Behavior of gases Ch.12 Remember the Kinetic Theory!! Gases are affected by changes in temperature and pressure. Both solids and liquids are affected very little by changes in temperature and pressure. Gases are used quite often to absorb energy and insulate / cushion abjects.

3 Properties of Gases 1.Compressibility is measure of how much the volume of matter decreases with increased pressure. Gases are easily compressed because of the space between molecules 2.No attractive or repulsive forces exist between atoms or molecules 3.Gas particles move rapidly in constant random motion in straight paths independently of each other

Variables That Describe a Gas 1.Pressure- (P) in kilopascals 2.Volume- (V) in liters 3.Temperature- (T) in kelvins 4.Number of moles- (n) Gas laws will enable you to predict gas behavior at specific conditions Work problems p. 328 # 1-4

Factors Affecting Gas Pressure Amount, Volume, and Temperature

Amount of Gas Increasing the number of particles, the number of collisions increases  the pressure increases Keeping the temperature constant, doubling the number of particles doubles the pressure When a sealed container of gas under pressure is opened, the gas moves from the region of higher pressure to the region of lower pressure

Volume Pressure can be raised by reducing the volume of the gas The more the gas is compressed, the greater the pressure it exerts inside the container Reducing volume by half doubles the pressure Increasing the volume has the opposite effect of decreasing the pressure Doubling the volume halves the pressure

Temperature Speed and kinetic energy of gas particles increase as particles absorb thermal energy Faster moving particles impact the walls of their container with more energy, exerting more pressure If average kinetic energy of gas doubles, the Kelvin temperature doubles, and pressure of the enclosed gas also doubles Work problems p. 332 # 5-9 & p. 356 #47- 52

The Gas Laws Boyle’s, Charles’, Gay-Lussac’s, and the Combined Gas Laws Boyle Charles

Pressure-Volume Relationship Boyle’s Law For a given mass of gas at constant temp- erature, the volume of the gas varies inversely with pressure If volume goes , pressure goes  If pressure goes , volume goes  The product of pressure and volume at any 2 sets of conditions at given temp is constant  P 1 x V 1 = P 2 x V 2

High altitude balloon contains 30.0 L of He gas at 103 kPa. What is the volume when balloon increases altitude to where pressure is 25.0 kPa? P 1 x V 1 = P 2 x V 2 –P 1 = 103 kPa –P 2 = 25.0 kPa –V 1 = 30.0 L V2 = ?

103 kPa x 30.0 L = V 2 x 25.0 kPa V 2 = Does this make sense? Yes, a decrease in pressure at constant temperature corresponds to a proportional increase in volume.

The pressure on 2.50 L of anesthetic gas changes from 105 kPa to 40.5 kPa. What will be the new volume if the temperature remains constant? What is the unknown? What will happen to the size of the unknown? Answer:

A gas with a volume of 4.00 L at a pressure of 205 kPa is allowed to expand to a volume of 12.0 L. What is the pressure in the container if the temperature remains constant? What will happen to the pressure as volume increases? Answer:

Temperature-Volume Relationship Charles’Law

Charles’s Law 1n 1787, French physicist and balloonist Jacques Charles investigated the quantitative effect of temperature on volume of a gas at constant pressure Found increase in volume with every increase in temperature that he studied In practice the range is limited because at low temperatures gases condense to form liquids

Graph of Temperature-Volume Relationship T vs. V yields a straight line graph Graphs of all gas samples, when extrapolated to a volume of zero, intersect at the same point, ºC William Thomson (Lord Kelvin) realized the importance of this number and identified it as absolute zero where theoretically the average kinetic energy of gas particles is zero

Charles’s Law Volume of a fixed mass of gas is directly proportional to its Kelvin temperature if the pressure is constant Equation is:

A balloon 24 ºC has a volume of 4.00 L. The balloon is heated to 58ºC. What is the new volume if the pressure remains constant? V 1 = 4.00 L T 1 = 24ºC T 2 = 58 ºC V 2 = ? Does this make sense? Yes, from kinetic theory the volume should increase with increase in temperature at constant pressure.

Sample Problems If a gas occupies 6.80 L at 325ºC, what is the volume at 25 ºC if no pressure change? Will the volume go up or down? Answer: 5.00 L of air at –50.0 ºC is warmed to ºC. What is new constant pressure? What direction will the volume move? Answer:

Temperature-Pressure Relationship Gay-Lussac’ Law

Gay-Lussac’s Law In 1802, Joseph Gay- Lussac, a French chemist stated that the pressure of a gas is directly proportional to the Kelvin temperature is the volume stays constant. Equation:

Gas left in a used aerosol can pressure of ºC. If thrown into a fire, what is the 928 ºC? P 1 = 103 kPa T 1 = 25 ºC T 2 = 928 ºC P 2 =? Remember temperature must be in Kelvin!

A gas has a pressure of 6.58 kPa at 539K. What will be 211K given constant volume? Answer: Pressure in an automoble tire is 198 ºC. At the end of the trip, the pressure has risen to 225 kPa. What is the temperature of the air in the tire? Answer:

The Combined Gas Law Combines the 3 gas laws  Holding one value constant, you can obtain the other gas laws  Can be used when none of the variables are constant

Volume of a gas-filled balloon is ºC and 153 kPa. What volume will the balloon have at STP? –V 1 = 30.0 L –T 1 = 40 ºC –T 2 =273K –P 1 = 153 kPa – P 2 = kPa V 2 = ?

Does this make sense? Yes, temperature ratio is  1 ( 273K/313K) and the pressure decreases so the pressure ratio is  1 (153kPa/ 101.3kPa) Notice how the units cancel out and you are left with the one that you want.

