Molarity, Molality, Mass Percent & Mole Fraction

Solutions are homogeneous mixtures that result from the dissolving of a solute by a solvent.

Solutions and Intermolecular Forces

In the theory of "Likes" dissolving "Likes" the solvent can only completely dissolve the solute if they share similar polarity. 

Molarity & Solutions 

Concept: Solutions and Molarity. 

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Video Transcript

Welcome back, guys! In this new video, we're going to connect an old concept, molarity, with some new ones, solutions and intermolecular forces. Remember we talked about molarity a long time ago several videos back. Remember, molarity serves as the connection between the conversion of moles to liters and vice versa.
We're going to say for example if I give you 5.8 molar NaCl, that really means that I have 5.8 moles of NaCl per one liter. Remember, anytime they give you molarity, always assume that number they give you is in moles and it will be over 1 liter of solution.
Remember the formula for molarity is just molarity equals moles of solute over liters of solution. 

MOLARITY represents the moles of solute dissolved per liters of solution.

Concept: The Theory of “Likes” dissolve “Likes”. 

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Video Transcript

These terms solute and solution are important. Remember, we have mixtures. Mixtures can be either homogenous or heterogeneous. Here we’re saying a typical mixture consists of a smaller amount of one substance, which is called the solute. Remember, the solute is the portion of our entire amount of liquid that is smaller in amount and it’s dissolved in a much larger type of substance called the solvent.
Remember, it’s solute combined with the solvent and together they form a solution. We're going to say that a mixture can come either as heterogeneous or homogeneous. A solution is a special type of homogeneous mixture. The solute completely dissolves. Why? Because the solute and the solvent are both either the same polarity or they have the same intermolecular force. That's what connects us to this theory of likes dissolving likes.
We're going to say according to the theory of likes dissolve likes, compounds with the same intermolecular force or polarity will dissolve into each other to give us our solution. Remember, we’ve talked about the intermolecular forces. There are five types but the four major ones are ion-dipole, the interaction of ions from ionic compounds with a polar solvent such as water, that’s the strongest type. We also have hydrogen bonding. Anytime H is connected to after F, O, or N, we’re going to have hydrogen bonding. Then we have dipole-dipole. Dipole-dipole exists for polar covalent compounds.
In between dipole-dipole and the weakest one, there’s another force called dipole-induced-dipole. This one is not as major as before that we're talking about, but it is considered one of the intermolecular forces. Dipole-induced-dipole is when we have a polar compound interacting with a non-polar compound. Finally, our last intermolecular force which is the weakest force is London dispersion or Van Der Waals or induced-dipole induce-dipole. Remember, the last force is the weakest force. It has these three names that we can give it. If you don't quite remember that, go back to the previous videos and look at intermolecular forces and polarity to help you guide you on which type of force a compound has. 

A pure solvent with similar polarity can successfully dissolve a solute to create a solution. 

Example: Butane, a nonpolar organic compound, is most likely to dissolve in:

a. HCl

b. C6H5OH

c. C8H18

d. AlCl3

e. What the heck is butane? 

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Molarity & Molality of Solutions

Concept: Molarity vs. Molality. 

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Video Transcript

Welcome back, guys! In this new video, we're going to continue with our discussion on expressing solution concentrations. At this point, we should know what molarity is. Molarity is just simply the amount of solute, moles of solute dissolved per liters of solution.
Now we’re going to come face to face with a whole new term. This new term is the moles of solute dissolved per kilograms of solvent. It's similar to molarity. They both have the same top. They both have moles of solute. The only thing that’s really different about them is the bottom part. Molarity deals with solution. This new term which is called molality deals with solvent.
We have molarity, then we have molality. Remember, molarity uses capital M. Molality uses lower case m. Remember the difference between them.

As we already know MOLARITY represents the moles of solute per liters of solution. Now, we will deal with the new term of MOLALITY, which represents the moles of solute per kilograms of solvent. 

Example: If the molality of glucose, C6H12O6, in an aqueous solution is 2.56 what is the molarity? Density of the solution is 1.530 g/mL. 

