CHAPTER 11 PROPERTIES OF GASES Gases have an indefinite shape: a gas takes the shape of its container and fills it uniformly. If the shape of the container changes, so does the shape of the gas. Gases can expand: a gas continuously expands and distributes itself throughout a sealed container. This means that the volume of gas increases when we enlarge the volume of container. Gases can compress: the volume of gas in a sealed container decreases when we reduce the volume. If we reduce the volume sufficiently, the gas will eventually liquefy. Gases have low densities: the density of air is about 0.001g/mL (g/l). The density of water, on the other hand, is 1.0g/mL, thus air is about 1000 times less dense than water. Gases mix completely with other gases in the same container: air is a common example of gaseous mixture. During photosynthesis, plants release oxygen gas which mixes with other gases in the atmosphere. ATMOSPHERIC PRESSURE Gas pressure is the result of conversely moving molecules striking the inside surface of their container. The pressure that a gas exerts depends on how often and how hard these molecules strike the walls of the container. If the molecules collide more often, the gas pressure increases. If the molecules collide with more energy, the pressure increases. As temperature increase, the molecules move faster and collide more frequently and with more energy. Atmospheric pressure is the result of air molecules in the environment. The pressure of the atmosphere is about 15 pounds on every square inch of surface. Atmospheric pressure operates in all directions. A barometer is used to measure atmospheric pressure. Standard atmospheric pressure is 1 (atm), which at sea level, Torricelli showed that the height which of mercury measures 29.9 inches. The table below is an expression for the same standard pressure; we can relate one unit to the other: Unit Standard Pressure Atmosphere 1 atm Inches of mercury 29.9 in Hg Centimeters of mercury 76 cm Hg
Millimeters of mercury Torr Pounds per square inch Kilopascal 760 mmhg 760 torr 101 KPa Converting 2550 torr to atm, 2550 torr x 1 atm = 3.36 atm 760 torr Example: Given that the guage pressure of an automobile tire is 34.0 psi, express the pressure in each of the following units: atm, cmhg, torr, and KPa. 34.0psi x 1 atm = 2.31 atm 34.0 psi x 76 cmhg = 175.8 cmhg 34.0 psi x 760 torr = 1757.8 torr 34.0 psi x 101 KPa = 233.6 KPa VARIABLES AFFECTING GAS PRESSURE I. Increase or decrease the volume of the container. When we increase the volume, gas molecules are further apart and collide less frequently, and thus pressure decrease. When decrease the volume however, gas molecules are closer together and collide more frequently, and pressure increases, the pressure is INVERSELY related to volume. (Increase in volume brings about decrease in pressure and vice versa) II. Increase or decrease the temperature of the gas. When we increase the temperature, gas molecules move faster and collide with greater frequency and energy. When we decrease temperature however, the gas molecules move slower and collide less frequently. The pressure is said to be DIRECTLY related to temperature. (Increase in temperature brings about increase in pressure and vice versa) III. Increase or decrease the number of molecules in the container. Avogadro s theory states that equal volumes of gases, at the same temperature and pressure, contain equal number of molecules. When we increase the number of molecules, there are more collisions and pressure increases. When we decrease number of gas molecules, there are fewer collisions and pressure decrease. The pressure is said to be DIRECTLY
related to the number of moles of gas or the number of gas molecules. (Increase in the number of molecules increases the pressure and vice versa) BOYLE S LAW Boyles law states that the volume of a gas is INVERSELY proportional to the pressure when the temperature remains constant. Inversely proportional means two variables have reciprocal relationship, as one increases, the other decreases. Boyle s demonstrated this law using the J-tube experiment with varying pressure to illustrate this law. Vα 1 (temperature constant) P V = volume, P = pressure, α = proportional sign, 1/ = inverse V = K x 1 (cross multiplying) P PV = K P 1 V 1 = K = P 1 V 2 P 1 V 1 = P 2 V 2 Example: In an experiment 5.00L of propane gas is compressed and the pressure increases from 1.00atm to 1.5atm, calculate the final volume. Using, P 1 V 1 = P 2 V 2 P 2 P 2 V 2 = P 2 V 2 P 2 V 2 = 1.00atm x 5.00L 1.5atm CHARLES LAW Charles states that the volume of a gas is DIRECTLY proportional to the Kelvin temperature if pressure remains constant. As the Kelvin temperature increases, the volume also increases. V α T (pressure is constant) V = KT V = K T V 1 = K = V 2 Example: In an experiment, a sample of argon gas at 225K is heated and the volume increases from 3.50L to 12.5L, calculate the final temperature.
