Topic 12 Solutions

Topic 12

Solutions

SolutionsA solution is a homogeneous mixture of two or more substances or components.

Solutions may exist as gases, liquids, or solids.

The solute is the substance being dissolved. It is the gas or solid being dissolved in a liquid; if it is of the same state, it is the component of lesser amount.

The solvent is the substance doing the dissolving. In the case of a gas or solid being dissolved in a liquid, the solvent is the liquid; if it is of the same state, it is the component of greater amount.

i.e. coffee: sugar, coffee / water

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Solubility of Solutions Fluids that dissolve in each other in all proportions are said to be miscible fluids. Typically when discussing solubility the phrase “like dissolves like” is used.

A more appropriate way of expressing this is to state that two substances with intermolecular forces of about the same type and magnitude are likely to be soluble in one another. For example, CH3OH / H20 are both polar with similar forces and magnitude; therefore, they are miscible in each other.

If two fluids do not mix, they are said to be immiscible. i.e. oil (nonpolar) / water (polar)

Layers separate with less dense species on top (oil in this case). miscibleimmiscible

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Solute-Solvent InteractionIn most cases, “like dissolves like.”

– This means that polar solvents dissolve polar (or ionic) solutes and nonpolar solvents dissolve nonpolar solutes.

– The relative force of attraction of the solute for the solvent is a major factor in their solubility.

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– i.e. the dipole-dipole interactions of water (polar solvent) with a polar solute can be easily explained as electrostatic attractions (d-, d+) between the dipoles of the molecules.

d+d-polarsolute

HO

Hd+d-

HO

Hd+d-

Ionic SolutionsPolar solvents, such as water, also interact well with ionic solutes because of electrostatic attractions (d-, d+) between the cation and anion with water.

Ionic compounds are the extreme in polarity. When water is the solvent, the attraction of ions to water molecules is referred to as hydration.

+

-

HO

Hd+

d-HO

H

d-

d+

HO

Hd+d-

HO

Hd-

d+

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Nonpolar SolutesNonpolar solutes interact with nonpolar solvents primarily due to London forces.

Heptane, C7H16, and octane, C8H18, are both nonpolar components of gasoline and are completely miscible liquids.

However, for water (polar) to mix with gasoline (nonpolar), hydrogen bonds must be broken and replaced with weaker London forces between water (A) and the gasoline (B).

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Therefore, gasoline and water are immiscible because water has a stronger attraction for itself (stronger solvent-solvent interaction) causing the two substances to separate into layers with the less dense gas on top.

Solubility and the Solution ProcessSolubility is the amount of solute that can dissolve in a given amount of solvent at given conditions.

– Many factors affect solubility, such as temperature (most solids T, solubility).

– There is a limit as to how much of a given solute will dissolve at a given temperature.

– A saturated solution is one holding as much solute as is possible at a stated temperature.

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At 20oC, the solubility of NaCl in water (saturation point) is 36 g NaCl / 100 mL of water.

Solubility: Saturated SolutionsSometimes it is possible to obtain a supersaturated solution, that is, one that contains more solute than is possible at a given temperature.

Crystallization from a supersaturated solution of sodium acetate.

Supersaturated solutions are unstable and the slightest disturbance will cause the excess solute to crystallize out.

HW 70

8code: solubility

Effects of Temperature and Pressure on Solubility

The solubility of solutes is very temperature dependent.

– For gases dissolved in liquids, as temperature increases, solubility decreases.

– On the other hand, for most solids dissolved in liquids, solubility increases as temperature increases.

– Basically, an increase in temperature always shifts the position of equilibrium towards the endothermic process.

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Temperature ChangeUsually dissolving a solid in a liquid is an endothermic process because heat must be absorbed to break down the crystal lattice.

solid + liquid solution DH > 0 (endothermic)

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Any additional heat would shift the equilibrium to the right (favor forward endothermic reaction) causing more solid to dissolve. For example, more sugar dissolves in hot coffee than cold coffee.

The process of a gas condensing to a liquid is always an exothermic process.

gas + liquid solution DH < 0 (exothermic)

Any additional heat would shift the equilibrium to the left (favor reverse endothermic reaction) causing less gas to dissolve. For example, a warm beer goes flat faster than a cold beer.

Effects of Pressure on SolubilityHenry’s Law states that the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas in direct contact with the liquid.

– Expressed mathematically, the law is

where S is the solubility of the gas, kH is the Henry’s law constant characteristic of the solutionP is the partial pressure of the

gas.

PkS H

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Basically, the higher the pressure of a gas above the liquid, the more soluble the gas is in the liquid. For example, if a piston pushes down on a gas, more gas will dissolve in the liquid; P, solubilityFor example, the fizz that occurs when a soda can is opened results from reduced pressure of carbon dioxide over the liquid; P, solubility

Solution Concentration Expressions

Concentration expressions are a ratio of the amount of solute to the amount of solvent or solution.

