I can …… Describe Boyle’s Law of gases Perform calculations using Boyle's Law

Fourvariables describeagas Number of moles Pressure Volume Temperature

PVandPVPVandPV Boyle’s Law Boyle's law states that at constant temperature for a fixed mass, the absolute pressure and the volume of a gas are inversely proportional.

Boyle’s Law V PPV =kPPV =k Boyle's law can also be stated in a slightly different manner, that the product of absolute pressure and volume is always constant.

Boyle’s Law P V PV =kPV =k Volume (mL) Pressure (torr) P∙V (mL∙torr) x x x x 10 3

PV =kPV =k P1V1P1V1 =k=P2V2=k=P2V2 P1V1=P2V2P1V1=P2V2

P 1 =2 atmV 1 =10 L V 2 = ? P 2 =4 atm At constant T

P 1 =2 atmV 1 =10 L V 2 = ?P 2 =4 atm V 2 =10 L x 2 atm / 4 atm = 5 L At constant T

P 1 =2 atmV 1 =10 L V 2 = ?P 2 =4 atm V 2 =10 L x ( 2 atm / 4 atm ) = 5 L V1V1 = 10 LP1P1 =2 atm V2V2 =20 LP2P2 =? At constant T

P 1 =2 atmV 1 =10 L V 2 = ?P 2 =4 atm V 2 =10 L x ( 2 atm / 4 atm ) = 5 L V1V1 = 10 LP1P1 =2 atm V2V2 =20 LP2P2 =? P 2 = 2 atmx ( 10 L / 20 L ) = 1 atm At constant T

Charles’s Law I can ….. Describe Charles’s Law of gases Perform calculations using Charles’s Law

KelvinTemperature All gas law calculations must be done in Kelvin temperature! K = °C °C = K °C = = 298 K

I can …… Describe Charles’s Law of gases and perform calculations using Charles’s Law

TVandTV Charles’Law When the pressure on a sample of a dry gas is held constant, the Kelvin temperature and the volume will be directly related.

TVandTV Charles’Law T T VV kVV k

T V  k V T Charles’ Law Volume (mL) Temperature (K) V/T (mL/K)

T1T1 T2T2 V1= V2V1= V2 T V  k

V 1 =2.50 L T 1 =25.0ºC V 2 = 4.10 L T 2 =? Constant P Convert ºC to KT 1 =298 K T 2 =298 Kx 4.1 L / 2.5 L =489 K So in order to change the volume from 2.5 L to 4.1 L we need to increase temperature to 488 K

V 2 =?V 1 =8.30 L T 1 =17.0 ºCT 2 = 96.0 ºC Constant P Convert Temperature to Kelvin: T 1 =290 KT 2 =369 K V 2 = 8.30 L x 369 K / 290 K ) = 10.6 L

Gay­Lussac’s Law Discovered relationship between the temperature and pressure of a gas. The pressure of a fixed amount of gas at constant volume is directly proportional to it temperature A plot of P versus T will be a straight line

Pressure cooker- uses pressurized steam to cook food at around C Tire pressure should be checked when the tires are cold before driving. WHY?

CombinedGasLaw: Combines Boyle’s, Charles’s and Gay-Lussac’s laws into one. When the amount of gas is kept constant, the combined gas law describes the relationship among pressure, volume and temperature.

Combined GasLaw :

V 1 = 15 L P 1 = 4.8 atm V 2 =? P 2 =17 atm T 1 = 25 ºC(298K)T 2 =75 ºC(348K) 15 x 4.8 = 17 x V V 2 =15 L x 4.8 atm x 348K 17 atm x 298K = V 2 =4.95 L

A 1 L cylinder of gas at 0.8 atm pressure and 20ºC is heated to 35ºC and the pressure changed to 0.1 atm. What is the new volume? 0.8atm x 1 L = 0.1atm x V2 293K308 K P1V1=P2V2T1T2P1V1=P2V2T1T2 V 2 = 8.41L

If 2.6 L of gas at 700 mmHg and 18ºC is compressed to 0.2 L at 1800 mm Hg, what is the new temperature of the gas? P2 =57.56 K 700 mm Hg x 2.6 L = 1800 mm Hg x 0.2 L 291K?K

If 20 mL of gas at 1.2 atm and 16ºC is heated to 38ºC at 1.8 atm, what is the new volume of the gas? 20mL ( 1.2 / 1.8 )( 311 / 289 )=14.35 mL

If 200 mL of gas at 0.52 atm and 200ºC is cooled to 10ºC at 0.01 atm, what is the new volume of the gas? 200 mL ( 0.52 / 0.01 ) ( 283 / 473 ) = mL

The Ideal GasLaw: Combines theseparate gaslaws intooneequationthat allows youtosolve forall variables.

PV = nRT Ideal Gas Law

PV = nRT What is R?

