The GAS LAWS

Gas Properties Gases have mass Gases diffuse Gases expand to fill containers Gases exert pressure Gases are compressible Pressure & temperature are dependent

Gas Variables Units of volume (L) Units of amount (moles) Volume (V) Units of volume (L) Amount (n) Units of amount (moles) Temperature (T) Units of temperature (K) Pressure (P) Units of pressure (mmHg) Units of pressure (KPa) Units of pressure (atm)

A Little Review P1V1 = P2V2 V1 = V2 T1 T2 Boyle’s law pressure & volume as P then V at constant T, n P1V1 = P2V2 Charles’ law: Temperature & volume As T then V At constant P, n V1 = V2 T1 T2

A Little Review P1 = P2 T1 T2 Gay-Lussac’s law: Temperature & pressure As P then T At constant V, n P1 = P2 T1 T2

A Problem Blow up a balloon, measure its volume then take it to the top of Mt. Davis. Explain what would happen to its volume. What variables would you need to use to measure the change? How do those variables change as you go up to the top of Mt. Davis?

PV=k1 V/T=k2 P/T=k3 Now What?? If we combine all of the relationships from the 3 laws covered thus far (Boyle’s, Charles’s, and Gay-Lussac’s) we can develop a mathematical equation that can solve for a situation where 3 variables change : PV=k1 V/T=k2 P/T=k3

Combined gas law P1V1 T1 = P2V2 T2 P1V1T2 = P2V2T1 The law expresses the relationship between changes in volume, pressure, & temperature # of moles is held constant P1V1 T1 = P2V2 T2 P1V1T2 = P2V2T1

Example problem - V1  - T1  - P2  - V2  - T2  1atm 2.0 atm ? A gas with a volume of 4.0L at STP. What is its volume at 2.0atm and at 30°C? - P1  - V1  - T1  - P2  - V2  - T2  1atm 2.0 atm ? 4.0 L 273K 30°C + 273 = 303K

2.22L = V2 Example problem P1V1 T1 = P2V2 T2 (1 atm) (4.0L) (2 atm) (273K) (303K) 2.22L = V2

Gay-Lussac’s other Law Gay-Lussac’s Law of combining volumes of gases The law states that at constant temperature and pressure, the volumes of gaseous reactants and products can be expressed as ratios of small whole numbers.

Gay-Lussac’s other Law In the early 1800s, French chemist Joseph Gay-Lussac studied gas volume relationships involving a chemical reaction between hydrogen and oxygen. He observed that 2 L of hydrogen can react with 1 L of oxygen to form 2 L of water vapor at constant temperature and pressure. Hydrogen gas + Oxygen gas  Water vapor 2 L (2 volumes) 1 L (1 volume) 2 L (2 volumes) This reaction showed a simple and definite 2:1:2 relationship between the volumes of the reactants and the product. Gay-Lussac also noticed simple and definite proportions by volume in other reactions of gases, such as in the reaction between hydrogen gas and nitrogen gas. Hydrogen gas + Nitrogen gas  Ammonia gas (NH3) (3 volumes) + (1 volume) = (2 volumes)

Gay-Lussac Contributions This simple observation, combined with the insight of Avogadro, provided more understanding of how gases react and combine with each other. In fact it lead to the discovery of three vital chemistry concepts. 1) Diatomic Molecules 2) Gas Density and molecular mass comparison and determination (Led to determination of Atomic mass) 3) Avogadro's Principle  The Mole

Avogadro’s Contribution If the amount of gas in a container is increased, the volume increases. container is decreased, the volume decreases. This can be proven simple by blowing up a balloon.

Amedeo Avogadro Amedeo Avogadro lived in Italy, 6.022 x1023  The Mole And his work means an awful lot to chemistry. Amedeo Avogadro may be dead – but, We all should remember what he said. 6.022 x1023  The Mole

Chorus Equal Volumes of Gases, at the same temp and pressure, Have the same number of molecules. Amedeo…..Avogadro, that’s his hypothesis.