– The quantity of solute, solvent, or solution can be expressed in mass, volume, or moles.

– The common ways to express concentration are molarity, molality, mass percent, and mole fraction.

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MolarityThe molarity, M, of a solution is the moles of solute in a liter of solution (volume of solute + solvent).

A solution can be prepared to a specific molarity by weighing out the mass of the solute and dissolving in enough solvent to obtain the needed volume of solution. Note: volumes are temperature dependent.

solution of literssolute of moles)M(Molarity

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The mole fraction of a component “A”, A, in a solution is defined as the moles of the component substance divided by the total moles of solution (moles of solute + solvent).

Mole Fraction is a unitless quantity with the sum of mole fractions of all components of the solution equaling to 1.

solution of moles total Asubstance of moles A

Mole Fraction

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Mass Percentage of Solute

The mass percentage of solute is defined as:

Notes: - the “%” in the formula is a unit like grams, etc. and not

the % key on the calculator.- the unit of mass doesn’t matter as long as the same

unit is used for solute and solution.- mass of solution = mass of solute + mass of solvent

For example, a 3.5% by mass solution contains 3.5 grams solute per 100 grams of solution.

100% solution of masssolute of mass solute of percentage Mass

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Mass Percentage of SoluteHow many grams of water are needed to prepare 425.0 g of aqueous solution containing 2.40% by mass of NaCl?

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We know there is 2.40 g of NaCl needed per every 100 g of solution by the mass percent; therefore, we can determine how much NaCl is in 425.0 g of solution.

This is the amount of NaCl we need in a 2.40% by mass solution of NaCl; however, we need to determine how much water must be added to obtain the 425.0 g of solution.

Mass Percentage of Solute

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We know that of the 425.0 g of solution that 10.2 g consists of NaCl and the remainder is the solvent water.

Rearranging,

To prepare 425.0 g of 2.40% by mass NaCl, it would require dissolving 10.2 g NaCl in 414.8 g of H2O.

Note: masses are additive and temperature independent while volumes are not additive and are temperature dependent.

MolalityThe molality of a solution is the moles of solute per kilogram of solvent.

This expression is useful in situations when concentrations must be compared over a range of different temperatures because it is based on mass which is temperature independent.

solvent of kilogramssolute of moles)(molality m

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A Problem to ConsiderWhat is the molality of a solution containing 5.20 g of glucose, C6H12O6, dissolved in 90.0 g of water?

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First, convert the mass of glucose to moles and mass of water to kg

Plugging these values into the definition of molality

solvent of kilogramssolute of moles)(molality m

HW 71code: molality

Colligative PropertiesThe properties of a solution differ from those of the pure solvent.

The colligative properties of solutions are those properties that depend on the number of particles dissolved in solution rather than their nature.

These properties include:1. vapor pressure lowering2. freezing point depression3. boiling point elevation4. Osmotic pressure 20

Vapor Pressure Lowering (nonvolatile)The vapor pressure of a liquid is the pressure of the gas above the liquid.

Vapor pressure is a colligative property that decreases by the addition of a nonvolatile solute.

The vapor pressure of the solution (nonvolatile solute and nonelectrolyte solvent) will be lower than the vapor pressure of the pure solvent.

Vapor pressure lowering is independent of the nature of the solute but directly proportional to its concentration.

Any interference with the ability of solvent particles to vaporize results in a decrease in gas molecules and hence a lower vapor pressure.

Adding a nonvolatile solute to the solution decreases the surface area formerly occupied by just solvent (now mixture of solute and solvent particles on surface) and diminishes the rate of vaporization of the solvent; hence, a lower vapor pressure compare to pure solvent. 21

Raoult’s law states that the vapor pressure of a solution containing a nonelectrolyte nonvolatile solute is proportional to the mole fraction of the solvent:

where Psolution is the vapor pressure of the solution

solvent is the mole fraction of the solvent

Posolvent is the pure vapor pressure of the

solvent.

))(P(P solventosolventsolution

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Vapor Pressure Lowering (nonvolatile)

Basically, the vapor pressure of the solution is a fraction of that of the pure solvent and depends on the percentage of solvent making up the solution (partial vapor pressure).

If a solution contains a volatile solute, the vapor pressure of the solution will be a combination of the partial vapor pressures of each volatile component:

))(P())(P(P soluteosolutesolvent

osolventsolution +

HW 7223

Vapor Pressure Lowering (volatile)

code: vp

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van’t Hoff Factor (nonelectrolytes)

Colligative properties of solutions are directly proportional to the concentration of solute particle; therefore, the effect that solutes have on colligative properties depends on the quantity of solute particles present in the solution.

When one mole of glucose, C6H12O6, dissolves in water, one mole of solute molecules is obtained. Glucose is a molecular compound composed of covalent bonding and is a nonelectrolyte that does not ionize in water. For each mole of nonelectrolyte solute, there is one mol of solute particles.

