Ch.12 - SolutionsWorksheetSee all chapters
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Ch.1 - Intro to General Chemistry
Ch.2 - Atoms & Elements
Ch.3 - Chemical Reactions
BONUS: Lab Techniques and Procedures
BONUS: Mathematical Operations and Functions
Ch.4 - Chemical Quantities & Aqueous Reactions
Ch.5 - Gases
Ch.6 - Thermochemistry
Ch.7 - Quantum Mechanics
Ch.8 - Periodic Properties of the Elements
Ch.9 - Bonding & Molecular Structure
Ch.10 - Molecular Shapes & Valence Bond Theory
Ch.11 - Liquids, Solids & Intermolecular Forces
Ch.12 - Solutions
Ch.13 - Chemical Kinetics
Ch.14 - Chemical Equilibrium
Ch.15 - Acid and Base Equilibrium
Ch.16 - Aqueous Equilibrium
Ch. 17 - Chemical Thermodynamics
Ch.18 - Electrochemistry
Ch.19 - Nuclear Chemistry
Ch.20 - Organic Chemistry
Ch.22 - Chemistry of the Nonmetals
Ch.23 - Transition Metals and Coordination Compounds
Sections
Solutions, Molarity and Intermolecular Forces
Henry's Law
Calculate Molarity
Mass Percent
Molality
Mole Fraction
The Colligative Properties
Additional Practice
Making Solutions
Freezing Point Depression
Colloid
Additional Guides
ppm
The Freezing Point Depression
Boiling Point Elevation
LearnAdditional Practice
Next SectionThe Colligative Properties

Mole Fraction (X) relates the moles of solute and solvent within a solution. 

Understanding Mole Fraction

Concept #1:

Mole Fraction is depicted as moles of solute per moles of solution. 

 

Example #1: If the mole fraction of glucose, C6H12O6, in an aqueous solution is 0.320 what is the molarity? Density of the solution is 1.530 g/mL. 

Example #2: If the mole fraction of methanol, CH3OH, in an aqueous solution is 0.060 what is the molality? Density of the solution is 1.39 g/mL. 

Example #3:

Calculate the mole fraction of acetic acid, HC2H3O2, in a 27.13 mass % aqueous solution (d = 0.9883 g/mL). MW of HC2H3O2 is 60.054 g/mol. 

 

