Chemistry Notes Chapter 5 Gases and the Kinetic Molecular Theory http faculty sdmiramar edu nsinkaset studyguides Chap5SG pdf Gases are highly compressible thermally expandable have low viscosity allows to leak easily Gas density grams per liter Very low density Leads to miscibility gases mix in any proportion forming homogeneous mixtures Pressure Force Area Barometer measuring height fr mercury to top pressure exerted on outside norm atmospheric pressure 760 mmHg Torr or 30 in of Hg 1 mmHg 1 Torr Manometer measures in lab close ended mercury filled U shape tube Vacuum created on the closed end If flask not closed end under vacuum mercury levels Pressure measured by Delta H difference of height between two sides of the U shaped tube Open ended Mercury levels equal on each side atmospheric pressure pressure of gas Column on the gas side higher means gas pressure P atm Gas pressure P atm height of column Height of column higher on the open tube side P gas P atm P gar P atm height difference of column Units of Pressure SI unit Pa Pascal 1 Newton Meter 2 1 atm 1 01325 x 10 5 Pascals Kilopascals kPa 101 325 1 torr 1 760 atm 101 325 760 kPa 1 atm 760 mmHg 760 Torr 101 kPa Gas sample described by pressure P in atm Volume V in Liters Temperature T in Kelvin and of moles n Boyle s V and P Charles s V and T and Avogadro s laws V and n Combo to Ideal Gas Law Boyle s Law At given t vol of gas is INVERSELY related to pressure N and T constant J tube P atm 760 torr Delta H P atm P gas PT PT Charles s Law vol of gas directly proportional to T Kelvins Kelvin C 273 V T V T Avogadro s Law V proportional to N P and T fixed V n V n STP 0 degrees Celcius 273 15 K and 1 atm 760 torr Ideal gases at STP 22 414 standard molar volume Ideal Gas Law PV nRT R universal gas constant R 0 0821 Combo gas law PV nT PV nT Density m V Calculate density by n moles m mass of grams M molar mass PV m M RT Unit grams per liter Density proportional to pressure and inversely proportional to temperature d d t t Density Molar Mass x Pressure RT Molar Mass of Unknown Gas Molar Mass mRT PV or dRT P confirming experimental gases Dalton s Law of Partial Pressures Each gas in mix behaves as though it is the only gas present ideal gas law is valid for most gases at ordinary conditions P of humid air P dry air P added water vapor Total Pressure is sum of the partial pressures Mole Fraction moles of gas total moles in mix Vapor Pressure of water PH2O in textbook Collecting Gases over water P total P gas PH2O Total pressure break up into different gases then find moles with PVnRT then find mass in grams Ideal Gas Law and Rxn Stoich PVT of gas ideal gas law Amount mol of gas A molar ratio from balanced equation Amount of gas B PVT ideal gas law Using stoich and gas laws to calc amounts of reactants and products Use balanced equations to find mole ratios Find liters using PV NrT Kinetic Molecular Theory vol of gas molecules themselves negligible molec In constant random linear motion until collision or container walls hit btwn collisions molecs don t interact Collisions elastic total Ek Kinetic Energy constant Molecs have range of speeds u most probable speed avg speed temp inc avg speed inc too The KE of one gas molecule is 1 2mass x speed 2 Avg KE Ek x M x u 2 Bar means average m is molecular mass and bar u 2 is avg of the squares of molecular speeds At same T all gases have same KE Means that equation has same value for two compared masses but the two compensate for each other Smaller molecs go faster larger molecules go slower do so in the right way so that they both have same kinetic energy Avg speed of two gases will make the avg kinetic energy the same and they will produce the same pressure under the same conditions Effusion a gas escapes from its container through a tiny hole into an evacuated space Grahams Law Rate of effusion inversely proportional to square root of its molar mass Rate inv Proportional to 1 root Molar Mass Lighter gas effuses faster since acg speed of lighter molecules is higher more molecs escape through the holes per unit time Use grahams law to measure molar mass of unknown gases two types of problems 1 The effusion rate of gas X is often determined relative to that of a known gas such as He Ratex RateHe Root MHe Root Mx Or Mx Mhe x rate He rate X 2 Problem 2 time inv prop to rate Higher rate lower time Time x inv prop to Root Mx time x time he root Mx root Mhe Direct relationship between time for gas and the root of molar mass of gas Real Gases Deviations fr Ideal behavior PV RT 1 caused by intermolecular attractions which are weak forces between real molecules over short distances Deviations are greatest at high pressure and low temperature Favor side of attractions PV RT 1 when real gas molecules have finite molecular volumes At low pressures free volume is nearly equal to container vol As P inc real gas molecs occupy higher of container vol At free P free vol is smaller that container v so using container V makes PV RT too high review rules of deviation highest density in identical conditions belongs to the gas with the highest molar mass Question 7 Chapter 5 attempt 1 If a certain pressure supports a 256 mm high column of mercury how high a column of water would it support The density of mercury is 13 6 g cm3 256 mm is 10 inches Density of water is 1 g cm3 Hg has density of 13 6 g cm3 so water column is 13 6 times as high as the Hg column so masses are equal 10 inches times 13 6 is 136 inches which is 11 feet 4 inches not 11 4 ft Question 1 Chapter 5 Attempt 2 A gauge on a tank of compressed helium reads 1850 psi pounds per square inch What is this pressure in mm Hg One PSI 51 7149 torr Question 3 chapters 5 6 Attempt 1 Helium and methane CH4 are both found in natural gas and can be separated by diffusion What is the ratio of the diffusion rates for the two species rate of diffusion for He divided by the rate for CH4 Selected Answer Correct Answer c 2 00 c 2 00 Why not It asked for diffusion HE CH4 Carbon dioxide deviates more from the ideal gas law than diatomic hydrogen partly because Selected Answer b carbon dioxide has a larger molar mass and so has greater intermolecular forces