Main Ideas For a fixed amount of gas, a change in one variable – pressure, temperature, or volume – affects the other two. The ideal gas law relates the number of particles to pressure, temperature, and volume. When gases react, the coefficients in the balanced chemical equation represent both molar amounts and relative amounts.
The Gas Laws 12.1
The Gas Laws: Objectives State the relationship among pressure, temperature and volume of a constant amount of gas. Apply the gas laws to problems involving the pressure, temperature, and volume of a constant amount of gas.
Pressure UnitsPressure Units: 1 atm = 1 atmosphere 1 atm = 760 Torr (short for Toricelli) 1 atm = 760 mm Hg 1 atm = 101,325 Pa (short for Pascal) 1 atm = 101 kPa (kilopascal)
Boyles LawRobert Boyle (1629-1691), an Irishchemist, described this relationshipbetween pressure and the volume of agas. How are pressure and volume related? As volume goes down, pressure goes up. Inverse relationship Example:
Boyles LawBoyle’s law states that the volume of afixed amount of gas held at a constanttemperature varies inversely with thepressure. Formula: P1V1 = P2V2
Practice Problem #1A diver blows a 0.75 L air bubble 10 munder water. As it rises to the surface,the pressure goes from 2.25 atm to1.03 atm. What will be the volume ofair in the bubble at the surface?1.6 L
Charles LawJacques Charles (1746-1823), a Frenchphysicist, studied the relationshipbetween volume and temperature. How are temperature and volume related? As temperature goes up, volume goes up. Direct relationship Example:
Charles LawCharles’s law states that the volume of a givenamount of gas is directly proportional to itsKelvin temperature at constant pressure. Formula: V1 = V2 Temperature in 2Kelvin T1 T A temperature of 0 K corresponds to 0 ml, and doubling the temperature doubles the volume. Zero on the Kelvin scale is also known as absolute zero. This is the lowest possible theoretical temperature.
Practice Problem #2A helium balloon in a closed caroccupies a volume of 2.32 L at 40.0°C.If the car is parked on a hot day andthe temperature inside rises to75.0°C, what is the new volume of theballoon, assuming the pressureremains constant?2.58 L
Lussac’s LawJoseph Lussac (1778-1850), found that adirect pressure of a fixed amount of gasvaries directly with the Kelvin temperaturewhen the volume remains constant. How are temperature and pressure related? As temperature goes up, pressure goes up. Direct relationship Example:
Lussac’s LawLussac’s Law states that the pressure of afixed amount of gas varies directly with theKelvin temperature when the volumeremains constant. P1 P2 Formula: = T1 T2
Practice Problem #3The pressure of the oxygen gas insidea canister is 5.00 atm at 25.0°C. Thecanister is located at a camp high onMount Everest. If the temperaturethere falls to -10.0°C, what is the newpressure inside the canister?4.41 L
Combined Gas LawThe Combined Gas Law states therelationship amongpressure, temperature, and volume of afixed amount of gas. The relationships arethe same as the other laws but combinedinto one mathematical statement. Formula: P1V1 P2V2 = T1 T2
Practice Problem #4A gas at 110kPa and 30.0°C fills aflexible container with an initial volumeof 2.00 L. If the temperature is raisedto 80.0°C and the pressure increasesto 440 kPa, what is the new volume?0.58 L
The Ideal Gas Law: Objectives Relate number of particles and volume using Avogadro’s principle. Relate the amount of gas present to its pressure, temperature, and volume using the ideal gas law. Compare the properties of real and ideal gases.