Previous SectionMolality
Next SectionThe Colligative Properties
Additional Problems
The molecular formula of Vitamin E (tocopherol is C29H50O2 (MW = 420.71). If the mole fraction of vitamin E in a methyl alcohol (CH3OH) solution is 0.002, what is the molality of the Vitamin E solution? a. none of the other answers is even close (within 10% error) b. 0.00273 c. 0.00503 d. 0.0625 e. 0.1570
A solution of sodium methoxide, NaOCH 3, in water has a mole fraction of 0.1750. What is the molality?
A sulfuric acid solution containing 571.5 g of H2 SO4 per liter of aqueous solution has a density of 1.329 g/cm3.Calculate the mole fraction of H2 SO4 in this solution.
The density of acetonitrile (CH3 CN) is 0.786 g/mL, and the density of methanol (CH3 OH) is 0.791 g/mL. A solution is made by dissolving 23.0 mL CH3 OH in 98.7 mL CH3 CN.What is the mole fraction of methanol in the solution?
What is the mole fraction of methanol, CH 3OH, if 55.18 g of methanol are added to 208.00 g of water?A. 0.633B. 0.130C. 8.277D. 0.149E. 0.321
What is the mole fraction of ethanol, C 2H5OH, if 42.52 g of ethanol is added to 125.00 g of water?a. 0.480 b. 7.382c. 0.133d. 0.117e. 0.465
Calculate the mole fraction of total ions in an aqueous solution prepared by dissolving 0.400 moles of MgCl2 in 850.0 g of water.A. 0.00841B. 0.0270C. 0.00900D. 0.0248E. 0.0167
What is the mole fraction of Ethanol in a solution composed of 10 g Ethanol (C  2H6O), 10 g H2O, & 10 g CH3OH? A) 0.217B) 0.201C) 0.33D) 0.289E) 0.410
A solution is made by mixing equal masses of methanol, CH 4O, and ethanol, C2H6O.Determine the mole fraction of each component to at least three significant figures.
A solution is prepared by dissolving 28.4 g of glucose (C 6H12O6) in 355 g of water . The final volume of the solution is 378 mL. For this solution, calculate the concentration in each unit.a. Molarityb. Molalityc. Percent by massd. Mole fractione. Mole percent
If the mass of sodium chloride, NaCl (MW = 58.5 g/mol), is 40.0 g and the mass of water is 30.0 g, what is the mole fraction of NaCl in the solution?a. 0.291b. 0.60c. 0.40d. 40.0e. 0.240     What is the mass percent of NaCl in the solution in the previous question?a. 0.291b. 0.60c. 0.40d. 40.0e. 0.240
What is the mole fraction of NaCl in a solution that contains 40.0 g NaCl and 60.0 g H2O?a) none of the given answersb) 3.33c) 0.205d) 0.170e) 0.300
A solution is prepared by dissolving 38.6 g sucrose (C12H22O11) in 495 g of water.  Determine the mole fraction of sucrose if the final volume of the solution is 508 mL.A) 1.28 × 10 -3      B) 2.45 × 10 -3 C) 7.80 × 10 -2D) 4.09 × 10 -3 E) 7.23 × 10 -2
Which of the following chemical terms is affected by temperature? MolalityMass percentMolarityMole fraction
What does each of the following statements mean? a.) 1.80 M NaCl    b.) 39 percent by mass HBr   c.) CO2 has a mole fraction of 0.310 in aqueous solution             d.) 1.25 m KOCH2CH3   e.) 45 percent by volume NO3 
A solution is made by mixing equal masses of methanol CH 4O (MW = 32.01 g/mol) and ethanol C2H6O (MW = 46.02 g/mol). Determine the mole fraction of methanol. a) 0.129 b) 0.388c) 0.410d) 0.590
What is the mole fraction of water in 200 g of 95% (by mass) ethanol, C 2H5OH?Formula Molar Mass of C2H5OH is 46 g•mol –1.a) 0.050b) 0.12c) 0.56d) 0.88
If the mass of sodium chloride, NaCl (MW= 58.5 g/mol), is 40.0 g and the mass of water is 30.0 g, what is the mole fraction of NaCl in the solution? a) 0.291 b) 0.60 c) 0.40 d) 40.0 e) 0.240   What is the mass percent of NaCl in the solution in the previous question? a) 0.291 b) 0.60 c) 0.40 d) 40.0 e) 0.240
A solution of phosphoric acid was made by dissolving 10.0 g H 3PO4 in 100.0 mL water. The resulting volume was 104 mL. Calculate the density, mole fraction, molarity, and molality of the solution. Assume water has a density of 1.00 g/cm3.
The molecular formula of Vitamin E (tocopherol) is C29H50O2 (MW = 430.71). If the mole fraction of vitamin E in a methyl alcohol (CH3OH) solution is 0.002, what is the molality of the Vitamin E solution?a) none of the other answers is even close (within 10% error )b) 0.00273c) 0.00503d) 0.0625e) 0.1570
