7.1 THE LIQUID STATE
We learned in the previous chapter that the molecules of a sub-stance in the gaseous state are in constant and very rapid motion and that the space between the molecules is large compared to the sizes of the molecules. As the molecules of a gas are made to come closer together by increased external pressure, the distance between the molecules is decreased and VAN DER WAALS FORCES become stronger. As a gas cools, the velocity of the molecules decreases and their tendency to move apart after collision decreases. If the pressure is high enough and the temperature low enough, the intermolecular attractive forces overcomes the tendency of the molecules to fly apart, and the gas condenses to the liquid state. Although molecules in the liquid state cling to one another, they still retain a limited amount of motion, as reflected in the capacity of liquids to flow, to take the shape of a container, to diffuse, and to evaporate.
The molecules in a liquid are held in such close contact by their mutual attractive forces that the volume of any liquid decreases very little with increased pressure; liquids are relatively incompressible as compared to gases. The molecules in a liquid are able to move past one another in random fashion (diffusion) but because of the much more limited freedom of molecular motion existing in liquids, they diffuse much more slowly than do gases.
When water is placed in an open vessel its volume decreases upon standing. This type of loss of volume is called EVAPORATION. Evaporation may be explained in terms of the motion of molecules. At any given temperature above 0oK (absolute zero) the molecules of a liquid move-some slowly, some at intermediate speed, and some very rapidly. An average velocity can be calculated. A rapidly moving molecule near the surface of the liquid may possess necessary kinetic energy to overcome the attraction of the surrounding molecules and escape (EVAPORATE) to the space above the liquid. Other fast moving molecules will leave the liquid phase and appear in the gaseous phase above the liquid as the process of evaporation continues. When the space above the liquid is confined, molecules cannot escape into the open but strike the walls of the container, rebound, and may strike the surface of the liquid, where they are again liquefied. The return of the molecules from the vapor state to the liquid state is known as CONDENSATION. As evaporation proceeds, the number of molecules in the vapor state increases, and in turn, the rate of condensation increases. The rate of condensation will soon become equal to the rate of evaporation and the vapor in the closed container will be in equilibrium with its liquid. This is called DYNAMIC EQUILIBRIUM because the opposing changes involved are in full operation. At equilibrium the space above the liquid is saturated with respect to molecules of the vapor. The pressure exerted by the vapor in equilibrium with its liquid, at a given temperature, is called the VAPOR PRESSURE of the liquid.
The equilibrium vapor pressure of a liquid is dependent upon the particular kind of molecules composing the liquid. We also know that the vapor pressure of a liquid increases as the temperature is raised; this is due to an increase in the rate of molecular motion which accompanies an increase in temperature. This results in the escape of more molecules from the surface of the liquid per unit of time and a greater velocity for each molecule which escapes. Thus, an increase in temperature results in a higher equilibrium vapor pressure. When bubbles of vapor form within a liquid and rise to the surface where they burst and release the vapor, the liquid is said to BOIL. A liquid exposed to the air will boil when its equilibrium vapor pressure becomes equal to the pressure of the atmosphere. The NORMAL BOILING POINT of a liquid is that temperature at which its equilibrium vapor pressure becomes equal to the standard atmospheric pressure of 760 Torrs. A liquid may boil at temperatures higher than normal under external pressures greater than one atmosphere; conversely, the boiling point of a liquid may be lowered below normal by decreasing the pressure on the surface of the liquid below one atmosphere. Thus at high altitudes where the atmospheric pressure is less than 760 Torrs, water boils at temperatures below its normal boiling point of 100oC. Food cooked in boiling water cooks more slowly at high altitude because the temperature of boiling water there is lower than it would be nearer sea level. The temperature of boiling water in pressure cookers is higher than normal due to higher equilibrium vapor pressures, thus making it possible to cook foods faster than in open vessels. It should be emphasized that boiling does not refer to the hotness nor coldness of a liquid, as these are biological sensations, but rather the change in physical state. The boiling point is also related to van der Waals forces. The magnitude of the van der Waals attraction increases with increase in the number of electrons per molecule, and therefore with the molecular weight. Thus the greater the number of electrons, or molecular weight, the higher will be the boiling point.
