Major Concept Area: Electrical Forces and Bonding
Specific Concepts in this Chapter:In this chapter we begin an examination of the phases (physical states) in which a pure substance may exist. For most substances there are three phases -- solid (s), liquid (l), and gas (g). The gas phase is the simplest of the three to deal with theoretically, primarily because the molecules behave completely chaotically and therefore give rise to simply-formulated average properties. The solid phase is also relatively easily dealt with, because it is so highly organized. The liquid phase, intermediate in its degree of order, is the most difficult to model. This chapter deals with the gas phase. A subsequent chapter deals with the solid and liquid phases. We follow the chapter on the liquid phase with chapters on the energetics of conversions among phases, and equilibria between two or more phases. Of interest throughout will be the question, "Why do some substances exist as solids, some as liquids, and still others as gases at room temperature and subjected to 1 atmosphere of pressure?"
Gases and their properties play an ubiquitous and critical role in our daily lives. Life is supported by the oxygen of the air, which reacts with glucose in biochemical combustion. Living systems have evolved complex molecular architecture to absorb oxygen from the air; carry it to the cells; deliver it to the cells; transport it within the cell; and supervise its multistep, controlled reaction with glucose. It is the rapid expansion of gases produced in the explosive combustion of gasoline that performs the work of the internal combustion engine. Expansion and contraction of gases in response to temperature and pressure changes is at the basis of continually changing weather patterns. Clearly an understanding of the properties, behavior, and chemical reactivity of gases is an important foundation for developing an appreciation of complex biological and technological systems. These properties, behaviors, and reactivities are the focus of this chapter. Following a discussion of the ideal gas law, a simple mathematical model for gas behavior, we discuss the Kinetic Molecular Theory of gases, which establishes a link between molecular motion and temperature. We finish the chapter with a look at the historical significance of gas phase chemical reactions in chemistry, and a treatment of double displacement reactions that produce gases as products.
5-1 Macroscopic Properties of Gases. All gases have observable properties in common:The state of a gas is described by the values of 4 macroscopic variables: the volume (V) occupied by the gas; the temperature (T) of the gas; the pressure (P) that the gas exerts on the walls of its container; and the amount of gas in moles (n). The values of these quantities are related by a very simple equation called the ideal gas law. We will discuss this equation after a brief word on pressure.
Pressure. Pressure is defined as force per unit area. We illustrate the concept of pressure with an example.
Gases exert pressure on the walls of their containers. Since a gas uniformly occupies a container, it exerts the same pressure on all the walls. The gases that make up the atmosphere exert pressure on the surface of the earth. This pressure, called the atmospheric pressure, can be measured using a barometer, pictured in Figure 5-1. The left side of the figure shows a beaker or cup containing mercury. A glass tube of length 1 m and cross-sectional area, A, fitted with a stopcock on top, is inserted into the beaker so that the end of the tube is below the level of mercury in the beaker. Initially, the stopcock is open and the levels of mercury inside and outside the glass tube are the same. A vacuum pump is then attached to the top of the glass tube, and the air is pumped out. As this occurs, the mercury level rises in the tube until it reaches a height, h. Despite further pumping, the mercury level rises no higher in the tube. When all air has been pumped out of the tube, the stopcock is closed, and the mercury maintains its position in the tube. This behavior is understood as follows. Initially, before pumping, the atmosphere exerts the same pressure on the surfaces of mercury inside and outside the tube. Since Pout = Pin = atmospheric pressure, the mercury levels inside and outside the tube are the same. As air is pumped out of the tube, its pressure on the mercury inside the tube decreases, and mercury rises in the tube to a height, h, such that the force due to the mass of mercury in the tube just counterbalances the pressure of the atmosphere on the mercury outside the tube. The height h is found to vary from day to day because the pressure of the atmosphere varies with weather conditions. However, its value is always in the neighborhood of 0.76 meters. For this reason, a unit of pressure called the atmosphere (atm) is defined as the pressure that will support a column of mercury 76 cm, or 760 mm, in height.
