Chapter 5 Gases

Air Pressure & Shallow Wells Gases Are mostly empty space Occupy containers uniformly and completely The densities of gases are much smaller than those of liquids and solid and highly variable depending on temperature and pressure Because there is a lot of unoccupied space in the structure of a gas, gases do not have a lot of mass in a given volume, the result is they have low density Expand infinitely Diffuse and mix rapidly 2 Lower density Higher density

Gases Pushing gas molecules are constantly in motion as they move and strike a surface, they push on that surface ◦ push = force if we could measure the total amount of force exerted by gas molecules hitting the entire surface at any one instant, we would know the pressure the gas is exerting ◦ pressure = force per unit area 3 Pressure: Unit area Force

Atmospheric Pressure Effects differences in air pressure result in weather and wind patterns the higher up in the atmosphere you climb, the lower the atmospheric pressure is around you ◦ at the surface the atmospheric pressure is 14.7 psi, but at 10,000 ft it is only 10.0 psi rapid changes in atmospheric pressure may cause your ears to “pop” due to an imbalance in pressure on either side of your ear drum 4

The Pressure of a Gas result of the constant movement of the gas molecules and their collisions with the surfaces around them the pressure of a gas depends on several factors ◦ number of gas particles in a given volume ◦ volume of the container ◦ average speed of the gas particles 5

Measuring Air Pressure Barometer Pa (SI unit) torr mm Hg atm bar Units (exact) Conversions 1 torr = 1 mm Hg 1 atm = Pa (exact) 1 atm = 760 mm Hg (exact) 1 bar = 1 x 10 5 Pa 1 atm = 14.7 psi

Gases and Gas Pressure

Boyle’s law  V P 1 (constant n and T) o pressure of a gas is inversely proportional to its volume o constant T and amount of gas o as P increases, V decreases by the same factor Two sets of conditions P 1 x V 1 = P 2 x V 2

Boyles’ Law and Breathing During an inhalation, the lungs expand. the pressure in the lungs decreases. air flows towards the lower pressure in the lungs.

Charles’s Law In Charles’s Law, the Kelvin temperature of a gas is directly related to the volume. P and n are constant. when the temperature of a gas increases, its volume increases. For two conditions, Charles’s law is written V 1 = V 2 (P and n constant) T 1 T 2 Charles’s Law can be used to approximate absolute zero. At a temperature of absolute zero (0K), theoretically an ideal gas has no volume.

Avogadro’s Law V  n (constant T and P) = k n V = n final V final n initial V initial

Gay-Lussac's Law Gives the relationship between pressure and temperature when volume and amount are held constant. ◦ If the temperature of a container is increased, the pressure increases. ◦ If the temperature of a container is decreased, the pressure decreases. Why? Suppose the temperature is increased. This means gas molecules will move faster and they will impact the container walls more often. This means the gas pressure inside the container will increase, since the container has rigid walls (volume stays constant). Gay-Lussac's Law is a direct mathematical relationship. This means there are two connected values and when one goes up, the other also increases.

Examples A cylinder with a movable piston has a volume of 7.25 L at 4.52 atm. What is the volume at 1.21 atm? A gas has a volume of 2.57 L at 0.00°C. What was the temperature at 2.80 L? A mol sample of He has a volume of 4.65 L. How many moles must be added to give 6.48 L? The pressure in an automobile tire is 1.88 atm at 25.0°C. What will be the pressure if the temperature warms up to 37.0°C?

The Gas Laws Ideal Gas: A gas whose behavior follows the gas laws exactly. The physical properties of a gas can be defined by four variables: Ppressure (atm) Ttemperature (calculation must be in Kelvin) Vvolume (L) nnumber of moles The Ideal Gas Law, PV = nRT, - models the behavior of ideal gases. Other gas laws can be derived from the Ideal Gas Law for either one set of conditions or for two sets of conditions (initial and final conditions). To derive gas laws for two sets of conditions, solve the Ideal Gas Law for R PV ---- = R nT R = K mol L atm

Examples A mol sample of argon gas has a volume of 9.00L at a pressure of 875 mmHg. What is the temperature (in o C) of the gas? What volume is occupied by 25.7 g of carbon dioxide gas at 25.0 o C and 371 torr?

The Ideal Gas Law Standard Temperature and Pressure (STP) for Gases P = 1 atm T = 0 °C ( K) since the volume of a gas varies with pressure and temperature, chemists have agreed on a set of conditions to report our measurements so that comparison is easy – we call these standard conditions

Molar Volume solving the ideal gas equation for the volume of 1 mol of gas at STP gives 22.4 L ◦ x molecules of gas we call the volume of 1 mole of gas at STP the molar volume ◦ it is important to recognize that one mole of different gases have different masses, even though they have the same volume 17

Examples What is the volume occupied by 2.75 moles of N 2 gas at STP? Assuming ideal behavior, which of the following gas samples will have the greatest volume at STP? a.1 g H 2 b. 1 g O 2 c. 1 g Ar

Gas Density and Molar Mass 19 The density of a gas is proportional to its molar mass. As the molar mass of a gas increases, so does the density of the gas. Matter often separates according to its density, with less dense matter floating on matter of higher density

Examples Calculate the density of gaseous hydrogen at a pressure of 1.32 atm and a temperature of o C. A sample of gas has a mass of 0.827g. Its volume is 0.270L at a temperature of 88.0 o C and a pressure of 975 mmHg. Find its molar mass

Partial Pressure when gases are mixed together, their molecules behave independent of each other the pressure of a single gas in a mixture of gases is called its partial pressure we can calculate the partial pressure of a gas if the sum of the partial pressures of all the gases in the mixture equals the total pressure ◦ Dalton’s Law of Partial Pressures 21 P T = P 1 + P 2 + P

Mole Fraction 22 the fraction of the total pressure that a single gas contributes is equal to the fraction of the total number of moles that a single gas contributes the ratio of the moles of a single component to the total number of moles in the mixture is called the mole fraction,  the partial pressure of a gas is equal to the mole fraction of that gas times the total pressure

Example What is the mole fraction of N 2, in a mixture of 12.45g of H 2, 60.67g of N 2, and 2.38g of NH 3 ? Find the partial pressure of neon in a mixture with total pressure 3.9 atm, volume 8.7 L, temperature 598 K, and 0.17 moles Xe.

Collecting Gases gases are often collected by having them displace water from a container the problem is that since water evaporates, there is also water vapor in the collected gas the partial pressure of the water vapor, called the vapor pressure, depends only on the temperature 24

Vapor Pressure of Water 25

Examples 1.02 L of O 2 collected over water at 293 K with a total pressure of mmHg. Find mass O moles of H 2 is collected over water in a 10.0 L container at 323 K. Find the total pressure.