7.4 HEAT OF VAPORIZATION
While water or any liquid boils, the temperature remains constant. As heat is absorbed by the molecules, they gain more kinetic energy. Eventually the kinetic energy of these molecules is increased to the point that the attractive forces between them are overcome. The now highly energetic molecules break away from each other, forming a gas, or vapor.
When the liquid is boiling, the heat that is added causes more and more molecules to pull away from the liquid. Additional heat at this point does not increase the kinetic energy of the molecules. For this reason, the temperature remains constant. The amount of heat needed to change a given amount of liquid to a gas without a change in temperature is its HEAT OF VAPORIZATION, sometimes referred to as latent (hidden) heat. The heat of vaporization for water is 540 calories per gram (9720 cal/mole) and the heat of vaporization for ammonia is 327 calories per gram (5559 cal/mole).
|Substance||Melting Point (oC)||Boiling Point (oC)||Solid <--> Liquid Heat of Fusion||Liquid <-->Vapor Heat of Vaporization|
|Oxygen||-218||-183||3.3 cal/g||51 cal/g|
|Nitrogen||-210||-196||6.1 cal/g||48 cal/g|
|Alcohol||-114||78||26.0 cal/g||204 cal/g|
|Water||0||100||80.0 cal/g||540 cal/g|
|Lead||327||1750||5.5 cal/g||205 cal/g|
|Silver||961||2212||26.5 cal/g||563 cal/g|
Liquids may contain dissolved materials which make them unsuitable for a particular purpose. The life of a storage battery may be shortened by using water containing dissolved mineral matter. Water and other liquids may be purified by a process known as DISTILLATION. By heating ordinary water in a distillation flask the liquid is converted to vapor which passes over into a condenser. The vapor is condensed to a liquid in the water-cooled condenser, and the liquid flows into the receiving vessel. The dissolved mineral matter is not volatile at the boiling point of water and remains in the distillation flask. Distillation makes use of the facts that the addition of heat to a liquid speeds up the rate of evaporation, an endothermic change, and the cooling of a vapor favors condensation, an exothermic change.
7.6 SURFACE TENSION
The molecules within the bulk of a liquid are attracted equally in all directions by neighboring molecules; the resultant force on any one molecule within the liquid is therefore zero. However, the molecules on the surface of a liquid are attracted only inward and sideways. This unbalanced molecular attraction pulls some of the surface molecules into the bulk of the liquid, and a condition of equilibrium is reached when the surface area is reduced to a minimum. The surface of the liquid, therefore, behaves as if it were under a strain or tension. This contracting force is called SURFACE TENSION. A small drop of liquid tends to assume a spherical shape because in a sphere the ratio of surface area to volume is a minimum. We may define surface tension as the force which causes the surface of a liquid to contract. A liquid surface acts as if it were a stretched membrane. A steel needle carefully placed on water will float. Some insects can move on the surface of water, being supported by the surface tension. One of the forces causing water to rise in capillary tubes, or a root system, is its surface tension.
When crystals of sugar are stirred with a sufficient quantity of water, the sugar disappears and a clear mixture of sugar and water is formed. The sugar is said to have DISSOLVED (or gone into solution) in the water. The solution consists of two components, the SOLUTE (the dissolved sugar) and the SOLVENT (the water). In this solution the molecules of sugar are uniformly distributed among the molecules of water forming a homogeneous mixture. The molecules of sugar diffuse continuously through the water, and although each of them is heavier than a single molecule of water, the sugar does not settle out on standing.
An aqueous solution of sugar which contains only a small amount of sugar (the solute) in comparison with the amount of water is said to be DILUTE; the addition of more sugar makes the solution more CONCENTRATED. The solution is said to be SATURATED when the concentration of dissolved solute is such that it exists in EQUILIBRIUM WITH THE EXCESS UNDISSOLVED SOLUTE. The SOLUBILITY of a given solute is defined as the quantity of that solute which will dissolve in a specified quantity of solvent to produce a saturated solution. The composition of a solution may be varied continuously between certain limits. Thus solutions are not compounds because the latter always contain the same elements in the same proportions by weight.
