Gas Laws

Kinetic Molecular Theory Describes the behavior and properties of gases Gases are made of particles in rapid, random motion. Not affected by the force of gravity in a container (do not fall to the bottom) The gas is mostly ______________. Collisions are ___________ (no loss of kinetic energy). Particles ______ intermolecular forces between them

Ideal vs Real Gases Ideal gases follow KMT Real gases come close (especially at high temperatures and low pressures) Small attractions between particles can be found

Properties of Gases No definite ____________________ Spread out to fill the space of their container Can be compressed easily (because of all that empty space) Exert ___________ on its surroundings (created by molecules hitting the surface) Exhibit diffusion and effusion

Diffusion and Effusion Diffusion- mixing of two gases together Effusion- Rate at which gas molecules escape from a container with a small opening

Graham’s Law RateA =  MassB RateB  MassA The rate of effusion and diffusion is inversely proportional to the square root of the molar mass of the molecules. Gases with molecules of lower molar mass have higher velocities and therefore diffuse or effuse faster RateA = rate of diffusion or effusion for gas A RateB = rate of diffusion or effusion for gas B MassA = molar mass of gas A MassB = molar mass of gas B RateA =  MassB RateB  MassA

Using Graham’s Law Rank the following gases in order of increasing particle velocity (slowest first to fastest last): O2, He, CO2, CH4, H2 A certain gas effuses 4 times as fast as oxygen gas. What is the molar mass of the unknown gas?

Using Graham’s Law (cont) A sample of N2 effuses through a hole in 38 seconds. What must be the molecular weight of gas that effuses in 55 seconds under identical conditions?

Pressure Created by gas molecules bouncing off the surface of an object Defined as: Force per unit area (F/A) SI Unit is pascal (Pa) which equals N/m2 Pascal unit is small so often kPa is used instead Other pressure units Atmosphere (atm) mm of Hg (mmHg) and in of Hg (in Hg) Torr bar and millibar (mb) Pounds per square inch (lb/in2 or psi)

Converting Between Pressure Units All of these are equal to each other 101.325 kPa 1 atm 760 mmHg 760 Torr 29.921 in Hg 1.01325 bar 14.696 psi

Pressure Conversions If the pressure inside a container is measured at 1.22 atm, what is the pressure in mm Hg? If a pressure is given as 720 Torr, what is the pressure in kPa?

Atmospheric Pressure Pressure from gas particles in the atmosphere

Measuring Pressure Barometer Device measuring atmospheric pressure Consists of a tube of mercury being placed in bowl of mercury Mercury will flow into the bowl until the pressure from the height of the column equals the atmospheric pressure pressing on the mercury in the bowl The height of the mercury column is measured At sea level, atmospheric pressure is 760 mmHg

Measuring Pressure (cont) Manometer Measures the pressure of other gases Closed-end manometers Mercury rests in a U-shaped tube Without gas- mercury level is equal on both sides With gas- mercury level will rise on the far side Gas pressure is represented by the difference between the two heights Pgas = Ph Greater the difference the greater the pressure

Measuring Pressure (cont) Open-end manometers Mercury rests in a U-shaped tube Without gas or with gas whose pressure is lower than atmospheric- mercury level will rise on side away from open end Pgas = Patm - Ph With gas whose pressure is equal to atmospheric- mercury level is equal on both sides Pgas = Patm With gas whose pressure is higher than atmospheric- mercury level will rise on the far side Pgas = Patm + Ph

Manometer Problems In a closed-ended manometer, the mercury column in the arm is raised to a height of 780 mm above the other side, what is the pressure of the gas in atm? In an open-ended manometer, the mercury column in the atmospheric arm is 28.2 mm lower than the other side. If the atmospheric pressure is 762 mm Hg, what is the pressure of the gas attached to manometer?

Dalton’s Law of Partial Pressures Many gases are actually mixtures of different types of gases (like air) States: The total pressure exerted by a mixture of gases is equal to the sum of the partial pressures exerted by the separate gases. In other words: Ptotal = P1 + P2 + P3 …

Collecting Gases over Water A method of collecting and measuring gases produced as a product of a reaction Relies on water displacement. Gas sample will actually contain gas collected and water vapor Pdry gas = Ptotal – Pwater vapor This is just a rearrangement of Ptotal = Pdry gas + Pwater vapor Water vapor pressure is dependent on the water temperature

Partial Pressure Problems A container holds three gases (oxygen, carbon dioxide, and helium). The partial pressures of the gases are 2.00 atm, 3.00 atm, and 4.00 atm respectfully. What is the total pressure in the container? What is the partial pressure of oxygen in air at 770 Torr and containing 21% of O2? If 60.0 L of nitrogen is collected over water at 40.0°C when the atmospheric pressure is 760.0 mm Hg, what is the partial pressure of the nitrogen? The water vapor pressure at 40.0°C is 55.3 mm Hg.