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Problem: A solution is prepared by dissolving 43.0 g potassium chlorate, KClO3, in enough water to make 100.0 mL of solution. If the density of the solution is 1.760 g/mL, what is the molality of KClO3 in the solution? (MW of KClO3 is 122.55 g/mol)

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Mass Percent & Mole Fraction 

Molarity serves as the bridge between moles to liters and can also incorporate the concept of mass percent and mole fraction

Concept: Mass Percent & Mole Fraction 

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Video Transcript

Welcome back, guys! In this new video, we’re going to continue with expressing mass amounts. We’ve already talked about one of these mass amounts, mass percent. Remember, when we talk about mass percent in the past, we just said that mass or weight percent is the percentage of a given element in a compound.
Here we’re going to tweak it a little bit and we’re going to say now mass percent equals the mass of our solute over mass of solution times 100. Remember, this bottom portion here is mass of the solution, which really means mass of my solute plus the mass of my solvent. Because remember, it’s those two components that give us the mass of solution, the total mass. It’s times 100 to get the mass percent.
Related to mass percent are two other terms. One is called ppm, which is just parts per million and another one which is called ppb, which is parts per billion. We’re going to say that ppm, parts per million, is the same thing as mass percent except we don’t multiply by 100. What we do instead is we multiply it by 10 to the 6. We’re going to say parts per million is just mass percent but times 10 to the 6 instead of times 100. Parts per billion is the same thing as mass percent as well except again, we’re not multiplying by 100. Instead we’re multiplying by 10 to the 9.
Just remember, mass percent, parts per million, parts per billion. Related to these concepts here is another type of term. We’re going to say that this term is called mole fraction. The variable we use for mole fraction is x. mole fraction equals the moles of solute over the moles of solution. Again, the bottom part really means moles of solute plus the moles of solvent. Honestly, on the top it could also be moles of solvent. It all depends what they’re asking you to find the mole fraction of. If they’re asking us to find the mole fraction of a solute, then it’s the moles of solute on top. But if they’re asking us to find the mole fraction of a solvent, then the top portion will become moles of solvent. It really is all based on what they’re asking you to find.

Mass Percent is represented by the mass of the solute per mass of solution, which is the combined mass of the solute and solvent. 

Mole Fraction (X) is the mole component form of mass percent. Instead of using grams, mole fraction substitutes in moles as the units. 

Example: Commercial sulfurous acid, H2SO3, is 90.1% by weight, and its specific gravity is 1.51. Calculate the molarity of commercial sulfurous acid. (MW of H2SO3 is 82.086 g/mol).

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Often time the use of mass percent and density are the key components need to accurately calculate a solution’s molarity. 

Example: 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. 

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Often times the density will not help you find the molality. However, if both the density and volume of the solution were given then the molality could be calculated. 

Problem: What is the weight percent of nitric acid in 3.26 m HNO3 (aq)? (MW of HNO3 is 63.018 g/mol).

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Problem: 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).

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Problem: At 25.0 degrees Celsius, a solution is prepared by dissolving 12.7 g NaCl in 95.5 mL of water. What is the ppm of NaCl if the density of water at this temperature is 0.9983 g/mL.

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Molarity, Molality, Mass Percent & Mole Fraction Additional Practice Problems

A solution is prepared by mixing together cyclohexane (C 6H12, MW = 84.16 g/mol) and p-xylene (C6H4(CH3)2), MW = 106.17 g/mol). The mole fraction of p-xylene in the solution is X p = 0.1664. What are the molality and the percent by mass p-xylene in the solution?

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A stock solution of hydrofluoric acid is 15 M and has a density of 0.99 g/mL at 25 °C. What is the mass percent of HF at 25 °C?

a. 15%

b. 30%

c. 45%

d. 60%

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What is the molality of a 32.0% by weight aqueous solution of acetone (C  3H6O)?