When sodium chloride (NaCl), an ionic substance, dissolves in water, sodium ions and chloride ions become uniformly distributed throughout the water. This solution is a homogeneous mixture of water molecules, sodium ions, and chloride ions. As in the case of the molecular solute (sugar) there is diffusion of the solute particles (ion for ionic solutes) through the water, and no settling of the solute particles takes place upon standing.
All solutions are characterized by (1) homogeneity, (2) absence of settling, and (3) the molecular or ionic state of subdivision of the components. Because solutions differ in terms of the physical state of both the solute and solvent, many kinds of solutions are possible. In view of the fact that solutions are defined as HOMOGENEOUS MIXTURES, it is not surprising that almost any gas, liquid, or solid will act as a solvent for other gases, liquids, and solidsthereby forming a solution. Air is a homogeneous mixture of gases and thus a gaseous solution.
Oxygen (a gas), alcohol (a liquid), and sugar (a solid) will each dissolve in water (a liquid) and form liquid solutions. Liquid solutions exhibit the general properties characteristic of liquids. The most common and important solutions with which we work in chemistry are those in which the solvent is a liquid. The use of water as a solvent is so general that the word "solution" has come to imply a water solution unless some other solvent is designated. Water is referred to as the UNIVERSAL SOLVENT. Many alloys are solid solution of one solid dissolved in another solid. Nickel coins contain nickel dissolved in copper.
Solutions are extremely important in life processes. For example, oxygen and carbon dioxide are carried throughout the body in solution in the blood. Digestion is a process in which foods are converted into a form which will pass through the walls of the digestive tract and dissolve in the blood.
7.8 HENRY'S LAW
The extent to which a gas dissolves in a liquid depends on the following factors: (1) the nature of the gas and the solvent, (2) the pressure, (3) the temperature. The solubility of a gas in a given liquid is considered to be a specific property of the gas because its solubility differs from that of other gases in the same liquid. At standard temperature and pressure, one liter of water dissolves 0.0489 liters of oxygen, 1.713 liters of carbon dioxide, 79.789 liters of sulfur dioxide, and 1176 liters of ammonia.
The solubility of a gas in a liquid can be increased by increasing the pressure on the gas. This relationship is expressed by HENRY'S LAW: THE WEIGHT OF A GAS THAT DISSOLVES IN A DEFINITE VOLUME OF LIQUID IS DIRECTLY PROPORTIONAL TO THE PRESSURE ON THE GAS. This means that if 1 gram of a gas dissolves in 1 liter of water at one atmosphere of pressure, 5 grams will dissolve at 5 atmospheres of pressure. The effect of pressure does not follow Henry's Law when a chemical reaction takes place between the gas and the solvent. Thus, the solubility of ammonia in water does not increase as rapidly with increasing pressure as predicted by the law because ammonia reacts to some extent with water to form ammonium ions and hydroxide ions.
The effect of increased pressure upon the solubility of a gas in a liquid is illustrated by the behavior of carbonated beverages. Carbon dioxide is forced into the beverage under pressure, and the bottle is tightly capped to maintain the pressure and prevent escape of carbon dioxide. When the cap is removed, the pressure is decreased, and some of the gas escapes. The escape of bubbles of the gas from a liquid is known as EFFERVESCENCE.
The solubility of gases in liquids decreases with an increase in temperature. This characteristic is not one of inverse proportion and the solubility of a gas in a liquid at a given temperature must be determined experimentally. Many gases may be expelled from solvents by boiling their solutions.
