Chapter 13 Gas Laws

13-1 A Model to Explain Gas Behavior The Nature of Gases: Physical Properties of gases: Gases have mass: an empty basketball weighs less than a full one. It is easy to compress gas: This is why it is used in air bags and shock absorbers Gases fill their container completely: Explains why nowhere around you there is an absence of air.

Model of gases continued Different gases can move through each other quite rapidly. This is known as diffusion. (Explains smells, the smells diffuse through the air) Gases exert pressure. Tells you why balloons keep their shape The pressure of a gas depends on its temperature. The higher the temperature, the higher the pressure The lower the temp, the lower the pressure

Kinetic Molecular Theory Gas properties are explained by the Kinetic Molecular Model that describes the behavior of the submicroscopic particles that make up a gas.

Kinetic Molecular Theory Assumption: all gas consists of small particles, each which has a mass. the particles must be spread apart by relatively large distances. (explains easy compression) (the volume of the gas particles themselves is assumed to be 0 because it is negligible compared with the total volume in which the gas is contained.) the particles must be in constant, rapid, random motion.

Kinetic Molecular Theory Gases exert pressure because their particles frequently collide with the walls of the container in perfectly elastic collisions. (no energy of motion is lost) The average kinetic energy of gas particles depends only on the temp of the gas. Gas particles have higher kinetic energy at a higher temperature and lower kinetic energy at a lower temperature. Gas particles exert no force on one another. In other words, the attractive forces between gas particles are so weak that the model assumes them to be zero. (This is the reason that gases do not slow down and turn into liquids)

13-2 Measuring Gases In order to describe a gas sample completely and then make predictions about its behavior under changed conditions, it is important to deal with the values of four variables – amount of gas, volume, temperature and pressure.

Variables Amount of Gas (n) n = mass = m(g) molar mass M (g/mole) Volume (V) The volume of the gas is the volume of the container. Unit = L = 1000cm3 Temperature (T) Usually measured in C but needs to be changed to K. K = C + 273

Pressure (P) Why doesn’t a basketball burst (aside from the material of the ball) the atmosphere is putting pressure back on the ball. Atmospheric pressure – air has mass and is attracted to the Earth’s gravity. Calculated in units of force per unit area. SI = force = Newton, SI = pressure = pascal. Another unit is an atmosphere. 1 atm = 101.3 kPa

Pressure Continued Atmospheric pressure varies with altitude. The lower the altitude, the higher the pressure. Weather- when there is low pressure, there is a lot of water vapor in the air. Since water vapor is lighter than nitrogen and oxygen. Mm Hg – a glass tube upside down in mercury. The height of the mercury tells you how much pressure is being exerted on the resovoir of mercury. 1 atm = 760 mmHg.

Manometer Manometer – used to measure the pressure in a closed container. Use a container of gas and a U tube of mercury. If the pressures are equal, the Hg will be = STP 0oC or 273K, 1 atmosphere, or 760mmHg or 101,325pa.

13-3 The Gas Laws Boyle’s Law – The pressure and volume of a sample of gas at constant temperature are inversely proportional to each other or P1V1 = P2V2 Ex. You have volunteered to fill 300 He balloons. You found a store that has a 25-L tank with a pressure of 30.0atm. Each balloon holds 2.5 L of He at a pressure of 1.04atm. Will you have enough He? P1 = 30.0atm V1 = 25 L P2 = 1.04atm Solve for V2 = (30 atm)(25L) = 720 L 1.04L 720/2.5 = 290 balloons

Charles’s Law – At constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute temperature. He determined absolute zero. By graphing data of gas at different temperatures, he extrapolated the line to which no matter would move. This temperature is -273C or 0 degrees K. V1T2 = V2T1 Ex. On a cool morning 10oC, a group of hot air balloonists filled their balloon with air. They filled it ¾ full and turned on the propane to fill it to the max. of 1700m3. At what temp will it be full?

T2 = V2T1 V1 T2 = (1700m3)(283K) 1275m3 T2 = 377K or 104C

Avogadro’s Law: The Amount-Volume Relationship Avogadro’s Law – equal volumes of gases at the same temperature and pressure contain an equal number of particles Important points All gases show the same physical behavior a gas with a larger volume consist of a greater number of particles. V = K3n where n is the number of moles and k3 is another constant. The volume of one mole of a gas is called the molar volume (@ STP)

Dalton’s Law of Partial Pressures States-the sum of the partial pressures of all the components in a gas mixture is equal to the total pressure of the gas mixture. IE all gases press on the walls the same PT = pa + pb + pc + … PT is the total pressure

Example Ex. What is the atmospheric pressure if the partial pressure of N, O, and Ar are 604.5mm Hg, 162.8mm Hg, and 0.5 mm Hg PT = 604.5 mm Hg + 162.8 mm Hg, 0.5 mm Hg = 767.8 mm Hg.

13-4 The Ideal Gas Law This is a summary of the gas laws from the previous section. PV = nRT P= gas pressure V = gas volume n= the number of moles of gas R = a new gas constant T = temperature of a gas

The ideal gas equation describes the physical behavior of an ideal gas in terms of the pressure, volume, temperature, and the number of moles of a gas. Ideal gas – a gas that is described by the kinetic-molecular theory Real Gas – behave like ideal gases except at low temperatures and high pressures.

The gas constant R – 0.0821 atm-L/mol-K. Ex. How many moles of a gas at 100oC does it take to fill a 1.00-L flask o a pressure of 1.50 atm? PV = nRT n= PV RT 1.5atm 1.00L 0.0821atm-L x 373K Mol K N = 0.0490 moles