The pressure exerted by a column of mercury 1 mm in height is called a torr after Evangelista Torricelli, inventor of the barometer. Thus
In the English and SI systems, the units of pressure are respectively the pound per square inch and the pascal (1 Pascal = 1 Newton per square meter, where a Newton is the force required to accelerate a 1 kg body at 1 m/s2). The pressure in Pa exerted by a column of mercury 760 mm in height can be readily calculated and will provide a conversion factor between SI and traditional non-SI units. The force exerted by a mass, m, of mercury is mg, where g is the acceleration due to gravity. This force is distributed over the cross sectional area, A, of the tube. The mercury therefore exerts the pressure, P = mg/A on the surface of mercury at the bottom of the tube. The mass of mercury can be calculated from its density, r, and its volume, which is Ah. Substituting for m in the expression for pressure gives equation 5-1-1:
The pressure exerted by a column of mercury (or any liquid) of height h is independent of the cross sectional area of the column. The diameter of the barometer tube is therefore unimportant. Substituting the density of mercury (13.595 g/cm3), the acceleration constant (g = 9.80665 m/s2), and h = 0.760 m in 5-1-1 gives P = 1.0132 x 105 Nm-2 (1 Nm-2 = 1 Pascal). The following conversion relations are thus obtained:
Although the bar is official, the atmosphere and the torr are still the most commonly used pressure units in chemistry. We will therefore use the atm and the torr.
Note that atmospheric pressure is 14.7/3.1 = 4.7 times greater than the pressure exerted by the feet of the man in Example 1-1. The magnitude of the pressure exerted by the atmosphere is equivalent to having that 150-lb man, holding a 550-lb weight, standing on your stomach.
The pressure of a gas confined in a container cannot be measured with a barometer. For this a variety of devices may be used, the simplest being the manometer. A manometer is a U-shaped glass tube containing mercury or some less toxic fluid. The gas container is attached to one side of the manometer, and the other side is either open to the atmosphere (an open-end manometer) or evacuated (a closed-end manometer). An open-end manometer is shown in Figure 5-2. The difference in the levels of fluid in the two arms of the manometer is a measure of the pressure of gas in the bulb through the relationship, P1 = P2 + P. Here P1 is the pressure exerted by the gas on arm 1 of the manometer, P2 is the pressure exerted on the arm of the manometer not connected to the gas container (arm 2), and P is the height of fluid in arm 2 minus the height in arm 1. P is positive if fluid is higher in arm 2 and negative if it is higher in arm 1. For an open-end manometer, P2 is atmospheric pressure; for a closed-end manometer, P2 is zero. If the manometer fluid is mercury, the pressure is in torr and may be converted to atm using the conversion factor given above. If the manometer contains some other fluid, the height of fluid may be converted to an equivalent height of mercury using the densities of the fluid and mercury.
5-2 The Ideal Gas Law. The ideal gas law is a relationship between the pressure (P), the volume (V), the amount (n), and the temperature (T) of a gas. It is presented in Equation 5-2-1. The ideal gas law is called an equation of state, because it represents all possible states -- combinations of P,V and T -- in which the amount of gas, n, can be found.
In this equation, P is the pressure in atm; V is the volume in L; n is the amount of gas in moles, and T is the Kelvin temperature. R is a proportionality constant, remarkably the same for all gases, which relates the 4 variables. Equation 5-2-1 is of simple form, which belies the effort expended in developing it. Over 200 years elapsed between the first quantitative experiments on gases and the final enunciation of equation 5-2-1. The simple form of the equation hides a remarkable sophistication in understanding. We now examine what the equation says regarding gas behavior.
Volume-Pressure relation. If we rearrange the equation to solve for the volume, the equation states that volume decreases as the pressure exerted on (also by) the gas increases. The inverse relation of pressure and volume is a fact of every day experience. For example, when you compress the air in the chamber of a tire pump, you feel the increase in pressure of the air within. In 1662, Robert Boyle developed the quantitative relationship between pressure and volume that we now know as Boyle's Law, which states that the volume occupied by a fixed amount of gas at a fixed temperature varies inversely with the pressure exerted on the gas. Boyle's Law was the first-discovered component of equation 5-2-1. Note that the ideal gas law predicts that the volume should fall to 0 as pressure gets very large. For real gases this does not happen. At ordinary temperatures, most real gases will liquefy if pressure is made large enough. Once liquefication has occured, volume does not decrease much with increasing pressure. Real gases obey equation 5-2-1 closely only when P is not too large. This is why equation 5-2-1 is called the ideal gas law -- it applies strictly only to an idealized gas, which does not liquefy but instead shrinks to zero volume when pressure is made very large.