R =PV nT R =(1 atm) (22.4L) (1 mol)(273 K) R = L x atm/mol x K R = ideal gas law constant

PV = nRT What is n?

PV = nRT The#ofmolesofgas

Example Problem: How many moles of air are there in a 2.0 L bottle at 19ºC and 0.98 atm?

n = ? T=19 ºCso 292 K P=0.98 atm R= L atm/mol K V = 2.0 L PV = nRT n =(0.98 atm)(2.0 L) / ( )(292 K) n =0.082 mol gas n =PV / RT

What is the pressure exerted by 1.8 g of H 2 gas exert in a 4.3 L balloon at 27ºC?

P= ?V=4.3 LT=27 ºC so 300 K mass = 1.8 grams of H 2 gas PV = nRTP= nRT/ V 1.8 g H g H 2 1 mol H 2 = 0.89 mol H 2 P = nRT/V = (0.89 mol)( )(300 K) / (4.3 L) P= 5.1 atm You first need to change grams of H 2 to moles of H 2 1

We have a 1.4 g sample of NH 3 with a volume of 3.5 L at a pressure of 1.68 atm. What is the temperature of the gas ? 1.4 g 1mol= mol 17 g PV = nRTsoT = PV / nR (1.68 atm) (3.5 L) / (0.082 mol) ( ) = K

Avogadro’s Principle Equal volumes of gases under the same conditions of temperature and pressure have equal numbers of molecules and equal # of moles. H2H2 He CO2CO2 O2O2

Molar Volume 1 mole of any gas at STP = 22.4 L STP – standard temperature and pressure 273 K or 0 0 C 1 atm or 760 mmHg or 760 torr or 101.3kPa 22.4 L of H 2 = 1 mol H 2 or x 1023 molecules of H 2 ____ L of O 2 = 1 ___ O 2 or __________ molecules of O 2

Gas Stoichiometry Stoichiometry is the calculation of relative quantities of reactants and products in chemical reactions. is founded on the law of conservation of mass where the total mass of the reactants equals the total mass of the products. This means that if the amounts of the separate reactants are known, then the amount of the product can be calculated.

Gas Stoichiometry Problem How many grams of CaCO 3 are needed to produce 9.00 L of CO 2 at STP? = 40.2 g CaCO L CO 2 1 mol CO 2 1 mol CaCO g CaCO L CO 2 1 mol CO 2 1 mol CaCO 3 CaCO 3 CaO+CO 2 ? g? g9.00 L 1 mol CaCO 3 = 1mol CO 2 1 mol CO 2 = 22.4 L CO 2 1 mol CaCO 3 = g CaCO 3

A sample of a nitrogen gas has a volume of 1.75 L at STP. How many grams of nitrogen gas is present in the sample? 1.75 L1 mol N 2 28 g N L1 mol N 2 = 2.19 g N mol N 2 = 22.4 L N 2 1 mol N 2 = 28.02g N 2

152 grams of calcium carbonate is decomposed.How many liters of carbon dioxide is produced at STP?

CaCO 3  CaO+ CO g CaCO 3 1 mol1mol CO L g1 mol CaCO 3 1 mol = 34.1 L CO 2 at STP 1 mol CaCO 3 = 1mol CO 2 1 mol CO 2 = 22.4 L CO 2 1 mol CaCO 3 = g CaCO grams of calcium carbonate is decomposed. How many liters of carbon dioxide is produced at STP?

Dalton’s Law of Partial Pressures P total =P 1 +P

Daltons’ Law of Partial Pressures In a mixture of gases, each gas exerts a certain pressure as if it were alone. The pressure of each individual gas is called the partial pressure. The total pressure inside a container of mixed gases is equal to the sum of the partial pressures of each gas.

We can find out the pressure in the fourth container, by adding up the pressure in the first 3. 2 atm1 atm3 atm 6 atm

What is the total pressure in a container filled with 2 gases if the pressure of one gas is 170 mm Hg and the pressure of the other gas is 620 mm Hg? In a second container of N 2 and O 2 gases the total pressure is 1.3 atm. What is the pressure of O 2 if the pressure of N 2 is 1.0 atm? 790 mmHg 0.3 mmHg

Ideal Gases don’t really exist The Ideal Gas LawPV = nRT 1.Molecules have no volume 2.Molecules have no attractive forces

Ideal Gases don’t really exist Molecules do have volume and take up space There are attractive forces between molecules The true pressure and volume are different from what we calculate using PV = nRT.

RealGases Real gases are more ideal at… –__ L _ o _ w __ pressures –__ H _ i _ g _ h _ temperatures

Real Gases behave like Ideal gases: When the molecules are moving fast. The collisions are harder and faster. Molecules are not next to each other for very long, and can’t interact. When attractive forces can’t play a role. This is at high temperatures.

When the molecules are far apart The molecules do not take up as big a percentage of the space, we can ignore their volume. This is at low pressure Real Gases behave like Ideal gases: