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Gas Laws F2017 TEXT November 27, 2017 Gas Laws What are the typical behaviors of (ideal) gases? Why do gases behave the way they do? Gas Laws F2017 TEXT November 27, 2017 Why is it important to remember your chewing gum before flying...? When (and why) should you check your tire pressure? Gas Laws F2017 TEXT November 27, 2017 Important ideas: The Gas Laws: GayLussac's Law (Temp + pressure) Dalton's Law of Partial Pressures Avogadro's hypothesis (Avog's law) Boyle's law (volume + pressure) Charles' Law (volume + temperature) Combined Gas Law Ideal Gas Law Phase diagram (Incorporates Pressure) Entropy of a system Gas Laws F2017 TEXT November 27, 2017 What is Pressure? Hint: Have you ever measured the pressure in your tires? What are the units? Gas Laws F2017 TEXT November 27, 2017 Pressure is any force applied over a certain area. A greater force produces a greater _ F_ pressure, and a smaller P = A area results in a greater pressure. Ex: single nail vs. bed of nails Gas Laws F2017 TEXT November 27, 2017 What causes the force in a gas? Gas Laws F2017 TEXT Hint: How is the gas composed/ what is happening at a level which is not visible? November 27, 2017 Gas Laws F2017 TEXT November 27, 2017 Kinetic Molecular Theory (KMT) 1) Particles are discrete and have negligible volumepoints in space 2) Particles do not interact in any appreciable manner, except to collide occasionally (elastic collisions) Gas Laws F2017 TEXT November 27, 2017 Particles in a container (2D) The particles move in straight lines until they meet (collide) with other particles or the walls of the container Gas Laws F2017 TEXT November 27, 2017 "Kinetic" = motion Kinetic Energy 1 2 KE = mv 2 Gas Laws F2017 TEXT November 27, 2017 Temperature is the measure of the average kinetic energy of motion in the particles Some of the particles will be moving very quickly, and others barely at all, so it is the average (think of histograms or bell curvesthe temp will be closest to the highest bar or the peak of the bell) Generally, we think of temperature as resulting from the speed of the particles, as that has the greater effect, but mass also affects the KE. Larger particles will not move as quickly, but ultimately we concentrate on the speed and not the mass for a given samplemass it not as significant as speed in measuring temp. In many cases, the gas is not a mixture, so different masses would not be a factor anyway. Gas Laws F2017 TEXT November 27, 2017 GayLussac (Direct proportion b/t temp + pressure of a gas) Gas Laws F2017 TEXT November 27, 2017 GayLussac's Law Expressed Mathematically: P1/ T1 = P2/ T2 Gas Laws F2017 TEXT November 27, 2017 Dalton's law of Partial Pressures The individual pressure of each gas in a system combines (totals) to a sum = the total pressure (air pressure) Gas Laws F2017 TEXT November 27, 2017 Avogadro's Law Mathematical definition Avogadro's law is stated mathematically as: Where: V is the volume of the gas(es). n is the amount of substance of the gas. k is a proportionality constant. The most significant consequence of Avogadro's law is that the ideal gas constant has the same value for all gases. This means that: Where: p is the pressure of the gas in the sample and T is the temperature of the gas in the sample Gas Laws F2017 TEXT November 27, 2017 Avogadro's Hypothesis states: Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. Avogadro's Law states: The volume of a gas maintained at constant temperature and pressure is directly proportional to the number of moles of the gas (n). Avogadro's Law is expressed by the equation: Gas Laws F2017 TEXT November 27, 2017 Gas Laws F2017 TEXT November 27, 2017 Sample Problem: The volume of a sample of chlorine gas, Cl2, is 9.42 liters at STP. What is the mass of the sample, in grams? Hint: When conditions are at STP, it is known that 1 mole of any gas occupies 22.4 liters. We can assume this as V1 and n1. Gas Laws F2017 TEXT November 27, 2017 Gas Laws F2017 TEXT November 27, 2017 Boyle's law Pressure + Volume have an inverse relationship (Temp, amount of gas are constant) Gas Laws F2017 TEXT November 27, 2017 Charles' Law Relation b/t Temperature and Volume Direct Gas Laws F2017 TEXT November 27, 2017 Combined Gas law (we assume the amount of the gas, n, remains constant) Gas Laws F2017 TEXT November 27, 2017 Combined Gas law Gas Laws F2017 TEXT November 27, 2017 Ideal gas Law PV=nRT R is the gas constant If P is in atm V is in L n is in mol T is in K R = 0.0821 If P is in Pa (Pascals) R=8.31 Gas Laws F2017 TEXT November 27, 2017 PV=nRT at any given instant assuming no change constant at time 1 Gas Laws F2017 TEXT November 27, 2017 If constant T Boyle's law Gas Laws F2017 TEXT November 27, 2017 If const. V ("rigid container") GayLussac's law Gas Laws F2017 TEXT November 27, 2017 If constant P Charles' Law, Gas Laws F2017 TEXT November 27, 2017