Volume-Temperature relation. The ideal gas law states that the volume occupied by an amount of gas, n, varies directly with the absolute temperature of the gas. A particular sample of gas, then, should double in volume if heated from 300 to 600 K. This behavior, too, is quite well known, at least qualitatively, in every day experience, as in the expansion (contraction) of a heated (cooled) balloon.
The relationship between gas volume and Celsius temperature was first established by Jacques Charles in 1800. He clearly established the linear relationship between the two quantities. Similar experiments relating gas pressure and temperature were carried out at about the same time by Gay-Lussac, and similar proportionality was found. In both cases, the relationships obtained were not so simple as the ideal gas law, because the absolute scale of temperature was not then recognized. The relation between volume and Celsius temperature is in equation 5-2-2.
Plots of V versus t(oC) for gas samples containing different amounts of gas give different slopes and different intercepts on the V axis. However, they all give the same intercept on the t axis, -273.16 oC. This suggests that the zero of temperature be shifted 273.16 Celsius degrees to the left. The resulting scale of temperature is, of course, the Kelvin scale. Equation 5-2-2 takes the much simpler form, V = a*T.
A profound implication of equation 5-2-2 is that there exists a temperature at which the volume of gas should become zero. This temperature is called absolute zero. The Kelvin scale is set up so that 0 K corresponds to the temperature at which the volume of an ideal gas sample would become zero. This corresponds to -273.16 on the Celsius scale. Any temperature lower than this value would cause the gas to have negative volume. Since this is physically meaningless, the conclusion is that temperatures lower than absolute zero do not exist. That there is a lower limit on attainable temperature is not obvious from our everyday experience and from the manner in which we normally measure and think about temperature; the conclusion is nonetheless correct.
Relation Between Volume and Amount of Gas. The ideal gas law states that the volume occupied should increase in direct proportion with the amount (moles) of gas, when the gas is kept at the same pressure and temperature throughout. This is an extension of the hypothesis by Amadeo Avogadro in 1811 that equal volumes of different gases contain the same number of molecules. Avogadro made this statement in explanation of many observations about the relative volumes of gaseous elements that react to form compounds. It was in fact this hypothesis that finally allowed correct molecular formulas to be deduced and the atomic mass scale to be put on a firm basis.
The Value of the Gas Constant R. The gas constant R turns out to be an ubiquitous and extremely important quantity in physical science. We begin by obtaining a value for it based on the experimentally-measured volume of 1.0 mole of gas at 1.00 atm pressure and a temperature of 273.16 K. It is found that under these conditions the gas occupies a volume of 22.414 L. Rearranging equation 5-2-1 to solve for R, we can calculate its value:
The numerical value of R depends upon the units in which pressure and volume are expressed. P is commonly expressed in atmospheres or torr (both non-SI) or Pascal (SI), and V is commonly expressed in mL. Values of R in common P-V unit combinations are presented in Table 5-1.
| Pressure Unit | Volume Unit | R |
|---|---|---|
| atm | L | 0.08206 L-atm/K-mole |
| bar | L | 0.08314 L-bar/K-mole |
| torr | mL | 6.237 x 104mL-torr/K-mole |
| Pa | m3 | 8.314 J/K-mole |
From the Pascal-m3 value, we see that R has units of energy/K-mole. It follows that the combined units L-bar, L-atm, and mL-torr are also energy units. We can express R in terms of any desired energy unit by using an appropriate conversion factor (see Appendix C).
In using the ideal gas law, equation 5-2-1, the units of P, V, and R must be self-consistent, and the temperature must be expressed in Kelvins. A few examples of the use of the ideal gas law are now presented.
| Initial | Final |
|---|---|
| T(K) = 273 + 19 = 292 K | T(K) = 273 K |
| P = 730 torr = 730/760 atm = 0.961 atm | P = 1.00 atm |
| V = 326 mL = 0.326 L | V is unknown |
To shortcut this long process we take advantage of the constancy of the amount (moles) of gas. Since n is constant, PV/RT must also be constant, and its initial and final values are the same:
The value has units g/L, and is about 1000 times less than the density of water at the same temperature. Gases are much less dense than liquids, implying that the gas molecules are much further apart than are liquid molecules.