Using, V 1 = V 2 T 2 V 1 = T 1 V 2 V 1 V 1 (cross multiplying) T 2 = T 1 V 2 V 1 T 2 = 12.5L x 225K = 803.6K = 804K 3.50L GAY- LUSSAC S LAW Gay- Lussac s law states that the pressure of a gas is DIRECTLY proportional to the Kelvin temperature if the volume remains constant. As the pressure increases, there is increase in temperature. P α T (volume is constant) P = K T T T P = K T P 1 = k = P 2 Example: A copper container has a volume of 555 ml and is filled with air at 25 o C. The container is immersed in dry ice, and the pressure of the gas drops from 761 torr to 495 torr. What is the final temperature of the air in the copper container? T 1 = 25 o C + 273 = 298 K Using, P 1 = P 2 (cross multiplying) T 2 P 1 = T 1 P 2 P 1 P 1 T 2 = T 1 P 2 P 1 T 2 = 495 x 298 761 = 193.8K = 194K (-79 o C) COMBINED GAS LAW These three laws- Boyles, Charles and Gay-Lussac s laws can be combined, considering the fact that we could limit our treatment of gases to two variables. Experiments showed that all these three variables
(temperature, volume and pressure) usually change simultaneously. The resulting expression is known as combined gas law. V 1 P 1 = V 2 P 2 Example: Consider the table below, Condition Pressure Volume Temperature Initial 1.00 atm 10.0L 300K Final P 2 20.0L 600K Using, V 1 P 1 = V 2 P 2 P 2 = V 1 P 1 T 2 V 2 T 1 = 1.00 atm x 10.0L x 600K 20.0L x 300K = 1.00 atm The standard temperature and pressure (STP) for a gas are 0 o C and 1 atm. We also express standard pressure in other units such as 760mmHg, 760 torr or 760mmHg. Example 2: A nitrogen gas sample occupies 50.5mL at -80 o C and 1250 torr. What is the volume at STP? Condition Pressure Volume Temperature Initial 1250 torr 50.5mL -80+273= 193K Final 760 torr V 2 273K Using, V 1 P 1 = V 2 P 2 V 2 = V 1 P 1 T 2 P 2 T 1 = 1250 torr x 50.5 ml x 273K 193K x 760 torr = 117 ml THE VAPOR PRESSURE CONCEPT Vaporization occurs when molecules have enough energy to escape from liquid phase to gaseous phase. This process occurs when the container is opened, but when the container is closed, the molecules are
trapped above the liquid. As the molecules vaporize into gaseous phase, they also turn from gas to liquid phase (condensation) at constant temperature. A kind of pressure is introduced due to this effect, the pressure is known as vapor pressure. The barometer is used to measure vapor pressure. DALTON S LAW (PARTIAL PRESSURE) Dalton s law of partial pressures states that the total pressure of a gaseous mixture is equal to the sum of the individual pressures of each gas. P 1 + P 2 + P 3 = P total The pressure exerted by each gas in the mixture is called partial pressure. We can collect a gas over water to determine the volume by displacement. A wet gas collected over water contains water vapor. P gas + P water vapor = P atmosphere P gas = P atmosphere - P water vapor IDEAL GAS BEHAVIOR KINETIC THEORY OF GASES An ideal gas, is a gas that always behaves in a consistent and predictable manner. Experimentally, a real gas such as oxygen, hydrogen does not behave ideally under all conditions. According to kinetic theory of gases, an ideal gas has the following characteristics: Gases are made up of very tiny molecules, for example, molecules occupy a negligible volume. Gas molecules demonstrate rapid motion, move in straight lines, and travel in random directions. Gas molecules have no attraction for one another, example, they do not stick together after collision. Gas molecules undergo elastic collisions, for example, they do not lose kinetic energy after collision. The average kinetic energy of gas molecules is proportional to the Kelvin temperature that is K.E α T.At the same temperature; all molecules have the same kinetic energy. When you have two different elements in a compound, at the same temperature, they will have same K.E but the one that is lighter moves faster than heavier one.
ABSOLUTE ZERO The temperature at which the pressure and volume of a gas theoretically reaches Zero is referred to as ABSOLUTE ZERO. This is the coldest possible temperature and it corresponds to -273 0 C or 0K. An ideal gas at absolute zero has no kinetic energy and therefore no molecular motion. IDEAL GAS LAW P α nt V P = RnT (cross multiplying) V PV = nrt P = Pressure; n = number of moles; V = Volume; T = Temperature; R = gas constant ( 0.0821 atm.l/mol) This is called ideal gas law. Example: If a sealed container holds 1.10 mol of nitrogen gas at 25 0 C and 3.75 atm, what is the volume in Liter? Using, P = RnT V V = nrt P V = 1.10 x 0.0821 x 298 3.75 = 7.18L