Chapter 7 Gases CHEM 1310 Lecture Notes PDF

Chapter Seven Gases CHEM 1310 1  Objectives At the end of this chapter you should be able to: – Define gas pressure and its units. – Calculate the number of moles, pressure, volume, or temperature in a sample of gas using the quantit...

Chapter Seven Gases CHEM 1310 1  Objectives At the end of this chapter you should be able to: – Define gas pressure and its units. – Calculate the number of moles, pressure, volume, or temperature in a sample of gas using the quantities of the other three. – Calculate the properties of each gas in a mixture of gases. – Predict how the pressure in a fixed-volume container will change after a complete reaction. – Use the kinetic molecular theory to explain the behavior of gases. – Describe the relationship between molecular mass and speed. – Calculate the relative speeds and molecular masses of gases using root mean square speed and Graham's law of effusion. – Discuss the circumstances that lead to deviations from ideal gas behavior. 2  Gas Pressure (7.1) Matter occurs in three states, or phases: solids, liquids, and gases. Gases do not have definite volumes. – They expands to fill the entire volume of its container. 3 Figure 7.1 States of Matter Video  Gas Pressure (7.1) Pressure – Force exerted per unit area Figure 7.2 Simple Barometer 4  Gas Pressure (7.1) Because pressure is one of the important measurable properties of a gas, several different ways and units have been devised to measure it. – Atmospheres (atm) – mm Hg (“millimeters of mercury”) – torr – pascal and kilopascal (Pa and kPa) 5  Gas Pressure (7.1) Standard temperature and pressure (STP) – A specific set of temperature and pressure conditions. For a gas: 6  Boyle’s Law (7.2) Boyle’s Law – The pressure and volume of a gas are inversely proportional at constant temperature. 7 Figure 7.3 Boyle’s Law Video Figure 7.5  Charles’s Law (7.3) Charles’s Law The volume of a gas is proportional to its absolute temperature at constant pressure. 8 Figure 7.7 Charles’s Law Video I Figure 7.8 Charles’s Law Video II  Charles’s Law (7.3) Charles’s work was also used to develop the Kelvin temperature scale. Gas laws problems must ALWAYS be worked in Kelvin. 9  Ideal Gas Law (7.6) Example: A gas has a temperature of 14.0°C, and a volume of 45000 milliliters. If the temperature is raised to 29.0°C and the pressure is not changed, what is the new volume of the gas, in milliliters? 10  The Combined Gas Law (7.4) The combined gas law – A relationship derived from a combination of the other gas laws to demonstrate the relationship between the pressure, volume, and temperature of a sample of gas (when n is constant). 11  The Combined Gas Law (7.4) Example: If you initially have a gas at a pressure of 12 atm, a volume of 23 liters, and a temperature of 200. K, and then you raise the pressure to 14 atm and increase the temperature to 300. K, what is the new volume of the gas? 12  Avogadro’s Law (7.5) Avagadro’s law – The volume of a gas is proportional to the number of molecules or moles of the gas present at fixed pressure and temperature. Figure 7.12 13 Avogadro’s Law Video Figure 7.13  Ideal Gas Law (7.6) Charles’s law, Boyle’s law, and Avagadro’s law were empirical (based on observation). – Put together, they led to the ideal gas law. 14  Ideal Gas Law (7.6) Example: What volume is occupied by a 5.00 g sample of Ne at 256 Torr and 35 oC? 15  Ideal Gas Law (7.6) R has several possible sets of units. It is easiest always to use the same value for gas laws and make sure the units of P, V, n, and T all match. 𝑷𝑽 = 𝒏𝑹𝑻 16  Dalton’s Law of Partial Pressures (7.7) Dalton’s law of partial pressures – The pressure of a mixture of gases is the sum of the partial pressures of the component gases in a mixture. 17  Dalton’s Law of Partial Pressures (7.7) The pressure due to any individual component in a gas mixture is the partial pressure (Pi) of that component. 18  Dalton’s Law of Partial Pressures (7.7) Because of the relationship between moles and pressure, we can calculate partial pressures of individual gases based on the mole fraction of the gas. 19  Dalton’s Law of Partial Pressures (7.7) Example: In a sample containing 15.50 mol of mixed gases, if there are 4.50 mol O2 which account for a partial pressure of 3.10 atm, what is the total pressure of the system? 20  Gases in Chemical Reactions (7.9) Stoichiometry always is about moles. For gases, use the ideal gas law to determine moles of gas present. 21 Figure 7.19  Gases in Chemical Reactions (7.9) Example: A 2.00 g aluminum is combined with 1.5 L O2 at 20°C and 2.25atm. What mass of aluminum oxide can be formed? 4 Al(s) + 3O2(g) à 2 Al2O3(s) 22  Kinetic Molecular Theory of Gases (7.10) Kinetic-molecular theory A model which provides connections between the observed macroscopic properties of gases, the gas law equation, and the behavior of gas molecules on a microscopic scale. Figure 7.20 Gas Motion Video 23  Kinetic Molecular Theory of Gases (7.10) Five postulates of the kinetic molecular theory 24  Kinetic Molecular Theory of Gases (7.10) Explaining gas pressure: 25  Kinetic Molecular Theory of Gases (7.10) Explaining Dalton’s Law: 26  Movement of Gas Particles (7.11) Most probable speed is dependent on temperature and molar mass. 27 Figure 7.22  Movement of Gas Particles (7.11) Most probable speed is dependent on temperature and molar mass. Figure 7.23 28  Movement of Gas Particles (7.11) The root mean square speed, vrms, is the velocity of a particles possessing the average KE in a gas sample of known molar mass. 29  Movement of Gas Particles (7.11) Molecules travel only short distances before colliding with other molecules and changing direction. – Mean free path 30  Movement of Gas Particles (7.11) Diffusion – The process by which gas molecules spread out in response to a concentration gradient – Influenced by root mean square speed 31  Movement of Gas Particles (7.11) Effusion – The process by which a gas escapes from a container into a vacuum through a small hole – Graham’s law of effusion 32  Movement of Gas Particles (7.11) Example: A sample of hydrogen, H2, was found to effuse through a pinhole 5.2 times as rapidly as the same volume of unknown gas (at the same temperature and pressure). What is the molecular weight of the unknown gas? 33