Dalton's Law of Partial Pressure. The ideal gas law can be applied to mixtures of gases as well as to single pure gases. Consider a mixture of two non-reacting gases, A and B, in a container of volume V. According to the ideal gas law, the pressure exerted by the mixture is given by equation 5-2-3.
Here nT, the total moles of gas, is the sum of the moles of A and the moles of B:
Substitute equation 5-2-4 into equation 5-2-3 and expand:
Suppose that we could remove all of the molecules of B from the container. What pressure would A exert in the container alone? This is easily obtained from the ideal gas law to be PA = nART/V. Similarly, PB = nBRT/V. Substituting the expressions for PA and PB into equation 5-2-5 gives equation 5-2-6:
This is Dalton's Law of partial pressures. In words, it says that the total pressure of a mixture of gases (PT) is the sum of the partial pressures of the gases composing the mixture. The partial pressure of gas A is the pressure that nA moles of A would exert if present alone in the container.
Dividing the expression for PA by equation 5-2-5 gives equation 5-2-7:
The ratio of the moles of A to the total moles of all gases in the system is called the mole fraction of A, and is symbolized XA. Thus XA = nA/nT. Substituting this into 5-2-7 and rearranging, we obtain equation 5-2-8:
The partial pressure of A in a mixture of A and other gases is the total pressure multiplied by the mole fraction of A.
We close this section by emphasizing an implicit assumption of the above treatment. Figure 5-4 shows two gases, A and B, in a box. If the box has volume V, what fraction of this volume is occupied by A, and what fraction by B? A frequent answer might be that since half the molecules in the box are A, A occupies half the volume. This is, however, incorrect. If, when we fill the box with gas, we put A in first, the molecules of A will spread out to occupy the whole box. Now add some molecules of B. Since these molecules are "unaware" of the presence of A, they, too, will spread out in the entire volume. Thus both gases occupy the same volume -- the entire volume of the container. VA = VB = V, the box volume. This is implicit in equations 5-2-3 and 5-2-5. Similarly, we assumed that temperature is the same for both gases: TA = TB = T. In contrast, the total moles, nT, is the sum of the moles of A and B; and the total pressure is the sum of the partial pressures. These relationships are summarized in Table 5-2.
Dalton's Law is particularly useful in experimental situations involving the collection of gases over liquids. In such situations, the space above the liquid contains not only molecules of the gas, but also molecules of the vapor form of the liquid, produced by evaporation of the liquid. The vapor exerts a partial pressure that is part of the total pressure exerted by the gas mixture over the liquid. This partial pressure due to vapor that exists above the corresponding liquid phase is the vapor pressure, Pvap, of the liquid. According to Dalton's Law,
To calculate Pgas, we must correct the total pressure for the vapor pressure of the liquid, which we can look up in a table.
5-3 Kinetic Molecular Theory. The ideal gas law was developed from macroscopic observations, with no knowledge of the behavior of a gas at the molecular level. We now attempt to interpret the ideal gas law in terms of a reasonable molecular model (simple physical picture) of gas behavior. What are the individual molecules doing, and why does their behavior manifest itself in the ideal gas law? We now enter the domain of theory -- a mental interpretation of experimental results. The model of gas behavior currently accepted by scientists is the Kinetic Molecular model. The theory of gas behavior built on this model is called the Kinetic Molecular Theory (KMT). This theory is one of the oldest and most resoundingly successful in science.
First, we assume that gases consist of very small molecules. Since a gas occupies the entire volume of its container, and since gases readily diffuse, the molecules must move about in space. Consequently they have kinetic energy -- energy of motion. Since gases are compressible, the molecules must be far apart. Focussing on an individual molecule, it seems reasonable to assume that it is a small particle that moves about at random, occasionally colliding with a wall of the container and with other gas molecules. The molecule sometimes gains and sometimes loses energy in these collisions, so that it frequently changes speed. Sometimes it moves rapidly, sometimes slowly. Thus our picture of the gas is dynamic rather than static. Figure 5-6 is an attempt to portray this simple physical model of the gas phase.
