Chapter 11 Gases The Gas Laws of Boyle, Charles and Avogadro The Ideal Gas Law Gas Stoichiometry The Kinetic Molecular Theory of Gases Effusion and Diffusion Collisions of Gas Particles with the Container Walls Intermolecular Collisions 1

We start with gases because they are simpler than the others. States of Matter Solid Liquid Gas We start with gases because they are simpler than the others. 4/21/2017 2 2

Pressure (force/area, Pa=N/m2): A pressure of 101.325 kPa is needed to raise the column of Hg 76 cm (760 mm). “standard pressure” 760 mm Hg = 760 torr = 1 atm = 101.325 kPa 3

P1V1 = P2V2 Boyle’s Law Charles’ Law V1 / V2 = T1 / T2 Avogadro (fixed T,n) V x P = const 1662 Charles’ Law V1 / V2 = T1 / T2 (fixed P,n) V / T = const 1787 V / n = const (fixed P,T) Avogadro 1811 n = number of moles 4

Boyle’s Law: Pressure and Volume The product of the pressure and volume, PV, of a sample of gas is a constant at a constant temperature: PV = k = Constant (fixed T,n) 5

Pressure and Volume compared in two ways Directly P α V and Indirectly P α 1 / V 4/21/2017 6

Charles’ Law: T vs V T(°C) =273°C[(V/Vo)] At constant pressure, the volume of a sample of gas is a linear function of its temperature. V = bT T(°C) =273°C[(V/Vo)] When V=0, T=- 273°C 7

Kelvin temperature scale Charles’ Law: T vs V The Absolute Temperature Scale V = Vo ( 1 + ) t 273.15oC Kelvin temperature scale T (Kelvin) = 273.15 + t (Celsius) Gas volume is proportional to Temperature 8

(at a fixed pressure and for a fixed amount of gas) Charles’ Law: The Effect of Temperature on Gas Volume V vs T V1 / V2 = T1 / T2 (at a fixed pressure and for a fixed amount of gas) 9

n= number of moles of gas a = proportionality constant Avogadro’s law (1811) V = an n= number of moles of gas a = proportionality constant For a gas at constant temperature and pressure the volume is directly proportional to the number of moles of gas. 10

(at a fixed temperature) Boyle’s Law P1V1 = P2V2 (at a fixed temperature) V = kP -1 Charles’ Law V1 / V2 = T1 / T2 (at a fixed pressure) V = bT V = an (at a fixed pressure and temperature) Avogadro n = number of moles PV = nRT ideal gas law an empirical law V = nRTP-1 11

Example n1 = n2 V1 = V2 P2 = P1T2/T1 = (1 atm)(263K)/(303K) At some point during its ascent, a sealed weather balloon initially filled with helium at a fixed volume of 1.0 x 104 L at 1.00 atm and 30oC reaches an altitude at which the temperature is -10oC yet the volume is unchanged. Calculate the pressure at that altitude . n1 = n2 V1 = V2 P2 = P1T2/T1 = (1 atm)(263K)/(303K) 12

STP = standard temperature and pressure For 1 mole of a perfect gas at O°C (273K) (i.e., 32.0 g of O2; 28.0 g N2; 2.02 g H2) nRT = 22.4 L atm = PV At 1 atm, V = 22.4 L STP = standard temperature and pressure = 273 K (0o C) and 1 atm 13

PV = nRT The Ideal Gas Law What is R, universal gas constant? the R is independent of the particular gas studied 14

ideal gas law constants PV = nRT ideal gas law constants 15

2) Find the number of moles. Example What mass of Hydrogen gas is needed to fill a weather balloon to a volume of 10,000 L, 1.00 atm and 30 ̊ C? 1) Use PV = nRT; n=PV/RT. 2) Find the number of moles. 3) Use the atomic weight to find the mass. 16

(1 atm) (10,000 L) (293 K)-1 (0.082 L atm mol-1 K-1)-1 Example What mass of Hydrogen gas is needed to fill a weather balloon to a volume of 10,000 L, 1.00 atm and 30 ̊ C? n = PV/RT = (1 atm) (10,000 L) (293 K)-1 (0.082 L atm mol-1 K-1)-1 = 416 mol (416 mol)(1.0 g mol-1) = 416 g 17

The volume of a gas is easier to measure than the mass. Gas Stoichiometry Use volumes to determine stoichiometry. The volume of a gas is easier to measure than the mass. 18

Gas Density and Molar Mass See that n = m/M which in words is moles (n) equals a given mass (m) divided by the molar mass (M). Think about the units. Moles = grams / (grams per mole) 19

Example Gas Density and Molar Mass Calculate the density of gaseous hydrogen at a pressure of 1.32 atm and a temperature of -45oC. Remember to use units of Kelvin for the temp! Density = mass / volume = (pressure*molar mass) / (gas constant R*temperature) = (1.32 atm * 2.016 g/mol for H2) / (0.0821)*(273-45 K) = 0.142 g/L (grams per liter) Liters is the volume here because of the units of the constant R. 20

2NH4ClO4 (s) → N2(g) + Cl2 (g) + 2O2 (g) + 4 H2 (g) 21

The Kinetic Molecular Theory of Gases The Ideal Gas Law is an empirical relationship based on experimental observations. Boyle, Charles and Avogadro. Kinetic Molecular Theory is a simple model that attempts to explain the behavior of gases. 22

The Kinetic Molecular Theory of Gases 1. A pure gas consists of a large number of identical molecules separated by distances that are large compared with their size. The volumes of the individual particles can be assumed to be negligible (zero). 2. The molecules of a gas are constantly moving in random directions with a distribution of speeds. The collisions of the particles with the walls of the container are the cause of the pressure exerted by the gas. 3. The molecules of a gas exert no forces on one another except during collisions, so that between collisions they move in straight lines with constant velocities. The gases are assumed to neither attract or repel each other. The collisions of the molecules with each other and with the walls of the container are elastic; no energy is lost during a collision. 4. The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas. 23

Speed Distribution Temperature is a measure of the average kinetic energy of gas molecules. 24

Real Gases Ideal Gas behavior is generally conditions of low pressure and high temperature 25