Properties of Gases Chapter 1 of Atkins and de Paula The Perfect Gas States of gases Gas laws Real Gases Molecular interactions van der Waals equation Principle of corresponding states Kinetic Model of Gases (now in chapter 24!) Prof. Mueller Chemistry 451 - Fall 2003 Lecture 2-1
Phases of Matter Three basic phases of matter: Gas: Liquid: Solid: Prof. Mueller Chemistry 451 - Fall 2003 Lecture 2-2
Perfect Gases We shall consider a hypothetical perfect or ideal gas, which is a form of matter that completely fills any container. A perfect gas is pictured as a collection of molecules or atoms which undergo continuous random motion: 1. 2. 3. Prof. Mueller Chemistry 451 - Fall 2003 Lecture 2-3
States of Gases The physical state of a substance is defined by its physical properties. The state of a perfect pure gas is defined by: Each substance is described by an equation of state, which correlates the variables describing that state. For example, for a perfect gas: Prof. Mueller Chemistry 451 - Fall 2003 Lecture 2-4
Pressure Pressure is the amount of equal force applied (measured in N) to a specific area (measured in m 2 ). Pressure from a gas is the result of countless collisions of rapidly moving molecules with the walls of the container. Units of pressure: Name Symbol Value pascal 1 Pa 1 N m -2 bar 1 bar 10 5 Pa atmosphere 1 atm 101325 Pa torr 1 Torr 101325/760 Pa = 133.32 Pa mm of mercury 1 mm Hg 133.322 Pa pound per sq inch 1 psi 6.894 757 kpa Prof. Mueller Chemistry 451 - Fall 2003 Lecture 2-5
Pressure Exerted by Gases Gases can be stored in two separate containers separated by a movable wall (i.e., piston). The higher pressure gas will move the wall and compress the lower pressure gas, until an equilibrium pressure is established. The piston is said to be in mechanical equilibrium at this point. Pressures of the gases in a mechanical system involving a piston can be controlled via gas entry and release valves, that are set or controlled to let gases in and out at certain pressure thresholds. Prof. Mueller Chemistry 451 - Fall 2003 Lecture 2-6
Measuring Pressure One device used to measure pressure is a barometer (by Torricelli). When the column of mercury is in equilibrium with the atmosphere, the pressure at the base is equal to that from the atmosphere - so the height of the mercury is a measure of the external pressure. A simple pressure measuring device is a manometer, in which a non-volatile viscous fluid is contained in a U-tube The pressure in the apparatus (a) or from atmosphere (b) is directly proportional to the height difference of the two columns, h: Prof. Mueller Chemistry 451 - Fall 2003 Lecture 2-7
Temperature Temperature is a property that describes the flow of energy. Energy will flow between two objects in contact, resulting in change of state of these two objects. If objects A and B are touching, and A has a higher temperature than B, energy flows from A to B until some equilibrium condition is established. Separatory boundaries: Diathermic Adiabatic Prof. Mueller Chemistry 451 - Fall 2003 Lecture 2-8
Thermal Equilibrium Two objects are said to be in thermal equilibrium if no change in state occurs when they are in contact with one another. A: Block of iron B: Block of copper C: Flask of water Zeroth Law of Thermodynamics: If B is a thermometer (glass capillary with Hg), in contact with A the Hg column has a certain length. If B is placed in contact with another object C, one can predict the change of state when A and C are put in contact. Thus, the Hg column is used to measure the temperatures of A and C. Prof. Mueller Chemistry 451 - Fall 2003 Lecture 2-9
The Gas Laws Individual Gases Boyle s Law Charles Law Avogadro s Principle Perfect (Ideal) Gas Equation Mixtures of Gases Dalton s Law Mole Fractions Prof. Mueller Chemistry 451 - Fall 2003 Lecture 2-10
Boyle s Law Robert Boyle, (1627-91), was an experimental philosopher in the early years of the Royal Society, making a very important contribution in developing a description of the ideal gas (also developed ideas about vacuum, atomic nature of matter, etc.). In 1661, he showed that to a very good approximation that for a constant amount of gas at a fixed temperature: The pressure of a sample is inversely proportional to its volume, and the volume of a sample is inversely proportional to pressure. Prof. Mueller Chemistry 451 - Fall 2003 Lecture 2-11
Isotherms: p vs. V Here are some plots depicting Boyle s Law. Each plotted line corresponds to a different temperature, and are known as isotherms, as they depict the other variables of the state function at a constant temperature: Prof. Mueller Chemistry 451 - Fall 2003 Lecture 2-12
Rationalization for a Molecular System Boyle s law strictly only applies to ideal gases at very low pressures, when there are very few molecular collisions and very few interactions between the molecules. At the molecular scale: When the volume is halved, for example, twice as many molecules hit the walls in a given period of time, thus doubling the pressure. In this case, pv = constant. A similar argument holds for all pressure and volume combinations IF the gases are at a low enough pressure so that all particles are non-interacting. THUS, also independent of identity of the gas. Prof. Mueller Chemistry 451 - Fall 2003 Lecture 2-13
