Mark S. Cracolice Edward I. Peters Mark S. Cracolice The University of Montana Chapter 4 Introduction to Gases

4.1 Properties of Gases 1. Gases may be compressed.

4.1 Properties of Gases 2. Gases expand to fill their containers uniformly.

4.1 Properties of Gases 3. All gases have low density.

4.1 Properties of Gases 4. Gases may be mixed.

4.1 Properties of Gases 5. A confined gas exerts constant pressure on the walls of its container uniformly in all directions.

4.2 Ideal Gas Model 1. Gases consist of particles moving at any given instant in straight lines. At room temperature, the speeds of helium atom and carbon dioxide molecule are respectively 1300 m/s and 400 m/s.

4.2 Ideal Gas Model 2. Molecules collide with each other and with the container walls without loss of total kinetic energy. The frequency of collision of oxygen molecule at normal temperature and pressure is 6 billions collisions per second

4.2 Ideal Gas Model 3. Gas molecules are very widely spaced.

4.2 Ideal Gas Model 4. The actual volume of molecules is negligible compared to the space they occupy.

4.2 Ideal Gas Model 5. Due to the large distances between gas molecules, attractive forces between them are negligible.

4.2 Ideal Gas Model 6. The average kinetic energy of molecules is directly proportional to the absolute temperature. mv 2 /2 = (3/2) kT where k is known as Boltzmann’s constant

4.3 Gas Measurements By definition, pressure is the force exerted on a unit area: Pressure Using symbols,

4.3 Gas Measurements The Mercury Barometer The atmospheric pressure, P a, is equal to the pressure of the liquid mercury in the tube, P Hg (Hg is the symbol for the element mercury).

4.3 Gas Measurements Pressure Units Millimeters of mercury, mm Hg The height of a column of mercury of one milimeter in a barometer. Torr, torr Another name for a millimeter of mercury. Atmosphere, atm 760 mm Hg Approximately equal to atmospheric pressure at sea level.

4.3 Gas Measurements Pascal, Pa (metric system) One newton (a unit of force) per square meter (area) 1 atm = × 10 3 Pa Kilopascal (kPa ≡1000 Pa) Bar (bar ≡ 100 kPa) 1 atm = bar

4.3 Gas Measurements Pressure Units (USCS System) Inch of mercury, in. Hg (barometer-based) The height of a column of mercury of 1 inch in a barometer. Pound per square inch, psi (definition-based) One pound (weight of one pound) per square inch (area).

4.3 Gas Measurements Open-End Manometer Used to measure pressure in the laboratory. P g = P a + P Hg

4.3 Gas Measurements P g = P a – P Hg

4.3 Gas Measurements In pressure-volume-temperature problems, gas temperatures are expressed in Kelvin (absolute temperature scale) T K = T °C + 273

4.4 Charles’s Law Charles’s Law The volume (V) of a fixed quantity of gas at constant pressure is directly proportional to absolute temperature (T): V  T

4.4 Charles’s Law For a fixed quantity of gas at constant pressure, V T V = k × T Divide both sides of the equation by T: k = k =k = = k ==

4.4 Charles’s Law Applying Charles’s Law A fixed quantity of gas in a flexible-walled container is cooled from 44°C to 21°C. If the initial volume of the container is 3.20 L, what is the final volume? =V 1 T 2 = V 2 T 1 V 2 = V 1 × = 3.20 L× = 2.97 L Check: Temperature decreases, which leads to decreased volume. Temperature fraction is less than one. OK.

4.5 Boyle’s Law For a fixed quantity of gas at constant temperature, pressure is inversely proportional to volume:

4.5 Boyle’s Law Multiplying both sides of the equation by V yields: PV = k

4.5 Boyle’s Law PV = k P 1 V 1 = kP 2 V 2 = k P 1 V 1 = k = P 2 V 2 For a fixed quantity of gas at constant temperature, P 1 V 1 = P 2 V 2

4.5 Boyle’s Law Applying Boyle’s Law A fixed quantity of gas in a flexible-walled container is initially at 729 torr and a volume of L. The temperature is kept constant as the volume of the container is reduced to L. What is the resulting pressure at this volume? P 1 V 1 = P 2 V 2 P 2 = P 1 × = 729 torr × = 1.01 × 10 3 torr Check: Volume decreases, which leads to increased pressure. Volume fraction is greater than one. OK.

4.5 Boyle’s Law Applying Boyle’s Law A gas sample occupies 5.18 liters at 776 torr. Find the volume of the gas if the temperature is kept constant and the pressure is changed to 827 torr. V 2 P 1 V 1 = P 2 V 2 = 5.18 Lx 776 torr 827 torr

4.6 The Pressure–Temperature Law or Gay Lussac’s Law The pressure of a gas at constant volume is directly proportional to the absolute temperature As the temperature is raised, the molecules strike the wall more often and with greater force. P = kT

4.6 The Pressure–Temperature Law or Gay Lussac’s Law The gas in a flask exerts a pressure of 0.97 atm at 18 0 C. What will the pressure be if the temperature is raised to 31 0 C ? Volume remains constant. P 2 = P 1 x T 2 / T 1 = 0.97 atm x 304 K / 291 K = 1.01 atm

4.7 The Combined Gas Law Charles’s Law: V T Boyle’s Law: Rearranging Boyle’s Law: Combining the two proportionalities: Inserting a proportionality constant: Rearranging:

4.7 The Combined Gas Law This is the Combined Gas Law: For a fixed quantity of gas, the ratio PV/T is a constant.

The Combined Gas Law Standard Temperature and Pressure (STP) for gases: 25°C and 1 bar To two significant figures, 1.0 bar = 1.0 atm, so STP is also 25°C and 1 atm if measured quantities are limited to two significant figures or less.

The Combined Gas Law Applying the Combined Gas Law What is the STP volume of a sample of argon gas which had an initial volume of 729 mL when at 44°C and 881 mm Hg? Cross multiplying, P 1 V 1 T 2 = P 2 V 2 T 1 Check: Pressure down, volume up, pressure fraction > 1, OK. Temperature down, volume down, temperature fraction < 1, OK.

The Combined Gas Law Applying the Combined Gas Law What is the STP volume of a sample of argon gas which had an initial volume of 3.62 L when at 16°C and bar?

Homework Homework for chapter 4: 19, 21, 31, 37, 41, 51, 56