Concentrations can be calculated in several different sets of units. Molarity (M) is the number of moles of a solute dissolved in 1 liter of solution: . Molality (m) is concentration expressed as the number of moles of a solute divided by the mass of solvent in kilograms: . Molality is linked with the mass of the solvent, and molarity is linked with the volume of the solvent. Because volume is a function of temperature, it changes with the rise or fall in temperature. But mass is not a function of temperature. Neither the number of moles of the solute nor the mass of the solvent is affected by changes in temperature. Mass, and therefore molality, does not depend on temperature. Liquids expand as they warm, so if a 1 M solution is prepared at 20°C and the temperature is raised to 25°C, the volume of the solvent will increase slightly, and the molar concentration (in M) therefore will decrease slightly—the same mass of solute in a larger volume of solvent. The molal concentration (in m) of that same solution would remain unchanged—the same mass of solute in the same mass of solvent.Mole fraction () is concentration expressed as the moles of solvent divided by the total number of all moles in solution. For example, in a solution that contains 0.50 mol H2O, 0.70 mol CH3OH, and 0.30 mol CH3CH2OH, their respective mole fractions are:
Vapor Pressures, Melting Points, and Boiling Points
Because the vapor pressure of a solute A is lowered when it is part of a solution, the phase diagram (graph relating a substance's phases of matter, temperature, and pressure) of that solute is changed. Remember that where the vapor pressure curve intersects the sublimation curve defines the beginning of the solid-liquid transition curve—that is, the freezing curve—of a substance. If the vapor pressure is lowered, the curve intersects the sublimation (phase transition from a solid to a gas at a constant temperature and pressure) curve at a lower temperature, and the freezing point of the substance is also lowered. This is called freezing point depression.
In addition, because the vapor pressure is lowered, the vapor-liquid transition curve intersects the at a higher temperature than the curve for the pure substance. Because the boiling point of a substance is defined as the temperature at which , this means the boiling point for a component in a solution has been raised. This is called boiling point elevation.Recall that freezing point depression and boiling point elevation are colligative properties. Therefore, the amount by which the freezing point is lowered and the boiling point is elevated is proportional only to the mole fraction of the solute present, as with vapor pressure. This is represented mathematically by
Because and do not depend on the identity of the species (any specific type of chemical particle, such as a water molecule or a sodium ion) in solution, if Kf for the solvent is known, the molar mass of a solute can be calculated with precise measurement of .
The van 't Hoff Factor
The mole fraction of an electrolytic solution depends on the degree to which the electrolyte dissociates, and 1 mol of a strong electrolyte produces more than 1 mole of solute particles in solution. The number of moles depends on the stoichiometry (quantitative relationships among different elements and substances) of the electrolyte. For example, NaCl produces 2 moles, and MgCl2 produces 3 moles. Weak electrolytes, such as CH3COOH, only partially dissociate, so the number of particles resulting from 1 mol of a weak electrolyte is more than 1 but less than the stoichiometric ratio.Because colligative properties depend only on the number of particles in solution, electrolytes dissolved in water have a greater effect on the and than nonelectrolytes. This can be accounted for by including a factor i, called the van 't Hoff factor, in the equations for :
That the van 't Hoff factor depends on solution concentration may seem surprising, but it is because the motions of ions in solution are affected by one another. Ionic particles in solution are surrounded by particles with the opposite charge, so their mobility is reduced. Colligative properties depend on freely moving particles, so the effect of colligative properties is reduced in an ionic solution. The more dilute the solution, the more the ions are able to move, and the closer the van 't Hoff factor gets to its stoichiometric value.
Distillation and Osmosis
Because chemical purification is often the goal in chemistry, it is sometimes desirable to separate solutions of two liquids. This can be accomplished by a process called fractional distillation, which is the separation of two liquids by boiling in stages. Raoult's law states that the partial pressure of a solute is proportional to its mole fraction in solution. The vapor pressures and liquid composition of a solution exist in an equilibrium that can be plotted as a function of the mole fraction. This is called a graph of the liquid-vapor equilibrium.
Simple distillation is separation by boiling a solution, collecting the vapor, and recondensing it. Salt water can be purified through this process. When it boils, the vapor pressure of water is so much lower than the vapor pressure of salt that the water boils off before the salt, and the resulting condensate is pure water.Fractional distillation is used when the condensate from simple distillation is not pure, as in the case of a benzene-toluene mixture. The vapor pressures of benzene and toluene are close enough to each other that the vapor that is collected is a mixture of benzene and toluene vapors. However, because the Pvap values are not the same, the mole fraction of benzene in the vapor solution is higher than the in the liquid solution. Thus, if this vapor solution is condensed and redistilled, the vapor will be even more concentrated in benzene. Pure benzene can be collected after multiple distillation stages, and pure toluene is left behind.