General Chemistry - Standalone book (MindTap Course List)
General Chemistry - Standalone book (MindTap Course List)
11th Edition
ISBN: 9781305580343
Author: Steven D. Gammon, Ebbing, Darrell Ebbing, Steven D., Darrell; Gammon, Darrell Ebbing; Steven D. Gammon, Darrell D.; Gammon, Ebbing; Steven D. Gammon; Darrell
Publisher: Cengage Learning
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Textbook Question
Chapter 12, Problem 12.26QP

Equal numbers of moles of two soluble, substances, substance A and substance B, are placed into separate 1.0-L samples of water.

  1. a The water samples are cooled. Sample A freezes at −0.50°C, and Sample B freezes at −l.00°C. Explain how the solutions can have different freezing points.
  2. b You pour 500 mL of the solution containing substance B into a different beaker. How would the freezing point of this 500-mL portion of solution B compare to the freezing point of the 1.0-L sample of solution A?
  3. c Calculate the molality of the solutions of A and B. Assume that i = 1 for substance A.
  4. d If you were to add an additional 1.0 kg of water to solution B, what would be the new freezing point of the solution? Try to write an answer to this question without using a mathematical formula.
  5. e What concentration (molality) of substances A and B would result in both solutions having a freezing point of −0.25°C?
  6. f Compare the boiling points, vapor pressure, and osmotic pressure of the original solutions of A and B. Don’t perform the calculations; just state which is the greater in each ease.

(a)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

A and B are two substances having equal number of moles.  They are placed into separate 1.0 L samples of water.  The difference in freezing point of the substances A and B has to be explained.

Concept Introduction:

Freezing point of the substance is temperature at which liquid substance remains in equilibrium with solid substance.

Depression in freezing point of a substance can be determined by the formula, ΔTf = Kfm .

Where,

ΔTf = depression in freezing pointKf  = cryoscopic constantm    = molality of the solution

Explanation of Solution

While dissolving in solvent the solute particles don't dissolve in same way always.  This is why, even though the two sample solutions A and B are made of same type of solute and have equal number of moles has different freezing point.

(b)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

A and B are two substances having equal number of moles.  They are placed into separate 1.0 L samples of water.

500 mL of the solution B is poured into different beaker.  The difference between the freezing point of this 500 mL solution B and 1.0 L sample of solution A has to be explained.

Concept Introduction:

Freezing point of the substance is temperature at which liquid substance remains in equilibrium with solid substance.

Depression in freezing point of a substance can be determined by the formula, ΔTf = Kfm .

Where,

ΔTf = depression in freezing pointKf  = cryoscopic constantm    = molality of the solution

Explanation of Solution

Freezing point of a solution is a colligative property which depends only on the concentration of the solute.  Thus dividing the volume of solution of same concentration doesn't result in variation of freezing point.  So there will be no change in difference between the boiling point of 500 mL of solution B and 1.0 L of solution A.

Conclusion

Two different solutions made of same solute with same number of moles can have different freezing points.  Freezing point of a solution doesn’t vary with volume and it varies only with concentration of the solute in the solution.

(c)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

A and B are two substances having equal number of moles.  They are placed into separate 1.0 L samples of water.

Molality of the solutions A and B has to be calculated by assuming i = 1 for substance A.

Concept Introduction:

Molality is one of the many parameters that is used to express concentration of a solution.  It is expressed as,

Molality = number of moles of solutemass of solvent in kg

Depression in freezing point of a substance can also be used to determine molality of the solution by rewriting the formula, ΔTf = Kfm

Answer to Problem 12.26QP

Molality of the solutions A and B are calculated to be 0.27 m.

Explanation of Solution

Both the solutions A and B have same molality as both of them have same number of moles of solute.  As given i=1 , and freezing point of the solution, molality of both the solutions A and B are calculated to be,

cm ΔTfKf = 0.50°C1.858°C/m = 0.27 m

Conclusion

Since depression in freezing point depends upon the concentration of the solute, this parameter can be used to determine the molal concentration of the solution.

(d)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

A and B are two substances having equal number of moles.  They are placed into separate 1.0 L samples of water.  The molality at which both the solutions A and B would have same freezing point of 0.25°C has to be determined.