A concentrated solution of glucose (C6H12O6) in water 75.3 % glucose by mass. Calculate the mole fraction and the molarity of glucose solution. (The density of the solution is 1.03g/mL)
A solution is prepared by mixing 25 mL pentane (C5H12, d = 0.63 g/cm3) with 45 mL hexane (C6H14, d = 0.66 g/cm3). Assuming that the volumes add on mixing, calculate the mass percent, mole fraction, molality, and molarity of the pentane.
A solution is prepared by mixing 50.0 mL toluene (C6H5CH3, d = 0.867 g/cm3) with 125 mL benzene (C6H6, d = 0.874 g/cm3). Assuming that the volumes add on mixing, calculate the mass percent, mole fraction, molality, and molarity of the toluene.
Calculate the molarity and mole fraction of acetone in a 1.00-m solution of acetone (CH3COCH3) in ethanol (C2H5OH). (Density of acetone = 0.788 g/cm3; density of ethanol 5 0.789 g/cm3.) Assume that the volumes of acetone and ethanol add.
A 1.37-M solution of citric acid (H3C6H5O7) in water has a density of 1.10 g/cm3. Calculate the mass percent, molality, mole fraction, and normality of the citric acid. Citric acid has three acidic protons.
Ascorbic acid (vitamin C, C6H8O6) is a water-soluble vitamin. A solution containing 81.5 g of ascorbic acid dissolved in 220 g of water has a density of 1.22 g/mL at 55oC.Calculate the mole fraction of ascorbic acid in this solution.
A solution is prepared by dissolving 20.2 mL of methanol (CH3OH) in 100.0 mL of water at 25 oC. The final volume of the solution is 118 mL. The densities of methanol and water at this temperature are 0.782 g/mL and 1.00 g/mL, respectively. For this solution, calculate each of the following.Mole fraction
A solution is prepared by dissolving 20.2 mL of methanol (CH3OH) in 100.0 mL of water at 25 oC. The final volume of the solution is 118 mL. The densities of methanol and water at this temperature are 0.782 g/mL and 1.00 g/mL, respectively. For this solution, calculate each of the following.Mole percent
A solution is made containing 21.2 g phenol (C6H5OH) in 450 g ethanol (CH3 CH2OH).Calculate the mole fraction of phenol.
The density of toluene (C7H8) is 0.867 g/mL, and the density of thiophene (C4H4S) is 1.065 g/mL. A solution is made by dissolving 8.60 g of thiophene in 260 mL of toluene.Calculate the mole fraction of thiophene in the solution.
The normal boiling point of diethyl ether is 34.5°C. A solution containing a nonvolatile solute dissolved in diethyl ether has a vapor pressure of 698 torr at 34.5°C. What is the mole fraction of diethyl ether in this solution?
A solution is prepared by dissolving 52.3 g cesium chloride in 60.0 g water. The volume of the solution is 63.3 mL. Calculate the mass percent, molarity, molality, and mole fraction of the CsCl solution.
What are the mole fractions of HNO3 and water in a concentrated solution of nitric acid (68.0% HNO3 by mass)?(a) Outline the steps necessary to answer the question.(b) Answer the question.
The normal boiling point of methanol is 64.7˚C. A solution containing a nonvolatile solute dissolved in methanol has a vapor pressure of 556.0 torr at 64.7˚C. What is the mole fraction of methanol in this solution?
Calculate the mole fraction of each solute and solvent:(b) 0.86 g of NaCl in 1.00 × 102 g of water—a solution of sodium chloride for intravenous injection
Calculate the mole fraction of each solute and solvent:(c) 46.85 g of codeine, C18H21NO3, in 125.5 g of ethanol, C2H5OH
Calculate the mole fraction of each solute and solvent:(b) 125 g of NH4NO3 in 275 g of water—a mixture used to make an instant ice pack
Calculate the mole fraction of each solute and solvent:(c) 25 g of Cl2 in 125 g of dichloromethane, CH2Cl2
Acetonitrile (CH3 CN) is a polar organic solvent that dissolves a wide range of solutes, including many salts. The density of a 1.90 M LiBr solution in acetonitrile is 0.827 g/cm3 .Calculate the concentration of the solution in mole fraction of LiBr.