Ideal Gas Law Gives information about a gas at a single time point PV = nRT P = pressure V = volume n = number of moles of gas R = 0.08206 L atm mol-1 K-1 T = Temperature in Kelvin TemperatureK = Temperature°C + 273.15 Can also be rewritten PV = (m/M)RT n has been replaced with m/M m = mass in grams of gas M = molar mass of gas (grams/mol)

Ideal Gas Law Problems If 25g of oxygen gas is placed in a 2 liter container at a temperature of 292 K, what is the pressure in the container? What is the molar mass of a gas when 3.84g of the gas is placed in a 570mL container at STP?

STP Standard Temperature and Pressure Temperature is 273.15 K Pressure is 1 atm What is the volume of 1 mole of gas at STP?

Calculations at STP What is the mass in kg of 4.55 x 103 L of methane gas (CH4) at STP? If 125 mg of Ar(g) is added to a 505 mL sample of Ar(g) at STP, what volume will the sample occupy when the conditions of STP are restored?

Gas Densities Very low compared to solids and liquids Often given in g/L instead of g/ml D = m/V = (MP)/RT

Gas Density Problems What is the density of oxygen gas at STP? D = (MP)/(RT)

Reactions with Gases Ideal Gas Law can be used to find the number of moles reacted or produced. Stoichiometry can be used to get information about other reactants or products. Conditions for the equations such as temperature and pressure and given in the problem At STP only, conversion factor 1 mol / 22.4 L can be used

Combined Gas Law Gives information about a gas at two time points (P1V1)/(n1T1) = (P2V2)/(n2T2) 1- Values at first time point 2- Values at second time point P and V can be in any units but they must match on both sides n must be in moles T must be in Kelvin

Combined Gas Law Problems In a thermonuclear device, the pressure of 0.050 liters of gas within the bomb casing reaches 4.0 x 106 atm. When the bomb casing is destroyed by the explosion, the gas is released into the atmosphere where it reaches a pressure of 1.00 atm. What is the volume of the gas after the explosion?

Combined Gas Law Problems (cont) The temperature inside my refrigerator is about 4 °C. If I place a balloon in my fridge that initially has a temperature of 22 °C and a volume of 0.5 liters, what will be the volume of the balloon when it is fully cooled by my refrigerator?

Combined Gas Law Problems (cont) A gas that has a volume of 28 liters, a temperature of 45 °C, and an unknown pressure has its volume increased to 34 liters and its temperature decreased to 35 °C. If I measure the pressure after the change to be 2.0 atm, what was the original pressure of the gas?

Combined Gas Law Problems (cont) If I have 2.9 L of gas at a pressure of 5 atm and a temperature of 50 °C, what will be the temperature of the gas if I decrease the volume of the gas to 2.4 L and decrease the pressure to 3 atm?

Boyle’s Law Discovered in 1662 Determines the relationship between pressure and volume of a gas States: For a fixed amount of a gas at a constant temperature, the volume of a gas varies inversely with its pressure Boils down to P1 V1  P2 V2

Charles’s Law Discovered in 1787 Determined the relationship between volume and temperature Temperature must be in Kelvin (K) States: The volume of a fixed amount of gas at a constant pressure is directly proportional to its Kelvin temperature. Boils down to: V1/T1 = V2/T2

Gay-Lussac’s Law Boils down to: Discovered in 1802 Determined the relationship between pressure and temperature Temperature must be in Kelvin States: The pressure and Kelvin temperature of a gas are directly proportional, provided that the volume remains constant. Boils down to: P1/T1 = P2/T2

Avogadro’s Law Proposed in 1811 Determined the relationship between the amount of gas (number of molecules) and the volume States: At a fixed temperature and pressure, the volume of a gas is directly proportional to the amount of gas (that is, to the number of moles of gas, n, or to the number of molecules of gas). Boils down to V1/n1 = V2/n2