Concept Introduction:

Molality is one of the many parameters that is used to express concentration of a solution.  It is expressed as,

Molality = number of moles of solutemass of solvent in kg

Depression in freezing point of a substance can also be used to determine molality of the solution by rewriting the formula, ΔTf = Kfm

Answer to Problem 12.26QP

The new freezing point will be half of the freezing point of solution B that is -0.50°C.

Explanation of Solution

Adding 1.0 kg of water to the solution B reduces the molality to one half of the actual molality.  Consequently ΔTf will be reduced by one-half and thus the new freezing point of the solution would be -0.50°C.

Conclusion

Addition of excess solvent varies the solute concentration. Varying the solute concentration varies the freezing point of the solution.

(e)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

A and B are two substances having equal number of moles.  They are placed into separate 1.0 L samples of water.  Osmotic pressure, vapor pressure, boiling points of both the solutions A and B has to be compared by theoretical explanation.

Concept Introduction:

Molality is one of the many parameters that is used to express concentration of a solution.  It is expressed as,

Molality = number of moles of solutemass of solvent in kg

Depression in freezing point of a substance can also be used to determine molality of the solution by rewriting the formula, ΔTf = Kfm

Answer to Problem 12.26QP

The two solutions A and B have same freezing point at molality of 0.13 m.

Explanation of Solution

As given i=1 , and freezing point of the solution, molality of both the solutions A and B in which they both have same freezing point, is calculated to be,

cm ΔTfKf = 0.25°C1.858°C/m = 0.13 m

Conclusion

Since depression in freezing point depends upon the concentration of the solute, this parameter can be used to determine the molal concentration of the solution.

(f)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

A and B are two substances having equal number of moles.  They are placed into separate 1.0 L samples of water.

Osmotic pressure, vapor pressure, boiling points of both the solutions A and B has to be compared by theoretical explanation.

Concept Introduction:

Boiling point of a liquid substance is defined as the temperature at which the vapor pressure of the liquid becomes equal to the atmospheric pressure.

Elevation in boiling point of a substance can be determined by the formula,

ΔTb = iKbm .

Where,

ΔTb = elevation of boiling pointKb  = ebullioscopic constantm    = molality of the solution; i = Van't Hoff factor

Vapor pressure of a substance is known as the pressure exerted by molecules on the vapor phase when they are in equilibrium with their actual phase which can be liquid or solid.

Vapor pressure of a volatile solvent can be lowered by addition of a non-volatile solute. Raoult’s law deals with the vapor pressure of pure solvents and solution which states –

Partial pressure of solvent is equivalent to the product of vapor pressure of the solvent in its pure state and mole fraction of solvent in the solution.  It is expressed as,

PA = PA° XA

Where,

PA = Partial vapor pressure of solvent in solutionPA° = Vapor pressure of pure solventXA= mole fraction of solvent in the solution

When the solute is non-volatile, the vapor pressure of the whole solution is equal to PA.

The lowering of vapor pressure of the solvent due to the addition of non-volatile solute is expressed as,

ΔP = PA° XB

Where,

  XB is the mole fraction of the solute.

In the process of osmosis, the solvent molecules pass through a semi - permeable membrane from less concentrated solution to more concentrated solution.  The pressure that has to be applied to prevent the flow of solvent molecules is called osmotic pressure.  It is expressed as,

π = MRT

Where,

π = osmotic pressureM = Molar concentrationR =  Universal gas constantT =   Temperature

Answer to Problem 12.26QP

The solution A will have lower boiling point, lower osmotic pressure and higher vapor pressure than solution B.

Explanation of Solution

Vapor pressure and boiling point share inverse relationship. But decrease in vapor pressure leads to decrease in freezing point.  Higher the vapor pressure of the solution lower will be the boiling point of the solution.  Since solution A has lower freezing point than solution B, it indicates lower vapor pressure and higher boiling point than solution B.  Solution A has lower freezing point that it has lower osmotic pressure than solution B.

Conclusion

Vapor pressure and boiling point of the solution are dependent on each other.  Osmotic pressure of the solution can be determined on the basis of freezing point or depression in freezing point.

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Chapter 12 Solutions

General Chemistry - Standalone book (MindTap Course List)

Ch. 12.4 - Prob. 12.7ECh. 12.4 - A solution is 0.120 m methanol dissolved in...Ch. 12.4 - A solution is 0.250 mole fraction methanol, CH3OH,...Ch. 12.4 - Urea, (NH2)2CO, is used as a fertilizer (sec the...Ch. 12.4 - Prob. 12.11ECh. 12.5 - Naphthalene, C10H8, is used to make mothballs....Ch. 12.5 - Prob. 12.5CCCh. 12.6 - How many grams of ethylene glycol, CH2OHCH2OH,...Ch. 12.6 - A 0.930-g sample of ascorbic acid (vitamin C) was...Ch. 12.6 - A 0.205-g sample of white phosphorus was dissolved...Ch. 12.7 - Calculate the osmotic pressure at 20C of an...Ch. 12.7 - Prob. 12.6CCCh. 12.8 - Prob. 12.17ECh. 12.8 - Each of the following substances is dissolved in a...Ch. 12.9 - Prob. 12.18ECh. 12.9 - If electrodes that are connected to a direct...Ch. 12 - Prob. 12.1QPCh. 12 - Prob. 12.2QPCh. 12 - Explain in terms of intermolecular attractions why...Ch. 12 - Prob. 12.4QPCh. 12 - Using the concept of hydration, describe the...Ch. 12 - What is the usual solubility behavior of an ionic...Ch. 12 - Give one example of each: a salt whose heat of...Ch. 12 - What do you expect to happen to a concentration of...Ch. 12 - Prob. 12.9QPCh. 12 - Pressure has an effect on the solubility of oxygen...Ch. 12 - Prob. 12.11QPCh. 12 - When two beakers containing different...Ch. 12 - Prob. 12.13QPCh. 12 - Prob. 12.14QPCh. 12 - Prob. 12.15QPCh. 12 - Prob. 12.16QPCh. 12 - One can often see sunbeams passing through the...Ch. 12 - Prob. 12.18QPCh. 12 - Explain on the basis that like dissolves like why...Ch. 12 - Prob. 12.20QPCh. 12 - Calculate the number of moles of barium chloride...Ch. 12 - Prob. 12.22QPCh. 12 - If 291g of a compound is added to 1.02 kg of water...Ch. 12 - A 5.1-g sample of CaCl2 is dissolved in a beaker...Ch. 12 - Consider two hypothetical pure substances, AB(s)...Ch. 12 - Equal numbers of moles of two soluble, substances,...Ch. 12 - Even though the oxygen demands of trout and bass...Ch. 12 - You want to purchase a salt to melt snow and ice...Ch. 12 - Prob. 12.29QPCh. 12 - Prob. 12.30QPCh. 12 - Prob. 12.31QPCh. 12 - Consider the following dilute NaCl(aq) solutions....Ch. 12 - Prob. 12.33QPCh. 12 - Prob. 12.34QPCh. 12 - If l-mol samples of urea, a nonelectrolyte, sodium...Ch. 12 - Prob. 12.36QPCh. 12 - Prob. 12.37QPCh. 12 - Prob. 12.38QPCh. 12 - Prob. 12.39QPCh. 12 - Prob. 12.40QPCh. 12 - Arrange the following substances in order of...Ch. 12 - Indicate which of the following is more soluble in...Ch. 12 - Prob. 12.43QPCh. 12 - Which of the following ions would be expected to...Ch. 12 - Arrange the following alkaline-earth-metal iodates...Ch. 12 - Explain the trends in solubility (grams per 100 mL...Ch. 12 - The solubility of carbon dioxide in water is 0.161...Ch. 12 - Prob. 12.48QPCh. 12 - Prob. 12.49QPCh. 12 - Prob. 12.50QPCh. 12 - Prob. 12.51QPCh. 12 - Prob. 12.52QPCh. 12 - Vanillin, C2H2O3, occurs naturally in vanilla...Ch. 12 - Lauryl alcohol, C12H25OH, is prepared from coconut...Ch. 12 - Fructose, C6H12O6, is a sugar occurring in honey...Ch. 12 - Caffeine. C8H10N4O2, is a stimulant found in tea...Ch. 12 - A 100.0-g sample of a brand of rubbing alcohol...Ch. 12 - An automobile antifreeze solution contains 2.50 kg...Ch. 12 - Prob. 12.59QPCh. 12 - Prob. 12.60QPCh. 12 - Concentrated hydrochloric acid contains 1.00 mol...Ch. 12 - Concentrated aqueous