A. 8.10

B. 7.80

C. 7.12

D. 6.56

E. 5.74

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Which of the following statements is FALSE?

a) The minority component of a mixture is called the solute

b) The majority component of a mixture is called the solvent

c) A diluted solution contains a relatively small amount of solute relative to solvent

d) The molarity of a solution is the moles of solute divided by liters of solvent

e) The molality of a solution is the moles of solute divided by kg of solvent

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What is the molarity of a 1.484  m solution of sucrose, C12H22O11? The density of the solution is 1.127 g/mL.

A. 1.672 M

B. 1.484 M

C. 3.400 M

D. 1.109 M

E. 0.958 M

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What is the percent CdSO4 by mass in a 1.0 molal aqueous CdSO4 solution?

A. 0.10 %
B. 20.8 %
C. 17.2 %
D. 24.4 %
E. 0.001%

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Calculate the molality of a 23.0% by mass acetic acid, HC 2H3O2, solution. (molar mass = 60.05 g/mole)

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An aqueous solution of tartaric acid, H2C4H4O6, is 0.278 m and has a density of 1.006 g/mL. What is the molarity of the solution? (molar mass = 150.09 g/mole)

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2.489 g of cesium oxalate are dissolved in enough water to give 265.0 mL of a solution whose density is 1.0528 g/mL. What is the percent by mass concentration of the solution? (molar mass cesium oxalate = 353.83 g/mole)

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Which one of the following statements is false?

1. Gases are generally more soluble in water under high pressures than under low pressures.

2. Carbon tetrachloride (CCl4) is more miscible with hexane (C6H14) than it is with a polar solvent such as methanol (CH3OH).

3. As temperature increases, the solubilities of some solids in liquids increase and the solubilities of other solids in liquids decrease.

4. Water dissolves many ionic solutes because of its ability to hydrate ions in solution.

5. Gases are generally more soluble in water at high temperature than at low temperatures.

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Which of the following compounds is likely to be more soluble in water?

1. C6H13OH

2. C4H9OH

3. C4H9SH

4. C4H10

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Below is a tetrahedral molecule with one atom missing (the box).What atom would you add to make an uncharged molecule that is:

a. Soluble in water  _________________________
b. Soluble in CH4    _________________________

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Which of the following substances is more likely to dissolve in water? 

a. CHCl3

b. CCl4

c. CH3CH2OH

d. NaF

e. CF4

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Arrange these compounds in order of increasing vapor pressure and explain your reasoning.  

a. NCl3

b. CH3CH2CH2CH3

c. CH3CH2CH3

d. H2O

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Choose the substance with the highest melting point. 

a. I2 

b. HBr 

c. He 

d. CH3OH 

e. CH3Cl 

Choose the substance with the highest melting point. 

a. I2 

b. HBr 

c. He 

d. CH3OH 

e. CH3Cl 

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Choose the pair of substances that are most likely to form a homogeneous solution.

A) KI and Hg

B) LiCl and C6H14

C) C3H8 and C2H5OH

D) F2 and PF3

E) NHand CH3OH

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Select the major force between the molecules in pure, liquid acetone.

A. ion-ion

B. ion-dipole

C. hydrogen bonding

D. dipole-dipole

E. dispersion

 

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Give the major force between ethanol and water

A. dipole–dipole

B. dispersion

C. hydrogen–bonding

D. ion–dipole

E. ion–ion

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Based on the general concepts that govern intermolecular attractions, which of the following orderings of boiling points of the fluorocarbons

1. CF4

2. F3C - (CF2)4 - CF3

3. F3C - (CF2)2 - CF3

is correct when going from highest to lowest?

1. BP1, BP3, BP2

2. BP2, BP1, BP3

3. BP3, BP2, BP1

4. BP2, BP3, BP1

5. BP1, BP2, BP3

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Hint: By 'dissociation' here you can think of this as 'dissolving'.

1. strong binding in the solid and weak solvent-solute interaction.

2. weak binding of species in the solid and strong interaction between the solvent and solute.

3. None of these is correct.

4. strong interaction between solvent molecules.