These statements about gas molecules are consistent with the properties of gases listed at the beginning of the chapter. None of them have been proven, but they seem reasonable and constitute the postulates of the Kinetic Molecular Theory:
We now pursue the consequences of these postulates. Postulate 6, the origin of which is not obvious, will be considered later.
Our aim is to develop an expression for pressure. At the molecular level, pressure must result from collisions of gas molecules with the container walls. A molecule hitting the wall exerts a force on it. The collection of all such forces on a unit area of wall during a given time interval constitutes the pressure. We should be able to calculate P from the force exerted by each collision, multiplied by the number of collisions per unit area of wall:
From Newton's second law, force is the rate of change of momentum. Thus
We move the time factor over to the second term to obtain equation 5-3-2.
To obtain the momentum change per collision, envision a molecule moving directly toward a wall with velocity v, as shown in Figure 5-7. Since momentum is conserved in any collision, the change in momentum of the molecule is
The change of momentum of the wall must therefore be 2mv to give a total change of zero. We now have the first term in equation 5-3-2:
We take an intuitive approach to the second term. The number of collisions per unit time per unit area of wall should depend on 1) the number of molecules per unit volume in the container, N/V (the more there are, the more collisions there should be with the walls); and 2) the speed v at which a molecule moves (the faster the movement, the more collisions per unit time that should occur). Equation 5-3-4 is based on these ideas:
If we assume for simplicity that the container is cubical, there are 6 walls over which these collisions must be spread. The collisions with a particular wall are then
(Despite our restrictive assumptions about the shape of the container, equation 5-3-5 turns out to be valid for a container of any shape!) We now multiply the expressions in equations 5-3-3 and 5-3-5 to obtain the pressure:
Rearrangment gives equation 5-3-7.
This is as far as our molecular model takes us.
We are now at the interface between theory and experiment. Experiment (the ideal gas law) relates pressure and volume to temperature:
Theory, equation 5-3-7, relates pressure and volume to the mass and speed of a gas molecule. To bring experiment and theory into correspondence, we must equate the right sides of the preceding two equations. In order for KMT to successfully explain the ideal gas law, it is necessary that
Equation 5-3-8 can be simplified by replacing n with N/No (No is Avogadro's Number); mv2/2 by KE (the kinetic energy of an average gas molecule); and solving for KE. The result is
Hence postulate 6! We refine this equation by making two further realizations. First, since R and No are both constants of nature, so must their ratio be. It is symbolized k, and is called Boltzmann's constant. Its value is 1.381 x 10-23 J/K-particle. Second, we have recognized that the kinetic energy of a gas molecule changes frequently as it undergoes collisions. However, its average speed over time is constant. The refined equation, 5-3-10, is among the most important equations in science:
The average kinetic energy of a gas molecule, no matter what its chemical identity, depends only on the Kelvin temperature. This gives a deep insight into the concept of temperature: it is a measure of the average kinetic energies of the molecules of a substance, hence a measure of their average speed. As T is increased, molecules move faster; as it is lowered, they move slower. The temperature at which molecular motion ceases is absolute zero. Temperatures lower than absolute zero are impossible because a molecule may not have negative kinetic energy.
Equation 5-3-10 is simple and profound. Is there an experiment that can be done to test its validity? There is in fact a simple experiment that verifies equation 5-3-10 in a rearranged form. If we replace the average kinetic energy of a molecule with the expression m(v2)avg/2, where (v2)avg is the average of the square of the speed, and solve the resulting expression for (v2)avg, we obtain equation 5-3-11.
The square root of (v2)avg is called the root mean square speed, and is for our purposes approximately equal to the average molecular speed. Making this equality gives equation 5-3-12.
Multiplying both numerator and denominator of the argument on the right side of this equation by Avogadro's number No gives the useful variant in equation 5-3-13.