Charles (Gay-Lussac s) Law Charles (1746-1823), a French physicist, constructed the first hydrogen balloons, making an ascent to over 3000 meters (1.9 mi) in 1783. His name is chiefly remembered, however, for his discovery of Charles's law, which states that the volume of a fixed quantity of gas at constant pressure is proportional to its temperature. Hence all gases, at the same pressure, expand equally for the same rise in temperature. He communicated his early results to Joseph-Louis Gay-Lussac, who published his own experimental results in 1802, six months after Dalton had also deduced the law. Or, on the thermodynamic temperature scale devised by Kelvin: Prof. Mueller Chemistry 451 - Fall 2003 Lecture 2-14
Effects of Changing Temperature The volume of a gas should extrapolate to zero near -273 o C. Plots of volume and pressure as a function of temperature, at constant pressure and volume, respectively, are shown below: isobars isochors Prof. Mueller Chemistry 451 - Fall 2003 Lecture 2-15
Rationalization for Molecular Systems As the temperature is increased, the average speed of the molecules increases, thereby increasing the number and force of the collisions that the molecules have with the container s walls (again, this only really applies at low temperatures). We will revisit this in the section on the Kinetic Model of Gases. Prof. Mueller Chemistry 451 - Fall 2003 Lecture 2-16
Avogadro s Principle (Not a Law) From http://www.chemheritage.org/educationalservices/chemach/ppt/aa.html Amadeo Avogadro was a native of Turin, where his father, Count Filippo Avogadro, was a lawyer and government leader in the Piedmont. Avogadro succeeded to his father's title, earned degrees in law, and began to practice as an ecclesiastical lawyer. After obtaining his formal degrees, he took private lessons in mathematics and sciences, including chemistry. In 1811 Avogadro hypothesized that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. Thus Avogadro was able to overcome the difficulty that Dalton and others had encountered when Gay-Lussac reported that above 100 o C the volume of water vapor was twice the volume of the oxygen used to form it. According to Avogadro, the molecule of oxygen had split into two atoms in the course of forming water vapor. Avogadro's hypothesis was neglected for half a century after it was first published. Prof. Mueller Chemistry 451 - Fall 2003 Lecture 2-17
Combining the Gas Laws Boyle s Law: Charles Law: Avogadro s Principle: Single Expression: This is the perfect gas equation which becomes very accurate as the pressure decreases. This can be called a limiting law as it increases in validity as p Æ 0. A limiting law is strictly true at a particular limit. A real gas behaves like a perfect gas in the low pressure limit - at this point the gas constant R = 8.31451 J K -1 mol -1 can be determined very accurately. Standard ambient temperature and pressure (SATP) Standard temperature and pressure (STP) Prof. Mueller Chemistry 451 - Fall 2003 Lecture 2-18
Surface of States The perfect gas equation: pv = nrt can be represented as a three-dimensional surface of possible states, meaning that the gas cannot exist in states not on the surface Prof. Mueller Chemistry 451 - Fall 2003 Lecture 2-19
John Dalton John Dalton (1766-1844), an English chemist and physicist, was the first to provide a scientific description of color blindness (1794), a condition from which he suffered and which was long called "Daltonism. Dalton recorded over 200,000 observations of the atmosphere in his notebooks, and studied mixed gases and the expansion of gases under heat. Dalton's Law is still used to describe the law of partial pressures in chemistry. This work led him to his most important theoretical contribution to chemistry, a scientifically grounded atomic theory of matter. He lectured on his discoveries in 1803, and published them at greater length in A New System of Chemical Philosophy in 1808. Prof. Mueller Chemistry 451 - Fall 2003 Lecture 2-20
Mixture of Gases When we have a mixture of two or more gases, what contribution do each of the member gases make to the overall pressure of the system? Dalton s Law: The total pressure exerted by a homogeneous mixture of gases is equal to the sum of the partial pressures of the individual gases. The partial pressure of a gas is the pressure it would exert if all the other gases in the mixture were absent. If the partial pressure of gas A is p A, and the partial pressure of gas B is p B, etc. then the total pressures for gases in the same vessel is: So for each component i there is a pressure p i : Prof. Mueller Chemistry 451 - Fall 2003 Lecture 2-21
Mole Fractions For each component of a gaseous mixture J, the mole fraction, x J, is the amount of J expressed as a fraction of the total number of molecules: It should be obvious that: The partial pressure of gas J in the mixture is formally defined as: Where p is the total pressure. It follows that for both real and perfect gases that: Prof. Mueller Chemistry 451 - Fall 2003 Lecture 2-22
A Two-Component Mixture Prof. Mueller Chemistry 451 - Fall 2003 Lecture 2-23