C6H12O6 (s) C6H12O6 (aq)

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van’t Hoff Factor (electrolytes)Electrolytes ionize in water and for each mole of solute, there could be several moles of solute particles. For example, CaCl2 is an ionic compound that is an electrolyte that dissociates into three solute particles in water (1 mol of Ca2+ and 2 mol of Cl-).

CaCl2 (s) Ca2+ (aq) + 2Cl- (aq) Since calcium chloride has three times the number of solute particles as glucose, we would expect CaCl2 to have approximately three times the effect on the colligative properties as compared to glucose.

The ratio of moles of solute particles in solution to moles of formula units dissolved is referred to as the van’t Hoff factor (i):

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van’t Hoff FactorWe expect the moles of solute particles in solution and the van’t Hoff factor to be the same, but this actually only occurs for very dilute solutions.

For our purposes, we will assume that the ions of an electrolyte behave independently meaning i should be equal to the number of moles of ions per mole of electrolyte and 1 for nonelectrolytes.

For example, i should be 2 for NaCl [1Na+, 1Cl-], 5 for Al2(SO4)3

[2Al3+, 3SO42-], and 1 for C2H6O2 [1 C2H6O2].

In the previous section, we discussed the vapor pressure of nonelectrolytes. When we calculate the vapor pressure of a solution containing an ionic solute (electrolyte), we must account for the number of solute particles when we calculate the mole fraction of the solvent.

A solution contains 0.155 mol NaCl and 0.756 mol H2O. Calculate the vapor pressure of the solution at 55oC given the vapor pressure of pure water at 55oC is 118.1 mm Hg.

NaCl has 2 particles per every one mol of substance. This must be accounted for in the mole fraction of water before we use Raoult’s Law.

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van’t Hoff Factor

Boiling Point Elevation and Freezing Point Depression

For the same reason the vapor pressure reduces by the addition of a nonvolatile solute, the boiling point of a solution will be elevated.

The temperature at which the vapor pressure of a liquid equals 1 atm is called the normal boiling point. Since the addition of a nonvolatile solute will diminish the rate of vaporization of a solvent, the temperature of the solution must be increased to a value greater than the normal boiling point of the pure solvent to achieve a vapor pressure of 1 atm.

The opposite effect occurs for freezing. When a solution is cooled, it does not begin to freeze until a temperature is achieved that is below the freezing point of the pure solvent. 28


A good example of taking advantage of both properties is the addition of antifreeze solution to the radiator of a car.

Typically, ethylene glycol is used as antifreeze and is a nonvolatile solute. By adding antifreeze to our radiator, we have raised the boiling point and lowered the freezing point of our engine cooling system. It allows us to continue to use our cars on hot summer days and cold winter days that otherwise would not be possible with pure water.

The boiling point of a pure solvent remains constant while changing from liquid to a gas; however, the boiling point of a solution continues to increase as solvent is vaporized. 29

The relevant equations associated with these colligative properties are

where and are the change in temperature relative to that of the pure solvent in oC, and are proportionality constants called the molal boiling point elevation constant and molal freezing depression point constant that are dependent on the solvent, is the molality of the solution in moles per kilogram solvent, and i is the number of moles of solute particles per mole of solute.

))()(( imKT bb D

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))()(( imKT ff D


Once the change in temperature is calculated, the actual boiling point or freezing point of a solution is calculated by adding the change to the boiling point of the pure solvent or subtracting the change from the freezing point of the pure solvent.

fTTT solventfsolutionf D-

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bTTT solventbsolutionb D+


A Problem to ConsiderEstimate the freezing point of 0.35 m solution of Cr(NO3)3. Assume the value of is based on the number of solute particles per mole of solute and the of water is 1.86oC/m. Cr(NO3)3 has 4 particles per every one mol of substance which means = 4. Plugging into the change in temperature equation we obtain

oC

HW 73

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Cr(NO3)3 (s) 1Cr3+(aq) + 3NO3-(aq)

code: freezing

-2.6oC

Molar Mass Calculation ProblemA 1.25 g sample of a nonelectrolyte compound was dissolved in 75.0 g of benzene. The solution froze 1.20oC below that of pure benzene. Determine the molar mass of the compound if the of benzene is 5.12oC/m.

Re-arranging for the molality of the solution:

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Knowing the relationship between moles and molar mass, we can rewrite molality:

Re-arranging for molar mass:

Molar Mass Calculation Problem

HW 74 code: molar

Osmotic PressureOsmosis is a process whereby a solvent passes from a dilute solution into a more concentrated one through a membrane permeable only to the solvent.

The equalization of concentration between the two solutions in contact with one another across the membrane is what drives the process of osmosis.

The osmotic pressure, , is equal to the external pressure, P, just sufficient to prevent osmosis. Osmotic pressure is a colligative property and is directly proportional to the molar concentration of solute:

where M is the molarity of the solute, R is the ideal gas constant (0.0821 L . atm/mol . K), and T is absolute temperature (K).

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Topic 12 Solutions

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