Deviations from Raoult's Law Learning Goal: To understand deviations from the ideal vapor pressure for solutions of two liquids. Raoult's law is used to calculate the vapor pressure of an ideal solution that contains one or more volatile components. For example, if we mix a liquid with a vapor pressure of 100 with an equal amount of a liquid with a vapor pressure of 200 , the resulting solution would have a vapor pressure of approximately 150 . The only reason that this solution's vapor pressure would not be exactly 150 is that the molecules of these liquids interact. A vapor pressure above 150 would be called a positive deviation from Raoult's law. A vapor pressure below 150 would be called a negative deviation from Raoult's aw. Solutions, Suspensions and Colloids Learning Goal: To understand the differences between solutions, colloids and suspensions and how to distinguish between them. Suspensions and colloids are mixtures of two or more components. They are similar to solutions, but differ in that the molecule being dispersed through the solvent is not truly dissolved. In a suspension of colloid, the particles are distributed though the liquid phase. They are held suspended by intermolecular solvating forces that keep the particles from immediately precipitating into a separate phase.The difference between a suspension and a colloid is dependent on the size of the particles involved. In a suspension, the particles involved are generally on the order of 1 and bigger. This is large enough that even though the particles in the suspension are solvated, gravity will overcome diffusion and the particles will aggregate toward the bottom.In a colloid, the particles are smaller than in a suspension, on the order of 2 to 1000 nm. Depending on what is being suspended, this is small enough that diffusion forces will overcome the gravitational force and the particles in the colloid stays dispersed evenly through the solvent indefinitely.sometimes it can be difficult to distinguish a colloid from a true solution, because nothing is separating out in the colloid. But the particles suspended in the colloid are large enough to scatter light. So when a beam of light is directed through a colloid, the scattered light makes the beam visible. A true solution will not scatter light in this way. This light scattering effect is called the Tyndall effect named after the physicist who discovered it.Thomas Graham studied colloids in the 1860s. He coined the terms sol and gel to describe the different forms of colloids. A sol is a liquid form of a colloid and a gel is the gelatinous form of a colloid. Some sols can be converted into gels by careful manipulation of the temperature or pH conditions. For example, an aqueous sol of collagen can be boiled and when it cools, it turns into a gel, sometimes called gelatin. The boiling denatures the collagen protein, exposing hydrophobic parts of the protein that will form intermolecular aggregates.If you have a colloid in an aqueous solution which is stable because the particles have a charge on the surface and the water molecules solvate them through hydrogen bonding, but you want to precipitate the particles, sometimes it is possible to add charged species such as Aluminum Sulfate, , that will interact with multiple particles simultaneously and pull them together into aggregates that will precipitate out of solution.There are other forms of colloids than solids in liquids. For example, fog is a colloidal suspension of water droplets in air. Introduction to Units of Concentration The composition of a solution can be expressed in several different ways. Four of the most common concentration units are defined as follows:. A solution was prepared by dissolving 43.0 of in 225 of water. Molality, Freezing Point, and Boiling Point Learning Goal: To use freezing-point depression or boiling-point elevation to determine the molal concentration of a solution. The freezing point, , of a solution is lower than the freezing point of the pure solvent. The difference in freezing point is called the freezing-point depression, : The boiling point, , of a solution is higher than the boiling point of the pure solvent. The difference in boiling point is called the boiling-point elevation, : The molal concentration of the solution, , is directly proportional to and : Freezing points and molality Quantitatively, the freezing-point depression of a solution is related to the molality and the freezing-point-depression constant of the solvent by the equation where the freezing-point depression is the difference between the freezing points of the pure solvent and the solution. Boiling points and molality Similar to the freezing-point depression, the boiling-point elevation of a solution is quantitatively related to the molality and the boiling-point-elevation constant of the solvent by the equation where the boiling-point elevation is the difference between the boiling points of the solution and the pure solvent. Osmosis Learning Goal: To learn about osmosis and about isotonic solutions, hypertonic solutions, and hypotonic solutions. Osmosis is the net movement of water across a semipermeable membrane from an area of lower concentration to an area of higher concentration. The water will continue to move across the semipermeable membrane as the system attempts to reach equilibrium, where both solutions have the same concentration. There are three different ways a solution can be described in relation to a cell placed in the solution: isotonic, hypotonic, and hypertonic. Compared to a cell, an isotonic solution exerts the same osmotic pressure as the cellular fluids. In other words, it behaves as if it had the same solute concentration as the cell. A hypertonic solution behaves as if it had a higher solute concentration than the cell, and a hypotonic solution behaves as if it had a lower solute concentration than the cell. If a cell is placed in an isotonic solution, nothing happens to the cell because water is moving in and out of the cell at the same rate. If a cell is placed in a hypotonic solution, water will flow into the cell, causing it to swell (and possibly burst). If a cell is placed in a hypertonic solution, water will flow out of the cell, causing it to shrink. Crenation and hemolysis A cell placed in a hypertonic solution will shrink in a process called crenation. A cell placed in a hypotonic solution will swell in a process called hemolysis. To prevent