Some liquids will mix with water in all proportions. Such liquids are usually either ionic in solution, so that the charged ions attract the oppositely charged ends of the polar water molecules, or they are polar substances with polar character similar to that of water. For such polar liquids, the negative ends of the polar solute molecules attract the positive ends of the polar solvent molecules, and vice versa, with about the same degree of attraction that like molecules of either substance attract each other. Hence, the two kinds of molecules mix easily in all proportions. Liquids which mix with water in all proportions are said to be completely MISCIBLE in water.
Ethyl alcohol, sulfuric acid, and acetone are examples. Nonpolar covalent liquids, such as gasoline, carbon disulfide, and carbon tetrachloride, do not have a net charge separation in the molecule as a whole and hence do not effectively attract the polar water molecules. The water molecules have appreciable attractions only for other water molecules and "squeeze out" the molecules of the nonpolar liquid so that these liquids are very insoluble in water. Such liquids are said to be IMMISCIBLE with water. Two layers are formed when two immiscible liquids are in contact with each other.
7.10 STANDARD SOLUTIONS
The solubility of a solid substance in a pure solvent at a given temperature is a quantitatively definite physical property of the substance. The solubility of sodium chloride (NaCl) is 35.8 grams per 100 grams of water at 20oC; that of Sodium Fluoride (NaF) is 4.2 grams; and that of silver bromide (AgBr) is 0.00002 grams. A general idea of relative solubilities is conveyed by use of the terms QUITE SOLUBLE, MODERATELY SOLUBLE, AND SLIGHTLY SOLUBLE OR INSOLUBLE. No substance is absolutely insoluble, although for all practical purposes many sub-stances appear to be so. The relative concentrations of solutions may be expressed by the term DILUTE (containing a small proportion of solute) and CONCENTRATED (containing a large proportion of solute). Chemists often work with unsaturated solutions of known concentrations.
Solutions of known concentration are called STANDARD SOLUTIONS. The concentration of solutions may be expressed in a number of ways. It is important that the methods of expressing concentrations of solutions be thoroughly mastered.
7.11 CONCENTRATION EXPRESSED IN PHYSICAL UNITS
One method of expressing concentration in physical units involves the weight of solute in a given weight of solvent: 1 gram of NaCl in 100 grams of water. A second system expresses concentration by percentage composition by weight: A 10 percent NaCl solution by weight contains 10 grams of NaCl in 100 grams of solution (90 grams of water).
EXAMPLE: Calculate the weight of NaCl solution (10% NaCl by weight) that will contain 50 grams of NaCl. If 100 grams of solution contains 10 grams of NaCl, then
100 g. of sol./X = 10 g. of NaCl/50 g. of NaCl
X = (100 g. of sol.)(50 g. of NaCl)/(10 g. of NaCl)
X = 500 grams of solution
Thus, 500 grams of 10 percent sodium chloride solution will contain 50 grams of NaCl (450 grams of water).
In order to calculate the weight of solute in a given volume of solution from the percentage composition by weight, it is necessary to know the specific gravity (or density) of the solution.
EXAMPLE: Calculate the weight of hydrogen chloride (HCl) in 100 ml. of concentrated hydrochloric acid (HCl) of specific gravity 1.19 and containing 37.23 percent HCl by weight. We know from the specific gravity that one ml. of acid solution weighs 1.19 grams, therefore, 100 ml. of the solution will weigh
100 ml X 1.19 g/ml = 119 grams
Because the solution is 37.23 percent HCl by weight, 119 grams of the solution is
119 grams X 0.3723 = 44.3 grams of HCl.
7.12 MOLAR SOLUTIONS
It is frequently desirable to express concentration in terms of gram-formula weights, instead of grams, of solute. The MOLARITY OF A SOLUTION IS THE NUMBER OF MOLES OF SOLUTE PER LITER OF SOLUTION. A solution containing one gram-formula weight, or mole, of the solute in one liter of solution is a ONE-MOLAR SOLUTION. Note that a liter of solution rather than a liter of solvent is specified in this definition. Because gram-formula weights of different molecular substances contain the same number of molecules, it follows that equal volumes of one-molar solutions will contain the same number of molecules of the solute. If a given solution contains 1 mole of solute per liter of solution, then we can determine the number of moles of solute in 1 ml, 20 ml, 100 ml, 2000 ml, or any other volume. Molar concentration, sometimes referred to as MOLARITY and symbolized by M, may be expressed as
M = moles of solute/liters of solution
EXAMPLE: Calculate the molarity of a solution, 2.0 liters of which contain 2.6 moles of solute.