The implication of equation 5-3-12 and 5-3-13 is that a heavy gas molecule moves more slowly than a light one, in a quantifiable way. The ratio of the speeds of the light (L) and heavy (H) molecules should be the square root of the inverse ratio of their molar masses:
In 1846, Thomas Graham measured the rates of diffusion of various gases. Diffusion is the process by which gases disperse in space via random molecular motion. The results of Graham's experiments are summarized in equation 5-3-15:
But we have previously seen (Example 5-7) that gas density is proportional to MM. If we make the logical assumption that a gas diffuses at a rate that is directly proportional to the average speed of its molecules, then Graham's Law of Diffusion is in exact agreement with equation 5-3-14.
Please note that in applying equation 5-3-13 in Example 5-12, values of R and MM with appropriate units have been used, so that speed comes out with appropriate units. Use of R in units of, for example, atm-L, produces a speed with absurd units.
The Maxwell-Boltzmann Distribution Law. We have said that in a gas the molecules move randomly, and that the speed of a molecule changes frequently. In the mid 1800's, James Clerk Maxwell in England, and Ludwig Boltzmann in Austria, were concerned with using statistical methods to describe, precisely and mathematically, the distribution of molecular speeds. The result of their efforts is called the Maxwell- Boltzmann Distribution Law. They showed that at a given temperature, the molecular speed distribution follows a curve like that in Figure 5-8. The curve is a plot of the fraction of molecules having speed s, f(s) (we use s for speed, v for velocity), versus the possible values of speed between zero and infinity. The curve has several noticeable features:
We now do two calculations using equation 5-3-16. First, we calculate the most probable speed, smp. This is a good approximation to the average speed, but the average will be somewhat larger because the curve is biased to higher speeds. smp is the speed at which f(s) is maximum. At this maximum, the slope of the plot -- the derivative of f(s) -- is zero:
Dividing by the exponential, we obtain
This is readily solved for smp:
As expected, this is a bit smaller than the root-mean-square speed in equation 5-3-12.
Next we calculate the average KE of a gas molecule by a method of averaging; we multiply each possible kinetic energy by the number of molecules with that kinetic energy, and divide by the total number of molecules. The required mathematical procedure is integration, as shown in equation 5-3-17.
Even if you are not yet able to carry out the integration, you should note that the result is the same as equation 5-3-10, which came from KMT. This is gratifying. It reinforces the validities of both KMT and the M-B Distribution Law.
Finally, we calculate the KE per mole of gas from the average KEmolecule:
The kinetic energy of a mole of gas depends only on temperature. For this reason, kinetic energy of molecules is called thermal energy.
Summary of the Interpretation of the Ideal Gas Law in Terms of Molecular Behavior. The relationship between the macroscopic and microscopic views of gas behavior can be summarized in several statements.
5-4 The Historical Role of Gas Phase Chemical Reactions. The first decade of the 19th century must have been both exhilarating and frustrating for chemists. On the one hand, Dalton's atomic theory (1803) rationalized many known facts about chemical elements, compounds, and reactions. In particular, the theory provided an explanation for the laws of conservation of mass, definite proportions, and multiple proportions, and gave a rational basis for the idea of reproducible combining masses of the elements in compound formation (e.g., the combining masses of oxygen and hydrogen in forming water are in the ratio 7.94 to 1). On the other hand, attempts to develop a scale of atomic masses were thwarted by the ignorance of chemical formulas. Chemists, led by Dalton, assumed that the formula for water was HO, and that water was formed from hydrogen and oxygen by equation 5-4-1:
This was the simplest assumption to make in the absence of definite knowledge of the formulas of elemental hydrogen, elemental oxygen, and water.
In 1809, Joseph Gay-Lussac conducted a series of experiments with gases that ultimately enabled the development of the atomic mass scale. Specifically, for reactions in which gases react to form other gases, he studied the relationships among the volumes of gaseous reactants consumed and the volumes of gaseous products formed. His result is of tremendous importance. Gay-Lussac discovered that, as long as the experiments were conducted at a constant temperature and pressure, the volumes of reactants used and products produced always gave whole-number ratios. One of many reactions that he studied was that between hydrogen and oxygen to form water vapor. He found consistently and reproducibly that for every one volume of oxygen used, two volumes of hydrogen were required, and two volumes of water vapor were produced:
Gay-Lussac was not certain what to make of these results; however, Amadeo Avogadro was. He made the (to him) reasonable proposal that Gay-Lussac's results implied that equal volumes of gases, at the same temperature and pressure, contain equal numbers of molecules. In modern terms, we say that the volume occupied by a gas is proportional to the number of moles of gas present. Operating from this assumption, he concluded and stated that Dalton's view of the hydrogen/oxygen reaction, expressed in 5-4-1, was incorrect, because it was not consistent with the two-to-one-to-two hydrogen/oxygen/water volume ratios that Gay-Lussac observed. He then went on to propose that hydrogen and oxygen occur as diatomic molecules, and that water in fact contains two atoms of hydrogen per atom of oxygen, so that the water formation reaction becomes:
This is the simplest proposal consistent with the combining volumes observed; as we know today, it is entirely correct.