crenation or hemolysis, a cell must be placed in an isotonic solution such as 0.9 (m/v) or 5.0 (m/v) glucose. This does not mean that a cell has a 5.0 (m/v) glucose concentration; it just means that 5.0 (m/v) glucose will exert the same osmotic pressure as the solution inside the cell, which contains several different solutes. Henry's Law The solubility of a gas in a liquid increases with increasing pressure. To understand the above statement, consider a familiar example: cola. In cola and other soft drinks, carbon dioxide gas remains dissolved in solution as long as the can or bottle remains pressurized. As soon as the lid is opened and pressure is released, the gas is much less soluble and escapes into the air. The relationship between pressure and the solubility of a gas is expressed by Henry's law: , where is concentration in , is the Henry's law constant in units of , and is the pressure in . Note: Since temperature also affects the solubility of a gas in an liquid, the Henry's law constant is specific to a partcular gas at a particular temperature. The following table provides some information on carbon dioxide solubility in water. Boiling Point Elevation and Freezing Point Depression for Organic Solutions The temperature at which a solution freezes and boils depends on the freezing and boiling points of the pure solvent as well as on the molal concentration of particles (molecules and ions) in the solution. For nonvolatile solutes, the boiling point of the solution is higher than that of the pure solvent and the freezing point is lower. The change in the boiling for a solution, , can be calculated as in which is the molality of the solution and is the molal boiling-point-elevation constant for the solvent. The freezing-point depression, , can be calculated in a similar manner: in which is the molality of the solution and is the molal freezing-point-depression constant for the solvent. Raoult's Law and Ionic or Organic Solutions As solute is dissolved in a solvent, the vapor pressure of the solution changes according to Raoult's law where is the vapor pressure of the solution, is the vapor pressure of the pure solvent, and is the mole fraction of the solvent. If the solute dissociates into ions, the term must be modified to take into consideration the total number of moles of particles in the solution, both ions and molecules. When a solution contains two volatile components, and , the total pressure of the solution is equal to the sum of the individual vapor pressures according to Dalton's law as follows: The van't Hoff Factor Colligative properties, such as boiling point elevation, depend on the number of dissolved particles in solution. For nonelectrolytes, no dissociation occurs, and so you can use the number of moles of solute to calculate both molality and molarity. In contrast, electrolytes dissociate, and therefore the molality and molarity must be calculated based on the number of moles of dissociated particles or ions. There are two ions per formula unit of . Therefore, we would expect the freezing-point depression of a solution to be twice that of a sugar solution of the same concentration. However, it turns out that for the salt solution is only 1.9 times that of the sugar solution. This indicates that not all ion pairs in the solution are dissociated. The number 1.9 is called the van't Hoff factor (symbolized by ) and can be thought of as the number of dissociated particles per formula unit. Here are three different methods of expressing the van't Hoff factor: Energetics of Solution Formation A solution is formed when the solute uniformly disperses throughout (or dissolves in) the solvent. The process can be described though three steps: separation of solvent-solvent particles, breaking of solute-solute particles, and formation of solute-solvent interactions. The overall energy change for the solution process, , is the sum of the enthalpies of the three steps. Whether is endothermic or exothermic depends on the relative magnitudes of , , and , where the subscript indicates the step in the process corresponding to the enthalpy value. Exercise 12.51: Problems by Topic - Concentrations of Solutions An aqueous solution is made using 133 of diluted to a total solution volume of 1.30 . Exercise 12.39: Problems by Topic - Energetics of Solution Formation Lithium iodide has a lattice energy of and a heat of hydration of - 793 . Exercise 12.76: Problems by Topic - Vapor Pressure of Solutions An ethylene glycol solution contains 19.8 of ethylene glycol in 84.9 of water. Raoult's Law: Nonvolatile and Volatile Solutes As the concentration of a solution increases, its vapor pressure decreases. For a nonvolatile solute in a liquid solvent , the relationship between concentration and vapor pressure is expressed by Raoult's law: where is the vapor pressure of the solution, is the mole fraction of solvent, and is the vapor pressure of the pure solvent. In a two-component solution consisting of and , the mole fraction, , of component is defined as Solutions containing volatile solutes In solutions composed of two liquids ( and ), each liquid contributes to the total vapor pressure above the solution. The total vapor pressure is the sum of the partial pressures of the components: where and are the vapor pressures of pure and , respectively. Exercise 12.114: Challenge Problems A metal, , of atomic weight 96 reacts with fluorine to form a salt that can be represented as . In order to determine and therefore the formula of the salt, a boiling point elevation experiment is performed. A 9.18- sample of the salt is dissolved in 100.0 of water and the boiling point of the solution is found to be 374.38 . Molar Mass from Colligative Properties The molar mass of a compound expresses the ratio of mass to moles: This quantity can be determined experimentally by accurately measuring the mass of the sample and determining the corresponding number of moles based on some property of the sample. Freezing point depression and osmotic pressure measurements are frequently used for this type of determination. In each instance, the number of moles is determined from the colligative property of the solution. For osmotic pressure measurements, the number of moles is calculated from the volume of the solution and the molarity. In freezing point depression measurements, the number of moles is derived from the molality of the solution.
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