M = moles of solute/liters of solution
M = 2.6 moles/2.0 liters
M = 1.3 M
EXAMPLE: Calculate the molarity of a concentrated sulfuric acid solution of specific gravity 1.84 and containing 98% H2SO4 by weight. We know from the specific gravity that 1 ml. of the acid solution weighs 1.84 grams, therefore 1 liter (1000 ml) of the acid will weigh
1000 ml X 1.84 g/ml = 1840 grams
Because the solution is 98 percent H2SO4 by weight, 1840 grams of the solution contains
1840 grams X 0.980 = 1800 grams of H2SO4
The gram-formula weight of H2SO4 is 98, therefore, 1800 grams of solution contain:
Moles of H2SO4 = 1800 grams/98 g/mole = 18.4 moles
Since the concentrated sulfuric acid contains 18.4 moles of H2SO4 in 1 liter of solution, its concentration is 18.4 M.
In preparing a 1M solution of sodium hydroxide, 40.0 grams (1 mole) of pure sodium hydroxide is weighed out accurately and dissolved in sufficient water to form one liter of solution. A 1M solution of hydrochloric acid contains 36.5 grams of the acid per liter. A 2M solution of sodium hydroxide contains 80 grams (2 moles) of NaOH per liter, and a 0.1M solution contains 4.0 grams of NaOH per liter. Concentrations of substances such as ordinary salt, which do not exist as molecules in solution, are frequently expressed in terms of FORMALITY, defined as THE NUMBER OF FORMULA MASSES OF SOLUTE PER LITER OF SOLUTION. FORMALITY or FORMAL CONCENTRATION is symbolized by F. For all practical purposes MOLARITY and FORMALITY are the same.
7.13 NORMAL SOLUTIONS
Another widely used quantitative method expressing concentration of solutions is NORMALITY. A 1-NORMAL (1N) SOLUTION CONTAINS ONE GRAM-EQUIVALENT WEIGHT OF SOLUTE PER LITER OF SOLUTION.
For the purpose of this discussion, we may define the GRAM-EQUIVALENT WEIGHT OF A SUBSTANCE AS THE WEIGHT OF A MOLE OF THE SUBSTANCE DIVIDED BY THE TOTAL POSITIVE VALENCE OF THE COMPOUND. One mole of NaCl is 58.5 grams; its total positive valence is 1. Therefore, its equivalent weight is also 58.5 grams. One mole of calcium sulfate (CaSO4) is 136 grams; its total positive valence is 2. Therefore, its equivalent weight is one-half (68 grams) its formula weight. One mole of bismuth hydroxide (Bi(OH)3) is 396 grams; its total positive valence is 3. Therefore, its equivalent weight is 132 grams. One mole of aluminum sulfate (Al2(SO4)3) is 342 grams; its total positive valence is 6. Therefore, it has an equivalent weight of 57 grams.
It should be evident that a 1M solution of hydrochloric acid (HCl) is also 1N because a gram-equivalent weight of HCl is equal to one mole of it. However, a 1M solution of sulfuric acid (H2SO4) is 2N because the gram-equivalent weight (49 grams) is one-half its gram-formula weight (98 grams).
7.14 MOLAL SOLUTIONS
THE MOLALITY OF A SOLUTION IS THE NUMBER OF MOLES OF SOLUTE IN 1000 GRAMS OF SOLVENT. A solution which contains one mole of solute in 1000 grams of solvent is called a one-molal solution. This is another method of expressing concentration and differs from the molar method in that the final volume of the solution is usually greater than 1 liter.