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Both ammonia and phosphine (PH3) are soluble in water. Which is least soluble and why?

1. ammonia; it does not form hydrogen bonds with water molecules.

2. phosphine; the P−H bonds are so strong that they cannot break to enable phosphine to hydrogen-bond with water.

3. ammonia; it is too small to be hydrated by water molecules.

4. ammonia; the N−H bonds are so strong that they cannot break to enable the ammonia to hydrogen-bond with water.

5. phosphine; it does not form hydrogen bonds with water molecules. 

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Which of the following statements is/are true? 

a. Ethane (C2H6) will dissolve completely in acetone, CH 3COCH3

b. Hydrofluoric acid (HF) will form a heterogeneous mixture with carbon tetrachloride, CCl 4

c. Hexanol will form a homogeneous mixture with CBr 4

d. Methanethiol (CH3SH) is miscible in fluoromethane (CH3F). 

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Which of the following solvents will dissolve potassium bromide, KBr?

a. H2O

b. CCl4

c. S8

d. CH3CH3

e. All would dissolve potassium bromide at equal rates.

 

The predominant intermolecular force in the question above is: 

a. London Dispersion

b. Hydrogen Bonding

c. Ion-Dipole

d. Dipole-Dipole

e. Dipole-induced Dipole

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A student mixes 10.0 g of KCIO 3 with 45.0 g of H 2O and stirs it for a long time at 60 °C until the solution is completely clear, then allows it to cool slowly to 20 °C where it remains clear. Which statement about the final clear mixture at 20 °C is correct?

a) It is a saturated solution.

b) It is an unsaturated solution and can be made saturated by decreasing the temperature.

c) It is an unsaturated solution and can be made saturated by increasing the temperature.

d) It is a supersaturated solution.

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As temperature increases, solubility of a solid in liquid generally ____________ while solubility of a gas in liquid generally ______________.

A. Increases; Decreases

B. Increases; Increases

C. Decreases; Increases

D. Decreases; Decreases

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A 9.2 M perchloric acid (HClO 4) solution has a density of 1.54 g cm -3 at 25°C. Calculate the molality of the perchloric acid.

a) 5.97

b) 14.2

c) 10.6

d) 14.9

e) none of the given answers

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It is common to add Epson salts to bath water when one has been over exercising and has sore muscles. What is the primary intermolecular force that exists between magnesium sulfate, the primary in Epson salts, and the water in the bathtub?

a) dipole-dipole forces

b) ion-dipole forces

c) London forces

d) ion-ion forces

e) dipole-induced dipole forces

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An aqueous solution is 2.67 M in HNO 3 and has a  density of 1.1064 g cm -3 . Compute the molality of the HNO3 in this solution in mol/kg.

a) 2.42

b) 2.97

c) 3.72

d) 2.32

e) 2.84

 

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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) 0.00273

c) 0.00503

d) 0.0625

e) 0.1570

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 Choose the member of each pair that is expected to have the higher normal melting point. Na or CO2  ,  Al2O3 or NaCl  ,  CH3OH or LiF  ,  SiO2 or H2O

a) Na, NaCI, CH3OH, SiO2

b) CO2, Al2O3, LiF, H2O

c) Na, NaCI, CH3OH, H2O

d) CO2, Al2O3, LiF, SiO2

e) Na, Al2O3, LiF, SiO2

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Two pure chemical substances are liekly to mix and form a solution if:

a. The formation of the solution causes an increase in energy.

b. One substance is polar and the other is nonpolar.

c. The formation of the solution causes an increase in randomness.

d. Strong intermolecular attraction between the solute molecules.

e. More than one of these.

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Which of the following four substances is expected to have the highest contact angle to glass (beads up on glass into almost a ball) but have a concave meniscus in a glass test tube?

 

A. toluene, C6H5CH3

B. hydrazine, H2NNH2

C. hydrogen peroxide, HOOH

D. water, H2O

E. none

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Molality from weight percent: What is the molality of an 18.0% aqueous solution of KCl?

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