Avogadro’s PrincipleAvogadro’s Principle states that equalvolumes of gases at the same temperatureand pressure contain equal numbers ofparticles. The size of the molecules do not matter; therefore the identity of the gas does not matter. Example:
Molar VolumeMolar Volume of a gas is the volume that 1mol occupies at 0.00° C and 1 atmpressure. STP: The conditions of 0.00°C and 1.00 atm are known as standard temperature and pressure. 1 mol of gas at STP = 22.4 L
Practice Problem #5How many moles are in a sample ofgas that has a volume of 3.72 L atSTP?1.66 L
Practice Problem #6The main component of natural gasused for home heating and cooking ismethane (CH4). Calculate the volumethat 2.00 Kg of methane gas willoccupy at STP.2.80x103 L
Ideal Gas LawAvogadro’s principle, Boyle’s law, Charles’slaw and Lussac’s law can all be combinedinto a single mathematical statement thatdescribes the relationship among pressure,volume, temperature and number of molesof a gas.PV = ConstantnRT
Ideal Gas Law Since ideal gases react the same no matter their identity, every gas has the same constant when using the Ideal Gas Law. 0.08206 (L atm)/(mol K)
Practice Problem #7Calculate the number of moles ofammonia gas (NH3) contained in a 3.0L vessel at 3.00 x 102 K with apressure of 1.50 atm.0.18 mol
Real vs. Ideal GasesIdeal gases follow the assumptions of thekinetic molecular theory (KMT).Assumptions:1.An ideal gas is one whose particles do not take up space. Gas molecules do not have volume; their movement creates volume.
Real vs. Ideal GasesIdeal gases follow the assumptions of thekinetic molecular theory (KMT).Assumptions:2.Ideal gases do not experience intermolecular attractive forces. Gas molecules are too far apart to attract or repel each other.
Real vs. Ideal GasesIdeal gases follow the assumptions of thekinetic molecular theory (KMT).Assumptions:3.Ideal gas particles are in constant, random motion and collide with each other and the walls of the container. Collisions of the molecules are elastic and cause pressure.
Real vs. Ideal GasesIn reality, no gas is truly ideal. Most gases behave like ideal gases at a wide range of temperatures and pressures. Under the right conditions, calculations made using the ideal gas law closely approximate experimental measurements.
Real vs. Ideal GasesWhen do real gases not behave as idealgases?1. Low temperatures Gas molecules do not have the kinetic energy they usually do and do not move as fast. Because they are moving slowly, attractive forces can change the way they behave.
Real vs. Ideal GasesWhen do real gases not behave as idealgases?2. High pressures Gas molecules are crowded and their volume becomes significant to the overall volume of the container.
Gas Stoichiometry: Objectives Determine volume ratios for gaseous reactants and products by using coefficients from chemical equations. Apply gas laws to calculate amounts of gaseous reactants and products in a chemical reaction.
Gas StoichiometryStoichiometry of reactions involving gasesoften give pressure, volume and/ortemperature in order to find moles. The “core” process of the stoichiometry remains the same.
Practice Problem #8What volume of oxygen gas is neededfor the complete combustion of 4.00Lof propane gas (C3H8)? Assume thatpressure and temperature remainconstant. 20.0 L O2; because moles and volume are directly related, volume can be used with the mole ratios.
Practice Problem #9Ammonia is synthesized from hydrogenand nitrogen. N2(g) + 3H2(g) 2NH3(g)If 5.00 L of nitrogen reacts completelywith hydrogen at a pressure of 3.00 atmand a temperature of 298 K, how muchammonia, in grams, is produced? 21.0 g NH3
Practice Problem #10What volume of H2O(g) measured at STPis produced by the combustion of 5.73 gof natural gas (CH4) according to thefollowing equation? CH4(g) + 2O2(g) CO2(g)+2H2O(g) 16 L
Practice Problem #11Calcium hydride combines with wateraccording to the equationCaH2(s) + 2H2O(l) 2H2(g) + Ca(OH)2(s)Beginning with 84.0 g of CaH2 and 36.0 gof H2O, what volume of H2 will beproduced at 273 K and a pressure of1609 torr?
Practice Problem #12Ammonia is synthesized from hydrogenand nitrogen. N2(g) + 3H2(g) -> 2NH3(g)You have 15.0g of N2 and 5.0g of H2 atSTP. How many grams of NH3 can beproduced and what is the mass of theexcess reactant?
Accumulating Content 12.4
Accumulating Content: Objectives Apply knowledge and skills from previous units to content learned in this unit.
Accumulating Content PaperWrite a one page paper (single spaced) abouthow chemistry and gases are related.Ideas: Medical: hyperbaric chamber, ozone, anesthetic gases Ecological: greenhouse gases, gas pollution History: Haber, chemical warfare, pneumatic chemists