ammonia contains 1.00 mol NH3...Ch. 12 - Prob. 12.63QPCh. 12 - Prob. 12.64QPCh. 12 - A solution of vinegar is 0.763 M acetic arid,...Ch. 12 - A beverage contains tartaric acid, H2C4H4O6, a...Ch. 12 - Calculate the vapor pressure at 35C of a solution...Ch. 12 - What is the vapor pressure at 23C of a solution of...Ch. 12 - What is the boiling point of a solution of 0.133 g...Ch. 12 - A solution was prepared by dissolving 0.800 g of...Ch. 12 - An aqueous solution of a molecular compound...Ch. 12 - Urea, (NH2)2CO, is dissolved in 250.0 g of water....Ch. 12 - Prob. 12.73QPCh. 12 - Prob. 12.74QPCh. 12 - Safrole is contained in oil of sassafras and was...Ch. 12 - Butylated hydroxytoluene (BHT) is used as an...Ch. 12 - Prob. 12.77QPCh. 12 - Prob. 12.78QPCh. 12 - What is the freezing point of 0.0075 m aqueous...Ch. 12 - What is the freezing point of 0.0088 m aqueous...Ch. 12 - Prob. 12.81QPCh. 12 - In a mountainous location, the boiling point of...Ch. 12 - Prob. 12.83QPCh. 12 - Prob. 12.84QPCh. 12 - Prob. 12.85QPCh. 12 - Prob. 12.86QPCh. 12 - A gaseous mixture consists of 87.0 mole percent N2...Ch. 12 - A natural gas mixture consists of 88.0 mole...Ch. 12 - Prob. 12.89QPCh. 12 - Prob. 12.90QPCh. 12 - A 55-g sample of a gaseous fuel mixture contains...Ch. 12 - Prob. 12.92QPCh. 12 - A liquid solution consists of 0.30 mole fraction...Ch. 12 - What is the total vapor pressure at 20C of a...Ch. 12 - A sample of potassium aluminum sulfate 12-hydrate....Ch. 12 - A sample of aluminum sulfate 18-hydrate,...Ch. 12 - Urea, (NH2)2CO, has been used to melt ice from...Ch. 12 - Calcium chloride, CaCl2, has been used to melt ice...Ch. 12 - Prob. 12.99QPCh. 12 - Prob. 12.100QPCh. 12 - Which aqueous solution has the lower freezing...Ch. 12 - Which aqueous solution has the lower boiling...Ch. 12 - Commercially, sulfuric acid is usually obtained as...Ch. 12 - Prob. 12.104QPCh. 12 - A compound of manganese, carbon, and oxygen...Ch. 12 - A compound of cobalt, carbon, and oxygen contains...Ch. 12 - The carbohydrate digitoxose contains 48.64% carbon...Ch. 12 - Analysis of a compound gave 39.50% C, 2.21% H, and...Ch. 12 - Fish blood has an osmotic pressure equal to that...Ch. 12 - Prob. 12.110QPCh. 12 - Prob. 12.111QPCh. 12 - Prob. 12.112QPCh. 12 - How are phospholipids similar in structure to a...Ch. 12 - Prob. 12.114QPCh. 12 - Two samples of sodium chloride solutions are...Ch. 12 - Prob. 12.116QPCh. 12 - You have an aqueous, dilute solution of a...Ch. 12 - Prob. 12.118QPCh. 12 - Prob. 12.119QPCh. 12 - Prob. 12.120QPCh. 12 - When 79.3 g of a particular compound is dissolved...Ch. 12 - What is the boiling point of a solution made by...Ch. 12 - Prob. 12.123QPCh. 12 - Prob. 12.124QPCh. 12 - Prob. 12.125QPCh. 12 - Prob. 12.126QPCh. 12 - Prob. 12.127QPCh. 12 - Prob. 12.128QPCh. 12 - An aqueous solution is 0.797 M magnesium chloride....Ch. 12 - A CaCl2 solution at 25C has an osmotic pressure of...Ch. 12 - Prob. 12.131QPCh. 12 - Prob. 12.132QPCh. 12 - The lattice enthalpy of sodium chloride, H for...Ch. 12 - Prob. 12.134QPCh. 12 - Prob. 12.135QPCh. 12 - Prob. 12.136QPCh. 12 - Prob. 12.137QPCh. 12 - An aqueous solution is 20.0% by mass of sodium...Ch. 12 - Prob. 12.139QPCh. 12 - The freezing point of 0.109 m aqueous formic acid...Ch. 12 - A compound of carbon, hydrogen, and oxygen was...Ch. 12 - A compound of carbon, hydrogen, and oxygen was...
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