7.15 RAOULT'S LAW
The boiling point of a liquid is the temperature at which the vapor pressure of the liquid is equal to the pressure upon its surface. Because the addition of a solute lowers the vapor pressure of a liquid, a higher temperature is required to bring the vapor pressure of the liquid in an open vessel up to the atmospheric pressure and make the solution boil. According to the French chemist Francis Raoult THE LOWERING OF THE VAPOR PRESSURE OF A SOLVENT IS DIRECTLY PROPORTIONAL TO THE NUMBER OF MOLES OF THE SOLUTE WHICH IS DISSOLVED IN A DEFINITE WEIGHT OF THE SOLVENT.
It follows, then, that the elevation of the boiling point of the solvent is also proportional to the weight of the solute which is dissolved in a definite weight of solvent. For solutes which are nonelectrolytes (substances which do not give ions in solutions) and either nonvolatile or with a very low vapor pressure, the elevation of the boiling point of the solvent is the same when solutions of equal molecular concentrations are considered. For example, one mole of sucrose and one mole of glucose, each dissolved in 1000 grams of water, form solutions which have the same boiling points, 100.512oC at 760 Torrs. The elevation of the boiling point of the water is
100.512o minus 100.000o equals 0.512o
It is clear from this data that two moles of solute in 1000 grams of water give a solution which boils at 100o + (2 X 0.512o) = 101.024o. It should be emphasized that the extent to which the vapor pressure of a solvent is lowered and the boiling point is elevated depends upon the number of solute particles present in a given amount of solvent and not upon the mass or size of the particles. Properties of solutions which depend upon the number and not the kind of particles concerned are spoken of as COLLIGATIVE properties. It is not surprising to find that a mole of sodium chloride, which consists of two ions (Na+, Cl-), causes nearly twice as great a rise in boiling point as does a mole of a non-ionic (nonelectrolyte) substance. One mole of sugar contains 6.023 X 1023 particles (as molecules), whereas one mole of sodium chloride contains 2 X 6.023 X 1023 particles (ions). Similarly, calcium chloride (CaCl2), which consists of three ions, causes nearly three times as great a rise in boiling point as does sugar.
It is a common observation that solutions freeze at lower temperatures than do pure liquids. We use aqueous solutions of various anti-freezes such as alcohol and ethylene glycol (1,2-ethanediol) in place of pure water in automobile radiators because such solutions freeze at lower temperatures. Sea water, with its large salt content, freezes at a lower temperature than fresh water. The depression of the freezing point of a solvent by an added solute is a reflection of the vapor pressure lowering caused by the solute.
It has been found that one gram-molecular weight of such non-electrolytes as sucrose, glycerin, and alcohol, when dissolved in 1000 grams of water gives solutions which freeze at -1.86oC. A gram-formula weight of sodium chloride in 1000 grams of water will show nearly twice the freezing point depression characteristic of molecular compounds. Each ion individually produces about the same effect as a molecule upon the freezing point of a solution.
It is evident that the gram-molecular weight of any nonelectrolyte is that weight which, when dissolved in 1000 grams of water, lowers the freezing point 1.86oC. Molecular weights of nonelectrolytes are often determined by observing the effect that they have upon the freezing point or boiling point of a solvent.
EXAMPLE: 5 grams of a nonelectrolyte dissolved in 100 grams of water lowers the freezing point of the water 0.31oC. We know that the molecular weight of this substance is that weight which, when dissolved in 1000 grams of water, would lower the freezing point of water 1.86oC. Therefore, we must calculate the weight of the substance that would lower the freezing point of 1000 g of water 0.31oC.
X/1000 g. of water = 5 g. of solute/100 g. of water
X = (5 g. of solute)(1000 g. of water)/(100 g of water)
X = 50.0 grams
It is necessary to calculate the weight of substance required to lower the freezing point of 1000 grams of water 1.86oC; this value will be the gram-molecular weight of the substance.
X/1.86oC = 50.0 grams/ 0.31oC
X = (50.0 g)(1.86oC)/(0.31oC)
X = 300 grams
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