Amedeo Avogadro You got two balloons filled with different gases, Equal volumes but they both have different masses, If conditions are the same everywhere, Tell me how the number of molecules compare.

Chorus Equal Volumes of Gases, at the same temp and pressure, Have the same number of molecules. Amedeo…..Avogadro, that’s his hypothesis.

Amedeo Avogadro Why is his hypothesis so great? You can use it to find Mendeleev used it Why is his hypothesis so great? You can use it to find atomic weights. Its based on the ratio of the masses, Of equal volumes of those gases. Atomic Mass

Chorus Equal Volumes of Gases, at the same temp and pressure, Have the same number of molecules. Amedeo…..Avogadro, that’s his hypothesis.

The GAS LAWS AT WORK

Amedeo Avogadro Avogadro helped shaped atomic theory But when I think about it I get sorta teary. Cause no one believed in what he said, Till four years after he was dead.

Amedeo Avogadro When you speak your mind and everyone ignores you, No one’s standing up and rooting for you, So what if they snicker and they laugh, Someday they will want your autograph.

Chorus Equal Volumes of Gases, at the same temp and pressure, Have the same number of molecules. Amedeo…..Avogadro, that’s his hypothesis.

V = kn Avogadro’s Law So far we’ve compared all the variables except the amount of a gas (n). There is a lesser known law called Avogadro’s Law which relates V & n. It turns out that they are directly related to each other. As # of moles increases then V increases. V = kn

Avogadro’s Law Equal volumes of gases at the same T and P have the same number of molecules. V = n (T/P) = kn V and n are directly related. twice as many molecules

Avogadro’s Law V1 n1 = V2 n2 Example : 5.00 L of a gas is known to contain 0.965 mol. If the amount of gas is increased to 1.80 mol, what new volume will result (at an unchanged temperature and pressure)? 5.00 L = V2 . 0.965 mol 1.80 mol V2 = 9.33 L

If conditions are the same the volumes are the same! IF the MOLE is BACK… STOICHIOMETRY is BACK !! Ammonia burns in oxygen to form nitric oxide (NO) and water vapor. How many liters of H2O are obtained from 3.5 liter of ammonia at STP? If conditions are the same the volumes are the same! 4NH3 + 5O2 4NO + 6H2O 3.5 L NH3 Y mol NH3 6 mol H2O X L H2O = 5.25 L H2O 1 X L NH3 4 mol NH3 Y mol H2O

What is Standard molar Volume? Experiments show that at STP, 1 mole of an ideal gas occupies 22.4 L.

Complete worksheet problems 1- 6 How can we use 22.4L? Example #1 : What is the volume of 10 moles of CO2 gas at STP? Ex. #2 What is the density of H2O vapor at STP? D = mass/volume Molar mass H2O = 18.0 g/mol Molar volume of H2O = 22.4 L/mol D = 18.0g/mol 22.4 L/mol 10 mol CO2 22.4 L of CO2 = 224 L CO2 1 1 mole CO2 = 0.8036 g/L Complete worksheet problems 1- 6

What would that formula look like? How would it be arranged? Would it not be Grand if we could have only one PERFECT law So far we have held at least one variable constant for every law we have used. What if we combined all the variables and created a constant to hold them together. What would that formula look like? How would it be arranged?

Temp is measured on the Kelvin Scale! How about another song? THE IDEAL GAS LAW Temp is measured on the Kelvin Scale! Pressure is P Volume is V n is number of mole Temperature is T P & V PV = nRT

PV = nRT BOYLES + CHARLES + Gay-LUSSAC + AVOGADRO LAWS THE IDEAL GAS LAW BOYLES + CHARLES + Gay-LUSSAC + AVOGADRO LAWS -------------------------------COMBINED TOGETHER PV = nRT

Ideal Gas Law PV = R nT PV = nRT If we combine all of the laws together including Avogadro’s Law mentioned earlier we get: PV nT = R Where R is the universal gas constant Normally written as PV = nRT