5-5 Gas Production via Double Displacement Reactions. In Chapter 1, we introduced three broad classifications of chemical reactions: electron transfer processes, proton transfer processes, and double displacement processes. We defined a double displacement reaction as one in which the positive and negative portions of the reactant molecules interchange to form products. It is appropriate in this chapter on gases to focus briefly on double displacement reactions that produce a gas as one of the products. An important series of examples of such reactions involves metal carbonate compounds (called carbonate salts) and acids as reactants. The reaction of a metal carbonate with an acid is shown generically in equation 5-5-1.
This reaction does not have a gas as one of its products. However, in a subsequent step, carbonic acid, H2CO3, decomposes to water and carbon dioxide, a gas that escapes in part from the aqueous solution in the form of effervescence:
A specific example of the acid-carbonate reaction is shown in 5-5-3. Here the net reaction, obtained as the sum of 5-5-1 and 5-5-2, is shown.
Acid-carbonate reactions are very important in at least two contexts. First, metal carbonates that have low solubility in water make up a substantial fraction of the earth's crust (limestone is an example). Deposits of carbonate rocks in contact with slightly acidic ground waters undergo reactions 5-5-1 and 5-5-2. In so doing, they serve to maintain the acidity level of the water at a fairly constant level, supporting aquatic plant and animal life. The details of this process will be understandable when we reach the end of Chapter 13. Second, reactions 5-5-1 and 5-5-2 are important in the context of acid rain, which results when nitric acid, HNO3, and sulfuric acid, H2SO4, are produced in the atmosphere from SO2, produced in coal combustion, and NO2, a byproduct of the internal combustion engine. Limestone (primarily calcium carbonate) is widely used in construction, and has been used for centuries as a medium for sculptors. Repeated and prolonged contact of building edifices and priceless works of art with acid rain results in their slow destruction as calcium carbonate reacts with nitric and sulfuric acids according to equations 5-5-1 and 5-5-2. Building edifices can be replaced; works of art cannot. Finally, dietary calcium tablets are made primarily of calcium carbonate. Contact of a stomach tablet with stomach acid (hydrochloric acid) causes the tablet to dissolve via reaction 5-5-4, after which the calcium can be utilized by the body.
Metal sulfites (for example, Na2SO3) react with acids in analogous fashion to form aqueous sulfurous acid, H2SO3. This subsequently decomposes to water and sulfur dioxide:
| Volume | mass, g | Pressure, atm | Temperature, oC |
|---|---|---|---|
| 0.8512 | 0.110 | 0.800 | 25.00 |
| 1.0652 | 0.110 | 0.650 | 30.00 |
| 1.3033 | 0.110 | 0.540 | 35.00 |
| 1.0334 | 0.110 | 0.670 | 30.00 |
| 1.62 | 0.110 | 0.420 | 25.00 |
| 2.26 | 0.204 | 0.570 | 30.00 |
| 5.60 | 0.204 | 0.230 | 30.00 |
| 0.578 | 0.110 | 1.20 | 30.00 |
| 2.47 | 0.110 | 0.280 | 30.00 |
| 1.83 | 0.110 | 0.390 | 40.00 |
| 0.615 | 0.110 | 1.20 | 50.00 |
| 0.539 | 0.110 | 1.20 | 10.00 |
| 0.558 | 0.110 | 1.20 | 20.00 |
| 0.714 | 0.110 | 0.970 | 30.00 |
| 4.73 | 0.316 | 0.420 | 30.00 |
| 8.28 | 0.316 | 0.240 | 30.00 |
| 4.00 | 0.0762 | 0.120 | 30.00 |