Gas Laws Unit 9 Chapter 11

Kinetic Theory (reviewed) All particles are in constant motion Gases are composed of molecules, atoms, or ions No attractive or repulsive forces exist between gas particles Empty space exists between gas particles Gas particles move rapidly in constant, random motion (straight paths, independently of each other) All collisions between particles are perfectly elastic (KE is transferred during collisions, total KE remains constant)

Gases Gas pressure: result of simultaneous collisions of billions of particles with an object and other particles Increasing number of particles of gas will increase pressure (more particles in same amount of space=more collisions) Gases move from areas of higher pressure to lower pressure (diffusion)

Gases Decreasing volume of a flexible container will increase gas pressure (less space for same amount of particles=more collisions) Raising the temperature (increasing KE) of enclosed gas particles increases gas pressure (particles moving faster=more collisions) Equal volumes of gases at the same temperature and pressure contain EQUAL number of particles (Avogadro’s hypothesis) STP: standard temperature (0 ○C )and pressure (1atm)

Pressure and Force Pressure (P) is defined as the force per unit area on a surface. P = F/A The greater the force on a given area, the greater the pressure. The smaller the area is on which a given force acts, the greater the pressure. The pressure exerted by a gas depends on volume, temperature, and the number of molecules present. The greater the number of collisions of gas molecules, the higher the pressure will be.

Units of pressure The common unit of pressure is millimeters of mercury, symbolized mm Hg. A pressure of 1 mm Hg is also called 1 torr in honor of Torricelli for his invention of the barometer. Pressures can also be measured in units of atmospheres. Because the average atmospheric pressure at sea level at 0°C is 760 mm Hg, one atmosphere of pressure (atm) is defined as being exactly equivalent to 760 mm Hg. In SI, pressure is expressed in pascals. One pascal (Pa) is defined as the pressure exerted by a force of one newton (1 N) acting on an area of one square meter.

Boyle’s Law: Pressure-Volume Relationship Boyle’s Law: the volume of a fixed mass of gas varies inversely with the pressure at constant temperature. P1V1= P2V2 Plotting the values of volume versus pressure for a gas at constant temperature gives a curve like that shown at right.

If you had a 2.0 L bottle filled with air at 760 mm Hg, and you took it into a plane where it increased in volume to 2.4 L before it burst….what was the pressure in the plane?(T is constant)

Charles’s Law: Volume-Temperature Relationship Charles’s law : the volume of a fixed mass of gas at constant pressure varies directly with the Kelvin temperature. Absolute zero, –273.15°C, and is given a value of zero in the Kelvin temperature scale. The relationship between the two temperature scales is K = 273 + °C. Gas volume and Kelvin temperature are directly proportional to each other at constant pressure, as shown at right.

A ball has a volume of 2. 8 L at 20 degrees Celsius A ball has a volume of 2.8 L at 20 degrees Celsius. What is the volume of the ball at 30 degrees Celsius? (P is constant)

Gay-Lussac’s Law: Pressure-Temperature Relationship Gay-Lussac’s : the pressure of a fixed mass of gas at constant volume varies directly with the Kelvin temperature. This law is named after Joseph Gay-Lussac, who discovered it in 1802.

Calculate the final pressure inside a scuba tank after it cools from 1 Calculate the final pressure inside a scuba tank after it cools from 1.00 x 103 ○C to 25.0○C. The initial pressure in the tank is 130.0 atm.

Dalton’s Law of Partial Pressures The pressure of each gas in a mixture is called the partial pressure of that gas. Dalton’s law of partial pressures: total pressure of a gas mixture is the sum of the partial pressures of the component gases. Ptotal = P1 + P2 + P3 … John Dalton, the English chemist who proposed the atomic theory, discovered that the pressure exerted by each gas in a mixture is independent of that exerted by other gases present.

If you have a mixture of gases that contains 0 If you have a mixture of gases that contains 0.78 atm of nitrogen, and 0.21 atm of oxygen, 0.01 atm of carbon dioxide, and other gases, what is the total pressure of the mixture?

Molar Volume of a Gas Avogadro’s law states: equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. According to Avogadro’s law, one mole of any gas will occupy the same volume as one mole of any other gas at the same conditions (regardless of mass) The volume occupied by one mole of gas at STP is known as the standard molar volume of a gas, 22.4L. In 1811, Amedeo Avogadro explained Gay-Lussac’s law of combining volumes of gases without violating Dalton’s idea of indivisible atoms. Avogadro’s law applies to the combining volumes in gas reactions, and helped him to deduce chemical formulas in reactions. Avogadro reasoned that, instead of gases always being in monatomic form when they combine to form products, gas molecules can contain more than one atom. Recall that one mole of a substance contains a number of particles equal to Avogadro’s constant (6.022 × 1023). example: one mole of oxygen, O2, contains 6.022 × 1023 diatomic molecules.

Gas Stoichiometry Coefficients can represent molecules, moles or volume ratios (assuming conditions remain the same). example—reaction of carbon dioxide formation: 2CO(g) + O2(g) → 2CO2(g) 2 molecules 1 molecule 2 molecules 2 mole 1 mole 2 mol 2 volumes 1 volume 2 volumes You can use the volume ratios as conversion factors in gas stoichiometry problems as you would mole ratios: Gay-Lussac’s law of combining volumes of gases and Avogadro’s law can be applied in calculating the stoichiometry of reactions involving gases.

Conversions Kelvin = ○C + 273.15 Convert 252K to ○C Convert -145○C to Kelvin

If a gas at 25. 0○C occupies 3. 60 liters at a pressure of 1 If a gas at 25.0○C occupies 3.60 liters at a pressure of 1.00 atm, what will its volume be at a pressure of 2.50 atm?

What is the new volume of a 400 What is the new volume of a 400.0mL gas sample as the temperature increases from 22.0○C to 30.0○C?

The volume of a gas originally at standard temperature and pressure was recorded as 488.8mL. What volume would the same gas occupy when subjected to a pressure of 100.0atm and a temperature of -245.0○C?

There’s a 50L tank of oxygen that is under 17 atm of pressure at 22 degrees Celsius. How many L does it expand to if it warms up to 27 degrees Celsius and some kid lets it all out of the tank (it is normal pressure outside)?

How many moles of carbon dioxide gas are contained in a 50 How many moles of carbon dioxide gas are contained in a 50.0L cylinder at a pressure of 100.0atm and a temperature of 35.0○C? What is the mass of carbon dioxide in the cylinder?