

Exercise $$\PageIndex{14}$$

_____ when dissolved in liquids are affected by greatly by pressure.

1. Gases
2. Solids
3. Liquids
4. All of the above
5. Solids and liquids
Answer

a. Gases

Exercise $$\PageIndex{15}$$

Of the following, which is correctly arranged in order of increasing solubility in water? (Least soluble to most soluble.)

1. LiF < NaNO3 < CHCl3
2. CH4 < NaNO3 < CHCl3
3. CH3OH < CH4 < LiF
4. CH3OH < CCl4 < CHCl3
5. CCl4 < CHCl3 < NaNO3
Answer

e. CCl4 < CHCl3 < NaNO3

Exercise $$\PageIndex{16}$$

The identity of the _____ determines the magnitude of the kfp and kbp.

1. Temperature
2. Solvent
3. Solution
4. Solute and solvent
5. Solute
Answer

b. Solvent

Exercise $$\PageIndex{17}$$

The _____ decreases when adding solute to the solution.

1. Vapor pressure
2. Osmotic pressure
3. Freezing point and vapor pressure
4. Freezing point
5. Boiling point
Answer

c. Freezing point and vapor pressure

Exercise $$\PageIndex{18}$$

What is the process of a substance sticking to the surface of another?

1. Effusion
2. Diffusion
3. Coagulation
4. Adsorption
5. Absorption
Answer

d. Adsorption

Exercise $$\PageIndex{19}$$

Which of the following produces the greatest number of ion when one mole dissolves in water?

1. Sucrose
2. NH4NO3
3. NH4Cl
4. NaCl
5. Na2SO4
Answer

e. Na2SO4

Exercise $$\PageIndex{20}$$

Consider an aqueous solution of a nonvolatile compound, the vapor pressure will be _____, the boiling point will be _____, and the freezing point will be _____ than for pure water.

1. Lower, lower, lower
2. Lower, higher, lower
3. Lower, higher, higher
4. Higher, lower, higher
5. Higher, higher, lower
Answer

b. Lower, higher, lower

Exercise $$\PageIndex{21}$$

A solution of 26.5g of methanol (CH3OH) is dissolved in 244g of water with a density of 0.975g/mL. What is the molarity, molality, and mole fraction of the solution?

Molarity

$26.5g\,MeOH*\frac{1mol\,MeOH}{32.0g\,MeOH}=0.828mol\,MeOH$

$total\,weight\,of\,solution=244g+26.5g=270.5g$

$270.5g*\frac{1mL}{0.975g}*\frac{1L}{1000mL}=0.27744L$

$M=\frac{moles\,of\,solute}{L\,of\,solution}=\frac{0.828mol}{0.27744L}=2.99mol/L$

Molality

$m=\frac{moles\,of\,solute}{kg\,of\,solvent}=\frac{0.828mol}{0.244kg}=3.39mol/kg$

Mole fraction

$244.0g\,H_{2}O*\frac{1mol\,H_{2}O}{18.0g\,H_{2}O}=13.65mol\,H_{2}O$

$total\,moles=0.828mol+13.64mol=14.388mol$

$X_{MeOH}=\frac{moles\,MeOH}{total\,moles\,solution}=\frac{0.828mol}{14.388mol}=0.0575$

Exercise $$\PageIndex{22}$$

Calculate the molarity of an aqueous sodium chloride solution that is 13.0% sodium chloride by mass and density of 1.10g/mL.

Answer

$mass\,of\,NaCl=\frac{13}{100}*1100g=143g$

$143g\,NaCl*\frac{1mol\,NaCl}{58.5g\,NaCl}=2.44mol\,NaCl$

$M=\frac{2.44mol\,NaCl}{1L}=2.44M$

Exercise $$\PageIndex{23}$$

Calculate the percent composition by mass of sodium chloride in an aqueous solution of sodium chloride with a concentration of 2.23M and density of 1.01g/mL.

Answer

$moles\,of\,NaCl=molarity*vol=2.23M*1L=2.23mol\,NaCl$

$mass\,of\,NaCl=moles*atomic\,weight=2.23*(23.0+35.5)=130g\,NaCl$

$\frac{0.130kg}{1.01}*100=12.9\%$

Exercise $$\PageIndex{24}$$

An aqueous solution of sodium chloride has a concentration of 2.22M and 11.0% sodium chloride by mass. What is the density (g/mL) of this solution?

Answer

$M=\frac{mass\%*10*density}{molar\,mass}$

$2.22mol/L=\frac{11.0*10*density}{58.5g/mol}$

$density=1.18g/mL$

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