Chemistry AP/IB Dr. Cortes Chapter 10: Gases Chemistry AP/IB Dr. Cortes

Elements that exist as gases at 250C and 1 atmosphere

homonuclear diatomic gases monatomic noble gases

Physical Characteristics of Gases Take on volume and shape of container Most compressible state of matter Flow Form homogeneous mixtures with other gases Example: air N2, O2, Ar, CO2, trace gases (includes H2) Lower densities vs. liquids and solids Exert pressure

Pressure: force exerted by gas molecules striking a given area (Force = mass x acceleration) SI Unit of Pressure: pascal (Pa) Conversion Factors: 1 Pa = 1 N/m2 1 atm = 760 mmHg = 760 torr = 101,325 Pa = 101.325 kPa

Measuring Standard Atmospheric Pressure Barometer: used to measure atmospheric pressure Hg will rise 760 mm up the tube at standard atmospheric pressure Standard Pressure: 1 atm 760 mmHg

Atmospheric Pressure and Altitude 10 miles 0.2 atm 4 miles 0.5 atm Sea Level 1 atm This bottle was closed at ~2,000 m altitude then brought back to sea level; it was crushed by air pressure

Manometers: used to measure gas pressure

Boyle studied the relationship between pressure and volume of a gas As pressure (h) increases – volume decreases

Boyle’s Law: Pressure-Volume Relationship For a fixed amount of gas at constant temperature, the volume of gas is inversely proportional to the pressure If pressure goes up, volume goes down and vice-versa P1 x V1 = P2 x V2

Sample Problem A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. What is the pressure of the gas if the volume is reduced at constant temperature to 154 mL? 4460 mmHg

As temperature increases – volume increases Charles studied the relationship between temperature and volume of a gas As temperature increases – volume increases

Charles’ Law: Temperature-Volume Relationship For a fixed amount of gas at constant pressure, the volume of gas is directly proportional to the Kelvin temperature If temperature goes up, volume goes up and vice-versa V1 V2 T1 T2 =

Kelvin = degrees celsius +273.15 -273 K, or absolute zero, is -546.3 degrees celsius All gases liquify or solidify before reaching absolute 0, so there are no gases that have a volume of 0: hypothetical situation that is never attained

Variation of gas volume with temperature at constant pressure: Charles’ Law V α T Temperature must be in Kelvin V1 V2 T1 T2 = T (K) = T (0C) + 273.15

Sample Problem A sample of carbon monoxide gas occupies 3.20 L at 125 0C. At what temperature will the gas occupy a volume of 1.54 L if the pressure remains constant? 192 K

Gay-Lussac’s Law: Temperature-Pressure Relationship For a fixed amount of gas at constant volume, the pressure of gas is directly proportional to the Kelvin temperature If temperature goes up, pressure goes up and vice-versa P1 P2 T1 T2 =

Combined Gas Law The other laws can be obtained from this law by holding one quantity (pressure, volume, or temp) constant It also enables you to do calculations for situations in which none of the variables are constant!!

Sample Problem The volume of a gas-filled balloon is 30.0L at 40.0 °C and 153 kPa. What volume will the balloon have at standard temperature and pressure? 39.5 L

Avogadro studied the relationship between number of molecules and volume of a gas Avogadro’s Hypothesis: equal volumes of gases (at the same temperature and pressure) contain equal numbers of molecules. At STP, 1 mol = 22.4 L

Avogadro’s Law: Quantity-Volume Relationship At constant temperature and pressure, the number of moles of gas is directly proportional to its volume If number of moles goes up, volume goes up and vice-versa V1 V2 n1 n2 =

The Ideal Gas Law Ideal Gas Law: used to describe the behavior of an “ideal gas” R: ideal gas constant with varying values (depending on required units) Advantage of ideal gas law over combined gas law is it permits you to solve for the of a contained gas

Molar Volume ANSWER: Molar volume of any gas at STP is ! Molar volume: volume occupied by 1 mol of a gas ( ) SI units: To solve for, rearrange ideal gas law: PV = nRT V/n = QUESTION: Find molar volume of a gas at STP (1 atm, and 273.15 K) ANSWER: Molar volume of any gas at STP is !

