Chapter 5 : Gases5.1 – Substances That Exist as GasesElements CompoundsHFHCl *Noble GASESCO He* NONe*Ar*Kr*Xe*Rn* HCNSubstances Found as Gases at 1atm and 25 ⁰CH₂N₂O₂O₃ CO₂F₂ CH₄Cl₂ NH₃NO₂N₂OSO₂H₂S All gases share the following characteristics They assume the volume and shape of their containers They are easily compressed They will mix evenly and completely when put into the same container (regardless of whether ornot a reaction takes place) They have much lower densities that liquids and solids5.2 – Pressure of a Gas Constantly in motion, so there is always a pressure value SI Units Force Force = mass x acceleration Unit is the newton (N) 1 N = 1kg m/s² Pressure Pressure = force/area Unit is the pascal (Pa) 1 Pa = 1 N/m² Atmospheric Pressure Much denser nearer the surface of the Earth Higher density = greater pressure Barometer is the tool used to measure this in mmHg (pressure impacts a tube of mercury, and isread as the height of the mercury in mm) Standard atmospheric pressure – 1 atm 1mmHG = 1torr 1atm = 760mmHg =760torr 1atm = 101.325kPa5.3 – The Gas Laws Pressure-Volume Relationship : Boyle’s Law Pressure is inversely proportional to volume Temperature remains constant P₁V₁=P₂V₂ Temperature-Volume Relationship : Charles’s Law Volume is directly proportional to temperature (in K) Pressure remains constant V₁ = V₂ T₁ T₂ Or if volume is constant P₁ = P₂ T₁ T₂ COMBINED GAS LAW – HELPFUL P₁V₁ = P₂V₂ T₁ T₂ Just eliminate the variable that is held constant Volume-Amount Relationship : Avogadro’s Law At constant pressure and temperature, volume is directly proportional to the number of moles5.4 – Ideal Gas Equation PV=nRT R is a gas constant, 0.08206 L x atm Mol x K Using this, we can assume P₁V₁ = P₂V₂ n₁T₁ n₂T₂- Eliminate any constants Density Essentially a rearrangement of the ideal gas law d = density (g/L) = m/v M = molar mass (g/mol) d = P M RT Molar Mass To find, rearrange the above equation5.5 – Gas Stoichiometry Amount of reactant (grams or volume)» moles of reactant» moles of product» amount of product (grams or volume)5.6 – Dalton’s Law of Partial Pressures Partial pressures – pressures of individual gas components in a mixture Dalton’s Law – total pressure of a mixture of gases is just the sum of the pressure of the individual gases alone Rearrangement of PV=nRT ; P=nRT V Mole fraction Expresses the ratio of number of moles of one component to the number of total moles X₁ - mole fraction n₁ - moles initial n₊ - moles total X₁ = n₁ n₊ If a system contains more than 2 gases, P₁ = X₁P₊ Collecting over water P(total) = P(gas) + P(water)5.7 – Kinetic Molecular Theory Energy = force X distance SI unit – joule (J) Kinetic energy – energy of motion KE = 1/2mu² = CT u² - average speed of all the speeds of all molecules C – proportionality constant Assumptions 1. Gas is composed of molecules that are separated from each other by large distances 2. Gas molecules are constantly moving in random directions and often collide with one another. These are elastic interactions 3. Gas molecules neither attract not repel each other 4. Average kinetic energy is proportional to the temperature Application to gas laws Compressibility – due to the large distances (assumption 1) gases are easily compressed Boyle’s Law – pressure exerted results from molecular collisions, so decreasing volume increasescollision and pressure Charles’s Law – due to assumption 4, raising the temp increases KE, which in turn increases pressure Partial Pressures – total pressure is given by sum of individual pressures since gas molecules are unaffected by other molecules (assumption 3) Root-mean-square speed (rms) U(rms) = √3RT/M R is still a constant, but in this case is 8.314 J/K x mol- Take what you know, R = 0.08206 (L x atm/ mol x K), and do a unit conversion with 1 L X atm = 101.3 J Gas Diffusion Gradual mixing of molecules of one gas with those of another in accordance with their kinetic properties Graham’s Law – rate of diffusion is inversely proportional to molar mass r₁ = √M ₁ (entire 2nd half should be under square root symbol)r₂ M₂ Gas Effusion A gas under pressure escapes from containers using small openings Also uses Graham’s Law5.8 – Deviation from Ideal Behavior Can be seen when pressure is high, or temperature is low Van der Waals equation (P + an² )(V-nb) = nRT V² ^ ^Corrected CorrectedPressure
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