Topic 12 Solutions

A 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 2

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, CH 3 OH / H 2 0 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 3

Solute-Solvent Interaction In 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. 4 –i.e. the dipole-dipole interactions of water (polar solvent) with a polar solute can be easily explained as electrostatic attractions (  -,  + ) between the dipoles of the molecules.   polar solute H O H   H O H  

Ionic Solutions Polar solvents, such as water, also interact well with ionic solutes because of electrostatic attractions (  -,  + ) 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. + - H O H   H O H   H O H   H O H   5

Nonpolar Solutes Nonpolar solutes interact with nonpolar solvents primarily due to London forces. Heptane, C 7 H 16, and octane, C 8 H 18, 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). 6 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 Process Solubility 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. 7 At 20 o C, the solubility of NaCl in water (saturation point) is 36 g NaCl / 100 mL of water.

Solubility: Saturated Solutions Sometimes 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 8 code: 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. 9

Temperature Change Usually dissolving a solid in a liquid is an endothermic process because heat must be absorbed to break down the crystal lattice. solid + liquid solution  H > 0 (endothermic) 10 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  H < 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 Solubility Henry’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, k H is the Henry’s law constant characteristic of the solution P is the partial pressure of the gas. 11 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, solubility For 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. 12

Molarity The 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. 13

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. Mole Fraction 14

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. 15

Mass Percentage of Solute How many grams of water are needed to prepare g of aqueous solution containing 2.40% by mass of NaCl? 16

Mass Percentage of Solute 17

Molality The 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. 18

A Problem to Consider What is the molality of a solution containing 5.20 g of glucose, C 6 H 12 O 6, dissolved in 90.0 g of water? 19 HW 71 code: molality

Colligative Properties The 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 lowering 2.freezing point depression 3.boiling point elevation 4.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 P solution is the vapor pressure of the solution  solvent is the mole fraction of the solvent P o solvent is the pure vapor pressure of the solvent. 22 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: HW Vapor Pressure Lowering (volatile) code: vp

24 van’t Hoff Factor (nonelectrolytes)

25 van’t Hoff Factor (electrolytes)

26 van’t Hoff Factor We 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 Al 2 (SO 4 ) 3 [2Al 3+, 3SO 4 2- ], and 1 for C 2 H 6 O 2 [1 C 2 H 6 O 2 ]. 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.

27 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

Boiling Point Elevation and Freezing Point Depression 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 30 Boiling Point Elevation and Freezing Point Depression

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. 31 Boiling Point Elevation and Freezing Point Depression

A Problem to Consider HW Cr(NO 3 ) 3 (s)  1Cr 3+ (aq) + 3NO 3 - (aq) code: freezing -2.6 o C

Molar Mass Calculation Problem 33

34 Molar Mass Calculation Problem HW 74 code: molar

Osmotic Pressure 35