Calculate the mole fractions of methanol, CH3OH; ethanol, C2H5OH; and water in a solution that is 40% methanol, 40% ethanol, and 20% water by mass. (Assume the data are good to two significant figures.)
Common commercial acids and bases are aqueous solutions with the following properties:Calculate the molarity, molality, and mole fraction of each of the preceding reagents.
Three gaseous mixtures of N2 (blue), Cl2 (green), and Ne (purple) are depicted below.(a) Which has the smallest mole fraction of N2?
A solution contains 0.35 mol of isopropanol (C3H7OH) dissolved in 0.85 mol of water. (a) What is the mole fraction of isopropanol?
Calculate the molarity and mole fraction of acetone in a 1.00 m solution of acetone (CH3COCH3) in ethanol (C 2H5OH). (Density of acetone = 0.788 g/cm 3; density of ethanol = 0.789 g/cm3.) Assume that the volumes of acetone and ethanol add.
What mass of cesium bromide must be added to 0.500 L of water (d = 1.00 g/mL) to produce a 0.400 m solution? What are the mole fraction and the mass percent of CsBr?
Calculate the molality, molarity, and mole fraction of NH3 in ordinary household ammonia, which is an 8.00 mass % aqueous solution (d = 0.9651 g/mL).
Water treatment plants commonly use chlorination to destroy bacteria. A byproduct is chloroform (CHCl3), a suspected carcinogen, produced when HOCl, formed by reaction of Cl2 and water, reacts with dissolved organic matter. The United States, Canada, and the World Health Organization have set a limit of 100. ppb of CHCl3 in drinking water. Convert this concentration into molarity, molality, mole fraction, and mass percent.
The solubility of oxygen gas in water at 40 oC is 1.0 mmol/L of solution. What is this concentration in units of mole fraction?
An automobile antifreeze mixture is made by mixing equal volumes of ethylene glycol (d = 1.114 g/mL; ℳ = 62.07 g/mol) and water (d = 1.00 g/mL) at 20°C. The density of the mixture is 1.070 g/mL. Express the concentration of ethylene glycol as:(e) Mole fraction
An aqueous solution contains 4.6 % NaCl by mass. Calculate the mole fraction of the solution.
Common commercial acids and bases are aqueous solutions with the following properties:Calculate the molarity, molality, and mole fraction of each of the preceding reagents.
Find the mass of urea (CH4N2O) needed to prepare 50.1 g of a solution in water in which the mole fraction of urea is 7.66×10−2.
Calculate the molality, molarity, and mole fraction of FeCl3 in a 28.8 mass % aqueous solution (d = 1.280 g/mL).
A solution is made containing 12.6 g of methanol CH 3OH (32.04 g/mol) in 154 g of water. H20 (18.02 g/mol)a) Calculate the mole fraction of methanol: a. 0.956b. 0.0440c. 0.0460d. 0.00241e. 0.0273
An aqueous solution contains 32% HCl by mass.Calculate mole fraction of the solution.
Which concentration unit does not require a measured amount (volume or mass) of solvent?A. mass percent of solute B. molalityC. mole fraction of soluteD. molarityE. mole fraction of solvent
Caffeine (C8H10N4O2) is a stimulant found in coffee and tea. A solution of caffeine in the solvent chloroform (CHCl3) has a concentration of 0.0510 m.Calculate the mole fraction of caffeine in the solution.
Pentane (C5H12) and hexane (C6H14) form an ideal solution. At 25°C the vapor pressures of pentane and hexane are 511 and 150. torr, respectively. A solution is prepared by mixing 25 mL pentane (density, 0.63 g/mL) with 45 mL hexane(density, 0.66 g/mL).b. What is the composition by mole fraction of pentane in the vapor that is in equilibrium with this solution?
A solution is prepared by dissolving 38.6 g sucrose (C12H22O11) in 495 g of water.  Determine the mole fraction of sucrose if the final volume of the solution is 508 mL.
Determine the mole fraction of glucose, C6H12O6, (molecular weight 180.18) in a 1.86 M aqueous glucose solution given the density of the glucose solution is 1.38 g/cm3.a. 0.0311b. 0.0237c. 0.0324d. 0.0243e. 0.0480