Ideal Gas Constant (R) R is a constant that connects all of the four gas variables R is dependent on the units of the variables for P, V, & T Temp is always in Kelvin Volume is in liters Pressure is in either atm or mmHg or kPa

Ideal Gas Constant L•atm R=.0821 mol•K L•mmHg R=62.4 mol•K L•kPa Because of the different pressure units there are 3 possibilities for our ideal gas constant R=.0821 L•atm mol•K If pressure is given in atm R=62.4 L•mmHg mol•K If pressure is given in mmHg R=8.31 L•kPa mol•K If pressure is given in kPa

Using the Ideal Gas Law ? = .3635 mol What volume does 9.45g of C2H2 occupy at STP? .0821 L•atm mol•K P  1atm R  ? V  T  273K 9.45g 26g n  = .3635 mol

PV = nRT V = 8.15L (1.0atm) (V) = (.0821 ) (.3635mol) (273K) (1.0atm) (.0821 ) L•atm mol•K (.3635mol) (273K) (1.0atm) (V) (8.147L•atm) = V = 8.15L

? = 68.2 mol 303kPa 298K 3000g 44g P  R  V  T  n  A camping stove propane tank holds 3000g of C3H8. How large a container would be needed to hold the same amount of propane as a gas at 25°C and a pressure of 303 kpa? 8.31 L•kPa mol•K P  303kPa R  ? V  T  298K 3000g 44g n  = 68.2 mol

PV = nRT V = 557.7L (303kPa) (V) = (8.31 ) (68.2 mol) (298K) (303kPa) (8.31 ) L•kPa mol•K (68.2 mol) (298K) (303kPa) (V) (168,970.4 L•kPa) = V = 557.7L

The Ideal Gas Equations

Try These 5 problems = 1.96 g/L 44.0 g/mol 22.4 L/mol 1) Calculate the density of one mole of CO2 gas at STP. {D = m/V} D = m/V Molar Mass = 44.0 g/mol :: Molar volume = 22.4 L/mol D = 44.0 g/mol = 1.96 g/L 22.4 L/mol 2) What is the density of laughing gas(N2O4) released at 25°C and 1.02 atm? D = PM/RT = (1.02 atm)(92g/mol) (0.0821L*atm/mol*K)(298K) = 3.83 g/L

Try These 5 problems 3) A 0.519 g gas has a volume of 200 ml at STP. Is this gas propane (C3H8), butane (C4H10) or something else? Using the Ideal Gas Law PV = mRT/M  M = mRT/PV = (0.519 g)(0.0821 L atm/mol K)(273K) (1 Atm) (.200 L) = 58.1 g/mol the molar mass of butane 4) A 1.25 g sample of a gaseous product of a chemical reaction was found to have a volume of 350 ml at 20.0°C and 750 mm Hg. What is the molar mass of this gas? 5) What is the volume of a gas whose molar mass is 90.2 g/mol. 1.39 g of the gas is contained at 755 mm Hg and 22 °C

Try These 5 problems 4) Using the Ideal Gas Law PV = mRT/M  M = mRT/PV = (1.25 g)(62.4 L mm Hg/mol K)(293K) (750 mm Hg) (.350 L) = 87.0 g/mol 5) Using the Ideal Gas Law PV = mRT/M  V = mRT/PM = (1.39 g)(62.4 L mm Hg/mol K)(295K) (755 mm Hg) (90.2 g/mol) =.376 L

PV = nRT (1.00 atm) (1.00 L) nH2O= (573K) (.0821L atm/mol K) Ideal Gas Law & Stoichiometry What volume of hydrogen gas must be burned to form 1.00 L of water vapor at 1.00 atm pressure and 300°C? (hint: Solve for mole of H2O then convert) PV = nRT (1.00 atm) (1.00 L) nH2O= (573K) (.0821L atm/mol K) nH2O= .021257 mols

Ideal Gas Law & Stoichiometry 2H2 + O2  2H2O 2 mol H2O 2 mol H2 = 1mol H2 22.4 L H2 .021257 mol .476 L H2