Gases

Characteristics of Gases Uniformly fill any container Easily compressed Mix completely with any other gases Exert pressure on their surroundings

Pressure Created by collision of particles with each other and objects. So, how do we measure gas pressure?

Barometer Measures atmospheric pressure Invented by Toricelli in 1643

Elevation and atmospheric pressure are INVERSELY proportional The higher the elevation, the lower the pressure Why? Less air pushing down

Manometer Device used for measuring the pressure of a gas in a container.

Equivalent Units of Pressure 760 mm Hg (millimeters Mercury) 760 Torr 1 atm (atmosphere) 101.3 kPa (kilopascals) 14.69 psi (pounds/square inch)

SI unit is the Pascal 1 atm = 101, 325 Pa Too small to be useful in chemistry

Pressure Conversions Example The pressure of air in a tire is measured to be 28 psi. Represent this pressure in Atmospheres torr pascals.

Show your work: 28 psi 1 atm = 14.69 psi 28 psi 760 torr = 28 psi 101, 325 Pa =

Answers: a) 1.9 atm b) 1.5 x 103 torr c) 1.9 x 105 Pa

Kinetic Molecular Theory The Kinetic Molecular Theory explains gas behavior

Kinetic Molecular Theory Gas particles do not attract or repel each other (no I.M. forces). Gas particles are much smaller than the space between them. Gas particles are in constant, random motion. Collisions between gas particles are elastic.

Ideal gases don’t really exist Real gases behave most ideally at high temperatures and low pressures

TEMPERATURE Measures the Average Kinetic Energy of a gas. Temperature and Average Kinetic Energy are directly proportional. At the same temperature, all gases have the same average kinetic energy.

All gas temperatures are calculated using Kelvin °C + 273 = K

Absolute Zero Temperature at which all molecular motion ceases. Occurs at 0 K or -273 °C

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Gas Laws

Boyle’s Law At a constant temperature, the volume of a gas is inversely related to its pressure

P1V1 = P2V2

Example A sample of helium gas is compressed from 4.0 L to 250 mL at a constant temperature. If the original pressure of the gas is 210 kPa, what is the final pressure of the gas?

Show your work: P1V 1 = P2V2 (210 kPa)(4.0 L) = (.250 L)(x) 3360 3.4 x 103 or 3400 kPa Think about it: The pressure ↓ So, the volume should ↑

Charles’ Law At a constant pressure, the volume of a gas is directly proportional to the temperature V1 = V2 T1 T2

Plot of Volume vs Temperature is linear

Example At a pressure of 658 mm Hg, what is the volume of the air in a balloon that occupies 0.620 L at 25.0 °C if the temperature is lowered to 0.00°C?

Show your work: V1 = V2 T1 = T2 .620 L = x 298 K 273 K .568 L

Gay-Lussac’s Law At a constant volume, the pressure of a gas is directly proportional to the temperature (K) P1 = P2 T1 T2

Example The pressure in an automobile tire is 1.88 atm at 25.0 °C. What will the pressure be if the temperature increases to 37.0°C?

Show your work: P1 = P2 T1 T2 1.88 atm = x 298 K 310. K 1.96 atm

Avogadro’s Law If temperature and pressure are constant, the volume of a gas is directly proportional to the number of moles (n) V1 = V2 n1 n2

Example A 12.2 L sample containing 0.50 mole of oxygen gas, O2, at a pressure of 1.0 atm is converted to ozone, O3, at the same temperature and pressure. What is the volume of ozone produced?

Show your work: V1 = V2 3O2 → 2O3 n1 n2 .50 mol O2 2 mol O3 = .33 mol O3 3 mol O2 12.2 L = x .50 mol O2 .33 mol O3 8.1 L

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The relationship between the volume, pressure, and temperature of a gas can be mathematically determined.

Combined Gas Law P1V1 = P2V2 n1T1 n2T2

STP Standard Temperature and Pressure 0 °C and 1 atm

Gas Law Calculations at STP Example A sample of gas has a volume of 2050 mL at 0.95 atm and 36°C. What will be the volume of the gas at STP?

Show your work: P1V1 = P2V2 T1 T2 (.95 atm)(2.05 L) = (1 atm) (x) 309 K 273 K 1.7 L

Ideal Gas Law Ideal gases follow all gas laws under all conditions of temperature and pressure.

PV = nRT Where P = pressure V = volume (Liters) n = number of moles R = ideal gas constant T = temperature (Kelvin)

Universal Gas Constant R = 0.08206 L ∙atm mol·K

Example Calculate the number of moles of gas contained in a 3.0 L vessel at 33°C and a pressure of 1.50 atm.

Show your work: PV = nRT (1.5 atm)(3.0 L) = (n)(.08206 L∙atm/mol∙K)(306 K) n = .18 mol

Example Determine the Celsius temperature of 2.49 mol of gas contained in a 0.750 L vessel at a pressure of 143 kPa.

Show your work: 1) Convert pressure to atm 143 kPa 1 atm = 1.41 atm 101.3 kPa 2) Solve for Temp (K) using PV = nRT (1.41 atm)(.750 L) = (2.49 mol)(.08206)(x) x = 5.18 K 3) Convert from K to oC 5.18 -273 = -268 oC

Molar Mass of a Gas PV = nRT therefore n = PV RT n = m (given mass) M (Molar Mass)

Example Calculate the grams of N2 present in a 0.600 L sample kept at 765 mmHg and a temperature of 22.0 °C.

Show your work: m = PV M RT = x (1.01 atm)(.600 L N2) 28.0 g N2 (.08206)(295 K) 0.701 g N2

Gas Density PV = nRT and d = m therefore: V Molar Mass (M) = dRT P

Example What is the density of NO2 at 681 Torr and 23.0 °C?

Show your work: M = dRT P 46.0 = (x)(.08206)(296) .896 d = 1.70 g/L

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Dalton’s Law of Partial Pressure The total pressure of a mixture of gases is equal to the sum of the partial pressures of each component gas.

Ptotal = P1 + P2 + P3…

Example A scuba tank contains a mixture of gases including 0.42 atm N2, 205 torr O2 and 35.5 kPa CO2. What is the total pressure inside the tank, in atmospheres?

Show your work: Ptotal = P1 + P2 + P3 = .42 atm + .27 atm + .35 atm = 1.04 = 1.0 atm

Example What is the partial pressure of He gas in a mixture of He, Ar, and Ne if the total pressure of the mixture is 5.8 atm, and the partial pressure of Ne is 1.2 atm and Ar is 0.9 atm?

Show your work: Ptotal = P1 + P2 + P3 5.8 = x + 1.2 + .9 PNe = 3.7 atm

Collecting a Gas Over Water Total pressure is the pressure of the gas + the vapor pressure of the water.

Subtract the vapor pressure of the water from the total pressure to get the pressure of the gas

Ptotal = Pdry gas + Pwater vapor This is still a partial pressure calculation

Example A sample of oxygen gas was collected over water at 20.0°C and a barometric pressure of 731 mmHg. What is the pressure of the dry gas?

Show your work: Ptotal = Pdry gas + Pwater vapor 731 torr = x + 17.535 torr 713 mm Hg

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Remember Avogadro? Gas Stoichiometry Equal volumes of gases at the same temperature and pressure contain equal numbers of particles

Molar Volume of a Gas 1 mole of any gas at STP = 22.4 L

Remember…. 1 Mole = ___ grams (molar mass) 6.022 x 1023 atoms, mlc, fmu 22.4 liters (gas at STP)

Example What size container, in liters, would be needed to hold 0.0459 moles of N2 gas at STP?

Show your work: .0459 moles N2 22.4 L = 1.03 L 1 mol N2

Example What mass of carbon dioxide gas is in a 2.5 L flask at STP?

Show your work: 2.5 L 1 mol CO2 44.0 g CO2 = 4.9 g CO2 22.4 L 1 mol CO2

Example How many atoms of He are present in a 1.75 L balloon?

Show your work: 1.75 L He 1 mol He 6.022 x 1023 atoms He 22.4 L He 1 mol He 4.70 x 1022 atoms

Example If 25 Liters of butane combusts in an excess amount of air, how many liters of carbon dioxide gas are produced?

Show your work: Write the balanced equation: 2C4H10 + 13O2 → 8CO2 + 10H2O Calculate the volume of CO2 gas produced 25 L C4H10 1 mol C4H10 8 mol CO2 22.4 L CO2 22.4 L C4H10 2 mol C4H10 1 mol CO2 1.0 x 102 L C4H10

Example When ethane combusts, carbon dioxide and water are produced. If 6.50 grams of ethane is reacted with excess oxygen, and the carbon dioxide gas is collected over water at 18.0 °C and 725 Torr, what volume of gas, in mL, can be collected? The vapor pressure of water at 18.0 °C is 15.5 Torr.

Show your work: Write the balanced equation: 2C2H6 + 7O2 → 4CO2 + 6H2O 1) Determine moles of CO2 produced 6.5 g C2H6 1 mol C2H6 4 mol CO2 = .4333 mol CO2 30.0 g C2H6 2 mol C2H6

2) Calculate pressure of dry gas: Ptotal = Pdry gas + PH2O vapor 725 torr = PC2H6 + 15.5 torr PC2H6 = 709.5 torr 709.5/760 = .9335 atm

3) Solve for VCO2 in mL PV = nRT (. 9335)(V) = (. 4333)( 3) Solve for VCO2 in mL PV = nRT (.9335)(V) = (.4333)(.08206)(291) V = 11.1 L x 1000 mL/L = 11, 100 mL CO2

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