What is the mole fraction of CH3OH in an aqueous solution that is 12.0 m in CH3OH?A. 0.333B. 0.667C. 0.178D. 0.216 E. 0.400
In a 66.0-g aqueous solution of methanol, CH 4O, the mole fraction of methanol is 0.120. What is the mass of each component?a) Mass of CH4Ob) Mass of water
Methanol (CH3OH) and ethanol (C2H5OH) are miscible because the major intermolecular force for each is H bonding. In some methanol-ethanol solutions, the mole fraction of methanol is higher, but the mass percent of ethanol is higher. What is the range of mole fraction of methanol for these solutions?
A solution is made containing 14.6 g of CH3OH in 185 g H2O.Calculate the mole fraction of CH3OH.
In the flask diagrammed below, the left bulb contains 3.0L of neon at a pressure of 2.0 atm. The right bulb contains 2.0L of argon at a pressure of 1.0 atm. What is the mole fraction of neon and argon in the final mixture after the valve is opened and a uniform pressure is reached at constant temperature (25°C).(a) Ne 0.33, Ar 0.67(b) Ne 0.25, Ar 0.75(c) Ne 0.67, Ar 0.33(d) Ne 0.92, Ar 0.82(e) Ne 0.75, Ar 0.25
A gas mixture contains 0.60 mol of N2, 0.40 mol of H2, and 0.25 mol of CH4. What is the mole fraction of H2 in the mixture?
What is the mole fraction of oxygen gas in air (see the table on the left)?
An aqueous solution contains 56% NaCl by mass.Part ACalculate the molality of the solution. Express your answer using two significant figures. Part B Calculate mole fraction of the solution.Express your answer using two significant figures. 
In a mixture of argon and hydrogen, occupying a volume of 1.66 L at 910.0 mmHg and 54.9°C, it is found that the total mass of the sample is 1.13 g. What is the partial pressure of argon? (a) 455 mmHg (b) 319 mmHg (c) 866 mmHg (d) 591 mmHg (e) 43.7 mmHg
A solution was prepared by dissolving 39.0 g of KCl in 225 mL of water. Calculate the mole fraction of the ionic species KCl in the solution. Express the concentration numerically as a mole fraction in decimal form.
A solution is made by mixing 109. g of acetyl bromide (CH3COBr) and 70. g of thiophene (C4H4S). Calculate the mole fraction of acetyl bromide in this solution. Be sure your answer has the correct number of significant digits.
What is the mole fraction of O2 in this mixture? 12.3 g of CO2 and 38.2 g of O2.
A solation is prepared by dissolving 15.0 g of NH3, in 250.0 g of water. The density of the resulting solution is 0.974 g/mL. The mole fraction of NH3 in the solution is ________.(i) 0.0597 (ii) 0.0640 (iii) 16.8 (iv) 0.940 (v) 0.922
A 10.00 L tank at 0.8 degree C is filled with 16.8 g of dinitrogen difluoride gas and 13.2 g of sulfur hexafluoride gas. You can assume both gases behave as ideal gases under these conditions. Calculate the mole fraction of each gas. Round each of your answers to 3 significant digits.  
What is the mole fraction of lead(II) nitrate in an aqueous solution prepared by dissolving 25.4 g of the solute in 150 0 mL of water at 22°C? The density of water at 22°C is 0.998 g/mL.
A gaseous mixture contains 406.0 Torr of H2(g), 347.9 Torr of N2 (g), and 83.1 Torr of Ar(g). Calculate the mole fraction, X, of each of these gases.XH2 =XN2 =XAr =  
A 5.00 L tank at 30.7°C is filled with 15.2 g of boron trifluoride gas and 10.4 g of sulfur hexafluoride gas. You can assume both gases behave as ideal gases under these conditions. Calculate the mole fraction of each gas. Be sure each of your answer entries has the correct number of significant digits.
A solution is made by mixing 141. g of heptane (C7H16) and 121. g of chloroform (CHCl3) Calculate the mole fraction of heptane in this solution. Round your answer to 3 significant digits. 
What are the mole fractions of H3PO4 and water in a solution of 14.5 g of H3PO4 in 125 g of water?(a) Outline the steps necessary to answer the question.(b) Answer the question.
In lab you need to prepare at least 100 mL of each of the following solutions. Explain how you would proceed using the given information. d. 0.10 mole fraction of C6H12O6 in water (d = 1.00 g/cm3)