4 th Variable to be Considered in gas law problems Amount of gas in system expressed in # of moles Combined gas law can be modified by recognizing that the volume occupied by a gas at a specified temperature and pressure depends on the # of gas particles. The # of moles of gas is  to the # of particles  moles must be  to volume Divide each side of the combined gas equation by n

(P x V)(T x n) is a constant for ideal gases If you evaluate (P x V)(T x n), # of moles of gas at any specified P, V, and T can be calculated, symbolized by R, the ideal gas constant Since 1 mol of gas occupies 22.4 substitute #’s in to calculate R Work problems p. 340 # 19, 21

Ideal Gas Law Rearranging the equation for R, you get the usual form of the ideal gas law: PiVneRT or P x V = n x R x T This allows you to solve for the # of moles when P, V, and T are known

Fill a rigid steel cylinder that has a volume of 20.0 L with N 2 gas to a final pressure of 2.00 x ºC. How many moles does the cylinder contain? P = 2.00 x 104 kPa V = 20.0 L T = 28ºC Does this make sense? Yes, because the pressure is high but the volume is small so there are a large # of moles of gas compressed into the volume. Units cancel correctly.

A deep underground cavern contains 2.24 x 10 6 L of CH 4(g) at a pressure of 1.50 x 10 3 kPa and temperature of 42ºC. How many kilograms of CH 4 does this natural-gas deposit contain? P = 1.50 x 10 3 kPa V = 2.24 x 10 6 L T = 42ºC Mass = ? First calculate for # of moles, then use molar mass to convert to grams

Then convert moles of methane to grams Convert to kilograms = 2.05 x 10 4 kg CH 4 Does this make sense? Yes, volume and pressure are very large so should be large mass of methane

Sample Problems A child has a lung capacity of 2.20L. How many grams of air do her lungs hold at a pressure of 102kPa and a normal body temperature of 37ºC? (Molar mass of air ~29g/mol) Answer: What volume will 12.0 g of oxygen gas occupy at 25ºC and a pressure of 52.7kPa? Answer:

Ideal Gas Law and Kinetic Theory Ideal gas is one that follows the gas laws at all conditions of pressure and temperature which means conform precisely to the kinetic theory. Thus, particles have no volume and could not be attracted to each other at all. There are no ideal gases but at many conditions of temperature and pressure, real gases behave much like ideal

Important difference is that real gases can be liquefied and sometimes solidified by cooling and applying pressure where ideal gases cannot

Departures from Ideal Gas Law Deviations from ideal are based on 2 factors, attractions between molecules and volume of the gas molecules Gases could not be liquefied if there was no attraction between molecules Actual gases are made of actual particles that have volume Work problems p. 346 # 27-30

Avogadro’s Hypothesis Equal volumes of gases, at the same temperature and pressure contain equal numbers of particles This is possible because there is so much space between the particles that it doesn’t matter how large or small the particles are

Sample Problem Determine the volume in L occupied by mol of a gas at STP Does this make sense? Yes, because 1 mol of gas occupies 22.4 L at STP so mol of gas would occupy about 1/5 of that volume

How many oxygen molecules are in 3.36 L of oxygen gas at STP? Convert from volume  moles  molecules = Determine the volume of 14.0 g of nitrogen STP Convert mass  moles  volume

What volume is occupied by 4.02 x molecules of helium Answer: What is the volume of a container that holds 8.80 g of carbon Answer: A container holds 6.92 g of hydrogen What is the volume of the container? Answer:

Dalton’s Law Particles in a mixtures of gases (ex. Air) are at the same temperature  have the same average kinetic energy Gas pressure depends only on # of particles in a given volume and their average kinetic energy If you know the pressure exerted by each gas in the mixture, the pressures can be added to find the total gas pressure.

Partial Pressure One form of Dalton’s law of partial pressures: P total = P 1 + P 2 + P 3 + P 4 constant volume and temperature Fractional contribution to pressure by each gas in a mixture does not change with changes in temperature, volume or pressure This is very important in the area of anesthesiology.

Sample Problem Air contains O 2, N 2, CO 2, and trace amounts of other gases. What is the partial pressure of oxygen P O2 at kPa of total pressure if the partial pressures of nitrogen, carbon dioxide and other gases are 79.10kPa, 0.040kPa, and 0.94kPa P O2 = P total - (P N2 +P CO2 + P others ) = 21.22kPa

Sample Problems Determine the total pressure of a gas mixture that contains O2, N2, and He if the partial pressures of the gases are as follows:P O2 =20.0 kPa, P N2 =46.7 kPa, P He = 26.7kPa. Answer: A gas mixture containing O 2, N 2, and CO 2 has a total pressure of 32.9 kPa. If P O2 = 6.6 kPa and P N2 = 23.0 kPa, what is P CO2 ? Answer:

Graham’s Law Diffusion is the tendency of molecules to move toward areas of lower concentration until the concentration is uniform throughout Effusion is the process where a gas escapes through a tiny hole in its container Thomas Graham (in 1840’s) studies effusion Proposed that the rate of effusion is inversely proportional to the square root of its molar mass

KE = ½mv 2 If 2 bodies of different masses have the same kinetic energy, the lighter body must move faster Particles at the same temperature have the same kinetic energy so the particles with lower molar mass must move faster The rates of effusion are inversely proportional to the spare roots of their molar masses

Sample Problem Compare rates of effusion of the air component nitrogen (molar mass = 28.0g) and helium gas (molar mass = 4.0g) Work problems p. 353 # & p. 356 #54, 57, 62, 67