Ch. 11: Gases Dr. Namphol Sinkaset Chem 152: Introduction to General Chemistry

I. Chapter Outline I.Introduction II.Kinetic-Molecular Theory of Gases III.Pressure IV.Individual Gas Laws V.The Combined Gas Law VI.The Ideal Gas Law VII.Partial Pressures VIII.Gases and Stoichiometry

I. The Unique Gas Phase Physical properties of a gas are nearly independent of its chemical identity! Gas behavior is markedly different than solid or liquid behavior. We look at a theory that explains why gas behavior is universal and then at the origin of equations that allow us to do gas calculations.

II. Kinetic Molecular Theory This simple theory is very successful in explaining the physical behavior of most gases under “normal” conditions. Kinetic molecular theory can be summarized into 4 statements.

II. Kinetic Molecular Theory 1)A gas is a collection of particles in constant, straight line motion. 2)Gas particles do not attract nor repel one another. They collide with each other and the walls of the container. 3)There is a lot of space between gas particles. 4)The average KE is proportional to the kelvin temperature of the gas.

II. Kinetic Molecular Theory

II. Application of KM Theory KM theory predicts properties of gases well. For example: Compressibility. Gases can be compressed because of the amount of space between particles. Assume shape and volume of container. Gas particles are in constant motion and have no interaction with each other.

III. Pressure Pressure is simply a force exerted over a surface area.

III. Origin of Gas Pressure Gas pressure is the result of the cumulative force of many collisions between gas particles and container walls.

III. Pressure Imbalance

III. Atmospheric Pressure P atm is simply the weight of the earth’s atmosphere pulled down by gravity. Barometers are used to monitor daily changes in P atm. Torricelli barometer was invented in 1643.

III. Units of Pressure For historic reasons, we have units such as torr and mm Hg. (Why?) The derived SI unit for pressure is N/m 2, known as the pascal (Pa). Note that 1 atm = 760 mm Hg = 760 torr = kPa. Pounds per square inch, psi, is an everyday unit. 1 atm = 14.7 psi.

III. Sample Problem Perform the pressure unit conversions below.  Convert 575 torr to atm.  Convert 2.17 atm to mm Hg.

IV. Gas Laws A sample of gas can be physically described by its pressure (P), temperature (T), volume (V), and amount of moles (n). If you know any 3 of these variables, you know the 4 th (via calculation). We look at the history of how the ideal gas law was formulated.

IV. Pressure and Volume

IV. Boyle’s Law At constant temperature and constant amount of gas, the volume of a gas and its pressure are inversely proportional.

IV. Boyle’s Law and KM Theory

IV. Volume and Temperature

IV. Absolute Zero The graph shows an extrapolation to zero volume for the gas. Of course, zero volume is impossible, so the corresponding temperature is known as absolute zero. Absolute zero is the coldest possible temperature; 0 K = °C.

IV. Charles’s Law For constant pressure and constant moles of gas, the volume of a gas and its kelvin temperature are directly proportional.

IV. Charles’s Law and KM Theory

V. The Combined Gas Law Boyle’s and Charles’s Laws can be combined into a convenient form. The equation holds only when amount of gas remains constant.

V. Sample Problem What’s the final pressure of a sample of N 2 with a volume of 952 m 3 at 745 torr and 25 °C if it’s heated to 62 °C with a final volume of 1150 m 3 ?

V. Sample Problem A sample of N 2 has a volume of 880 mL and a pressure of 740 torr. What pressure will change the volume to 870 mL at the same temperature?

VI. Combined Gas Law to Ideal Gas Law The combined gas law is actual very close to the ideal gas law. The only quantity missing is the moles of gas. We need one more gas law derive the ideal gas law from the combined gas law.

VI. Volume and Moles

VI. Avogadro’s Law At constant temperature and pressure, the volume of a gas and the amount of moles of gas are directly proportional.

VI. Avogadro’s Law and KM Theory

VI. The Ideal Gas Law The ideal gas law is a combination of the combined gas law and Avogadro’s Law. R = L atm/K mole

VI. Sample Problem What volume, in mL, does a g sample of N 2 occupy at 21 °C and 750 torr?

VI. What Is An Ideal Gas? The ideal gas law works best when gases are acting ideally. To be an ideal gas, (1) the volume of the gas particles must be small relative to space between them and (2) the forces between the gas particles are not significant. Gases behave nonideally at low temperature and high pressure.

VI. Ideal Vs. Nonideal

VII. Mixtures of Gases According to KM theory, each gas in a mixture of gases acts independently of the others. Each individual gas pressure is called a partial pressure. Dalton’s Law of Partial Pressures: the sum of all partial pressures equals the total pressure.  P total = P 1 + P 2 + P 3 + … + P n

VII. Gas Collection Over Water When gas is collected over water, the total pressure is a sum of P gas and P H2O. Dalton’s Law of Partial Pressure is used to calculate the pressure of the gas by itself.  P total = P gas + P H2O Partial pressures of water are tabulated as vapor pressures.

VII. Collecting H 2 Over Water

VII. Water Vapor Pressures

VIII. Gases and Stoichiometry Gases can be either products or reactants in a reaction, so they can be involved in stoichiometry problems. Mole relationships allow gas calculations via the ideal gas equation. Note that at STP (0 °C and 1 atm) 1 mole of gas occupies 22.4 L.

VIII. Sample Problem How many mL of HCl (g) forms at 725 mm Hg and 32.3 °C when kg of NaCl reacts with excess H 2 SO 4 ? H 2 SO 4(aq) + 2NaCl (s)  Na 2 SO 4(aq) + 2HCl (g)

VIII. Sample Problem How many liters of oxygen at STP are needed to form g of water according to the reaction below? 2H 2(g) + O 2(g)  2H 2 O (g)