Gas Densities and Molar Mass Density = m/V Units: g/L Rearranging the ideal-gas equation with M as molar mass (g/mol) we get: PV = nRT or n/V = Multiply both sides by M nM /V = nM /V = (mol)(g/mol) / (L) = g/L = (density!) relates density to the properties of gases

Sample Problem A large natural gas storage tank is kept at 2.20 atm. On a cold day, when the temperature in -15°C, the volume of gas in the tank is 28,500 ft3. What is the volume of the same quantity of gas when the temperature is 31°C?

Sample Problems Cyclopropane is used as a general anesthetic. It has a molar mass of 42.0 g/mol. What is the density of cyclopropane gas at 25°C and 1.02 atm? Calculate the average molar mass of dry air if it has a density of 1.17 g/L at 21°C and 740.0 torr.

Sample Problem A 5.00 L container is filled with nitrogen gas to a pressure of 3.00 atm at 523 K. What is the volume of a container that is used to store the same gas at STP? Tennis balls are filled with air of nitrogen gas to a pressure above atmospheric pressure to increase their bounce. If a tennis ball has a volume of 144 cm3 and contains 0.33 g of nitrogen, what is the pressure inside the ball at 24°C?

Sample Problems What volume of nitrogen gas at 720 torr and at 23°C is required to react with 7.35 L of hydrogen gas at the same temperature and pressure to yield ammonia gas? 4NH3(g) + 5O2(g)  4NO(g) + 6H2O(g) How many liters of NH3(g) at 850°C and 5.00 atm are required to react with 1.00 mol of O2(g) in this reaction?

Dalton’s Law of Partial Pressure At constant volume and temperature, the total pressure exerted by a of the component gases Ptotal = P1 + P2 + P3 +………..

Sample Problem What is the total pressure exerted by a mixture of 2.00g of H2 and 8.00 g of N2 at 273 K in a 10.0 L vessel?

Kinetic Molecular Theory KMT gives us an understanding of gas pressure at the molecular level: Pressure results from the on the walls of container As temperature increases, average … …creating more chances for collisions with walls of container, so

Assumptions of Kinetic Molecular Theory Gases consist of a large number of molecules in (n is high) Volume of individual molecules is compared to volume of (V is high) forces (forces between gas molecules) are Energy can be transferred between molecules, but average KE is (at constant temperature) Average KE of molecules is proportional to At any given temperature, the molecules of any gas have the

Root-Mean-Squared Speed Root-mean-square speed (rms): the sq root of the avg of the squared speeds of gas molecules in a sample Symbol: SI unit: The higher the temp, the The lower the molar mass, M, the

The higher the temp, the higher the rms…

The lower the molar mass the higher the rms…

Graham’s Law of Effusion Effusion: the escape of a gas through A balloon will deflate over time due to Graham’s Law of Effusion: the rate of effusion of a gas (r) is inversely proportional to the square root of the gas’s molar mass

Diffusion and Mean Free Path Diffusion: is the Diffusion is faster for light gas molecules because

Behavior of Real Gases Real gases deviate from ideal gases! Especially at: Low High Small container Because… Gas molecules have “real” volume and take up space Gas molecules interact with one another We need to correct Ideal Gas Law for volume and intermolecular attractions…

The van der Waals Equation for Real Gases a and b are empirically-determined constants for each gas Corrects for Corrects for

Sample Problems What is the pressure exerted by one mole of argon at a volume of 2.00 L and at 300 K when it acts as an ideal gas and as a non-ideal gas? a = 1.34 L2-atm/mol2 b = 0.0322 L/mol Consider a sample of 1.00 mole of CO2 confined to a volume of 3.00 L at 0.0 °C. Calculate the pressure of gas when it acts as an ideal gas and a non-ideal gas? a = 3.59 L2-atm/mol2 b = 0.0427 L/mol