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## Chapter 5 Gases

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**The nature of gases**Indefinite shape and indefinite volume expand to fill their containers Compressible Fluid – they flow Low density 1/1000 the density of the equivalent liquid or solid Properties of a gas stem from atoms/molecules being far away from each other, great amount of space in between**Kinetic molecular theory**• Kinetic molecular theory explains the gas laws • A gas is a collection of particles (atoms or molecules) in constant motion • A single particle moves in a straight line till it collides with the wall or another particle**3 postulates of KMT**• 1. The size of a particle is negligibly small • Since the space between atoms is very large in comparison to the atoms themselves • 2. The average kinetic energy of a particle is proportional to the temperature in kelvins • Heat/Thermal energy causes movement of the molecules • The higher the temperature, the higher the average kinetic energy • 3. The collision of one particle with another (including container walls) is completely elastic • There is no loss of energy in elastic collisions • Energy can be transferred, but overall there is no net loss**Pressure**• Is equal to force/unit area • P=F/A • Is caused by the collisions of molecules with the walls of a container**Vacuum pumps**• Vacuum pumps – can remove gas from a container, in turn reducing the pressure of that container • Useful for performing air free chemistry (mainly to avoid H2O and O2 in the air)**GAS LAWS**Boyle’s Law Charles’ Law Gay-Lussac’s Law Avogadro’sLaw Ideal Gas Law Daltons Law**Gas law intro**• Each law details the relationship between the following properties of gases • Volume • Pressure • Temperature • Moles • Each law is an equation • You must memorize all of the gas law equations • Solving problems typically involves rearranging the base equation to solve for a specific unknown**BOYLE’S LAW**The relationship between pressure and volume**Boyle’s law**• Robert Boyle – 1627-1691 • Boyle’s Law - The volume of a gas is inversely proportional to the pressure applied to the gas when the temperature and moles are kept constant. • Decrease in volume = Increase in pressure. • Increase in volume = Decrease the pressure**Charles’ law**• Jaques Charles – 1746-1823 • At a fixed pressureand moles, the volume of a gas is directly proportional to the temperature of the gas • As the temperature increases, the volume increases • As the temperature decreases, the volume decreases • TEMPERATURES MUST BE IN KELVIN**Gay-Lussac’s law**The relationship between pressure and temperature**Gay-Lussac’s Law**• Joesph Louis Gay-Lussac – 1778-1850 • At a fixed volumeand moles, the pressure of a gas is directly proportional to the temperature of the gas • As the temperature increases, the pressure also increases • As the temperature decreases, the pressure also decreases • TEMPERATURES MUST BE IN KELVIN**Avogadro’s law**• AmedeoAvaogadro – 1776-1856 • At a fixed pressureand temperature, the moles of a gas is proportional to the volume of the gas • As the molesincreases, volume also increases • As the molesdecreases, volume also decreases • n = moles**Ideal gas law**• Combining all previous relationships into one equation • The ideal gas law is most often written as • R - universal gas constant • R = 0.082 L x atm x K-1 x mol-1 • R = 62.36 L x torr x K-1 x mol-1 • R = 62.36 L x mmHg x K-1 x mol-1 • R = 8.315 L x kPa x K-1 x mol-1 • ALL TEMPERATURES MUST BE IN KELVIN!!**Molar volume and STP**• One mole of any gas occupies exactly 22.4 liters (dm3) at STP. • STP = Standard Temperature and Pressure • Temp = 0ºC = 273K • Pressure = 1atm = 760 mmHg = 760 torr etc. • This is often referred to as the “molar volume” of a gas.**Equal volumes of gases, at the same temperature and**pressure, contain the same number of particles, or molecules • Thus, the number of molecules in a specific volume of gas is independent of the size or mass of the gas molecules • Therefore, the rules applies the same to all gases**Problems**• A cylinder contains 5.00L of gas at 225K. If the temperature is increased to 345K, what will the new volume be? • Rosy has a 5.00L tank of H2 gas. If the pressure inside the tank is 800.0torr and the temperature is 300.0K, how many moles of hydrogen does her tank contain?**Density of a gas**• Density = mass/ volume • What is the mass of a gas? • M = molar mass of gas (grams/mole) • m = mass of gas (grams) • n = moles of gas (moles) • V = volume of gas (Liters) • dgas = density of the gas**Density of a gas**• Make sure to choose the R value that cancels out the correct pressure units • g/L should be the final density units**Dalton’s law**• John Dalton – 1766 - 1844 • Dalton’s Law: The total pressure exerted by a mixture of gases is the sum of the individual pressures of each gas in the mixture • Dalton’s Equation:**Deep-sea diving and partial pressures**• Lungs need to breathe oxygen within a certain partial pressure range 0.21 -1.6 atm • Hypoxia – O2 partial pressure to low, not enough O2 • Oxygen toxicity – O2 partial pressure too high, too much O2**Problems**• The air in this room contains the gases shown below at their respective partial pressures in kPa. What is the pressure your body feels from the air in this room?**Mole fraction (χa)**• In a gas mixture, there is a certain amount of moles of each individual gas • The number of moles of one of those gases divided by the total number of moles from all the gases is the mole fraction • χa = mole fraction • na= moles of a • ntotal = total moles of gas in gas mixture**Problem**• If you had 101.3 moles of air, what is the mole fraction of O2 in that sample?**Stoichiometry with gases**• General stoichiometry • Solution Stoichiometry • Gas Stoichiometry**Molar volume and stoichiometry**• 1 mole of gas at STP = 22.4 L • An easy way to get to moles at STP • In general • Gas reactions still apply the same stoichiometry concepts • The chemical equation relates the reactants and products • To use the chemical equation mole ratios you need to convert reactants/products to moles • This lets you go from moles of one compound to another • The only new concept is that the ideal gas law allows us another way to get to moles**Problem**CO(g) +2H2(g) CH3OH(g) What volume in liters of hydrogen gas, at 355K and a pressure of 738 mmHg, is needed to synthesize 35.7g of methanol (CH3OH)?**Temperature and Molecular Velocities**• Gas particles at a given temperature have the same average kinetic energy • Lighter particles (Hydrogen) have faster average velocities than heavier particles (Argon) to compensate for lack of mass, so the kinetic energy can be equal**Root mean square velocity (urms)**• urms– the root of the average of the squares of the particles velocities • R = universal gas constant = 8.314 (J/(mol*K)) • M = molar mass of gas IN KILOGRAMS • O2 molar mass = 32g/mol = 0.032kg/mol • J = (kg*m2)/(s2), now units of kg match • T = temperature in Kelvin**Diffusion**• Diffusion- describes the mixing of gases. The rate of diffusion is the rate of gas mixing • Lighter gas particles diffuse faster than heavier gas particles**Effusion**• Effusion- describes the passage of gas into an evacuated chamber • Lighter particles effuse faster than heavier particles • Grahams law of effusion – rate of effusion of two gases is related**Real gases**• Ideal gas laws are suited for conditions close to STP and are based off of the 3 kinetic theory postulates • Negligible particle size, average KE related to T, elastic collision • At lower temperatures and higher pressures that Ideal gas laws begin to become less effective**Real gas - Volume**• Particle size has a greater impact at higher pressures (lower volumes) • This causes the actual volume to be greater than predicted with the ideal gas law**Correction for real behavior**• n = moles • b = constant dependant on gas, use chart **Real gas - Pressure**• Lower temperatures allow for intermolecular forces to have a greater effect, decreasing the collisions that occur • This causes the actual pressureto be less than predicted with the ideal gas law**Correction and van der Waals equation**• Combining the pressure and volume corrections give the van der Waals equation