Chapter 8 Gases The Gas Laws of Boyle, Charles and Avogadro The Ideal Gas Law Gas Stoichiometry Dalton’s Laws of Partial Pressure The Kinetic Molecular Theory of Gases Effusion and Diffusion Collisions of Gas Particles with the Container Walls Intermolecular Collisions Real Gases Chemistry in the Atmosphere

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

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

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)

Example Boyle’s Law: The Effect of Pressure on Gas Volume The cylinder of a bicycle pump has a volume of 1131 cm3 and is filled with air at a pressure of 1.02 atm. The outlet valve is sealed shut, and the pump handle is pushed down until the volume of the air is 517 cm3. The temperature of the air trapped inside does not change. Compute the pressure inside the pump.

T(°C) =273°C[(V/Vo)] Charles’ Law: T vs V 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

The Absolute 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 Temp

(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)

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.

(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

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

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

ideal gas law constants PV = nRT ideal gas law constants

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.

(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

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.

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.

Pressure and Molecular Motion Pressure  (impulse per collision) x (frequency of collisions with the walls) frequency of collisions  speed of molecules (u) impulse per collision  momentum (m × u) frequency of collisions  number of molecules per unit volume (N/V) P  (m × u) × [(N/V) × u]

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

Gaseous Diffusion and Effusion Diffusion: mixing of Gases e.g., NH3 and HCl Effusion: rate of passage of a gas through a tiny orifice in a chamber.

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

Kinetic Molecular Theory model Real Gases Kinetic Molecular Theory model assumed no interactions between gas particles and no volume for the gas particles 1873 Johannes van der Waals Correction for attractive forces in gases (and liquids) Correction for volume of the molecules Pcorrected Vcorrected = nRT

Johannes van der Waals (1837-1923) The Person Behind the Science Johannes van der Waals (1837-1923) Highlights 1873 first to realize the necessity of taking into account the volumes of molecules and intermolecular forces (now generally called "van der Waals forces") in establishing the relationship between the pressure, volume and temperature of gases and liquids. Moments in a Life 1910 awarded Nobel Prize in Physics