Gases Chapter 10 in Brown & LeMay

General characteristics Atmosphere is 78% nitrogen and 21% oxygen “Gas” vs. “vapor” – oxygen is a gas, water can be vapor Volume of gas = volume of container Highly compressible Form homogeneous mixtures spontaneously

Pressure Force/unit area High heels example What is the pressure inside a balloon Atmospheric pressure in Denver? 14 lbs/square inch, kPa, 760 mm Hg called torr), 1 atmosphere

Illustration

Open manaometer problem Gas pushes down on mercury Either add or subtract mm Hg difference Animation Try one

Gas Laws Consider P,V,T, and n Simple laws look at two when the other two are held constant Boyle’s, Charles’, and Gay-Lussac’s

Boyle’s Law At constant temperature, the pressure of an enclosed amount of gas will increase if the volume is decreased (syringe) V = k(1/P) or PV = k P 1 V 1 = P 2 V 2 What would this graph look like? Animation

Charles’ Law 1787 – hot air balloon rides When pressure is held constant for a volume of gas, temperature and volume increase linearly. Absolute temperature only! At a certain temperature, a volume of gas would have “0” volume. This is absolute zero. V = kT or V/T =k, V 1 /T 1 = V 2 /T 2 Graph?

Gay-Lussac’s Law At a given pressure and temperature, the volume of gases that react are in simple whole number ratios. One interpretation is that if a confined gas is at constant volume, pressure and temperature will vary directly. Avogadro – Equal volumes of gases at the same pressure and temperature contain equal numbers of molecules.

STP At 0 °C and 1 atmosphere of pressure, the volume of 1 mole is gas is 22.4 liters.

Ideal Gas Equation We now know how volume is affected by pressure and temperature. V ~ 1/P V ~ T V ~ n V ~ nT/P or V = knT/P k is the proportionality constant, called “R” Solve for “R” for I mole at STP PV = nRT

Values for “R” Determined by units used for pressure and volume Use the first one for this chapter, the second whenever J is involved.

Further Applications PV = nRT What is n? N = m/M (mass you have over molar mass PV = mRT/M What is density? Rearrange with density on the left m/V = d = PM/RT Molar mass from density equation? Look at equation sheets

Gas Stoichiometry Equation determines number of moles and/or grams. This is at STP. Change initial amounts to STP first, then do stoichiometry, or vice versa, depending upon the question. Airbags is a good example of gas stoichiometry. (animation) Try one.

Dalton’s Law of Partial Pressure P tot = p 1 + p 2 + p 3 …. What does this mean? bert/tutorials/ch8.htmhttp://www2.wwnorton.com/college/chemistry/gil bert/tutorials/ch8.htm Finding “n” or mole fraction for each will give you the partial pressure if you know P tot. Used most often when gas is collected over water. Why? See next slide Try a few.

P tot = p gas + p water

Kinetic Molecular Theory Large number of particles in constant, random, motion Volume of particle is negligible Forces between particles are negligible Collisions are perfectly elastic Average kinetic energy is proportional to average Kelvin temperature

KE Distribution

Speed of Different Gases, same temperature

Equations Average KE = 1/2mu 2 “u” is the root mean square speed which is almost the velocity or speed that we are used to. Explain the three gas laws with this

Effusion and Diffusion Average speed equation, no derivation The smaller the M, the faster the average speed Effusion – escape of a gas from a tiny hole into an evacuated space Diffusion – spread of a gas into a space or another substance (we usually mean this!)

Comparing two gases Derive ratio of speeds of gas “a” and gas “b” This is diffusion Same for effusion, use “r” for rate

Practice Calculate the ratio of the rates of effusion for N 2 and O 2 gases at the same temperatures.

Derivations from Ideal Behavior Increased Pressure PV/RT = n For 1 mole, this ratio should be equal to “1” Pressure less than 10 atmospheres, ideal behavior is seen. After that, what happens? Particles take up space within the volume of the gas.

Actually lowers pressure

Also causes attractive forces, again lowering pressure

Decreased Temperature Lower temperature, what happens? Particles begin to attract each other. Constants to correct for this available for each gas.