Gases Objective I will know the properties of gasses and be able to calculate the quantifiable properties of gasses Success Criteria I will be able to calculate each of the four quantifiable properties using the appropriate equation

Video Links Liquid Nitrogen and Balloon Demo Link Charles Law Balloon Demo Link Boyle’s Law Demo Link

Collecting Background 1. What are the physical properties of a gas? 2. What are the quantitative (measurable) properties of gasses? 3. What are the units of pressure? How do you convert between the units? 4. Describe the different ways that the measurable properties can be related (the laws)?

Characteristics What are the physical properties of a gas? Gases are fluid In essence, gases can flow Gases have low density Gases are highly compressible Gases completely fill their container

Pressure Pressure is defined as the amount of force exerted per unit area of surface How hard the gas is pushing on the container There are several units of pressure Atmosphere (atm) Kilopascal (kPa) Millimeters of Mercury (mm Hg) Torr (torr) Pounds per square inch (psi) http://www.youtube.com/watch?v=XfFdNNiIAJw http://www.youtube.com/watch?v=O9p8SRmQlPo

Pressure Converting Units of Pressure 1.00 atm=101.325 kPa=760 torr=760 mm Hg Practice Problems The vapor pressure of water at 50.0oC is 12.33kPa. What is the value in atmospheres? (12.33kPa)(1.00atm/101.325kPa)=0.122atm In thermodynamics, the standard pressure is 100.0kPa. What is this value in mm Hg? (100.0kPa)(760mm Hg/101.325kPa)=750.1mm Hg

Quantifiable Properties There are four measurable properties of gases P is pressure T is temperature (must be measured in Kelvin) K = oC + 273 V is the volume n is the number of moles of the gas

STP Standard Temperature and Pressure (STP) Standard Temperature is 0oC Standard Pressure is 1.00atm ΔG° = ΔH° – T ΔS° The superscript indicates at STP

Boyle’s Law Boyle’s Law discusses the relationship of pressure and volume This shows that as the pressure increases, the volume decreases. This is an inverse relationship PV = k1 P = k1/V where k1 is the pressure-volume constant And if we keep Temperature and the number of particles constant, but change either pressure or volume we then have: P1V1=P2V2

Boyle’s Law A sample of oxygen gas has a volume of 150.0mL at a pressure of 0.947atm. What will the volume be at a pressure of 1.000atm if the temperature remains constant? P1V1=P2V2 (0.947atm)(150.0mL)=(1.000atm)V2 V2=142mL Be sure your answers are in Significant Figures!

Boyle’s Law A balloon has a volume of 456mL at a pressure of 761torr. It is taken under water in a submarine to a depth where the air pressure in the submarine is 3.3atm. What is volume of the balloon if the temperature remains constant? Be sure all variables are in the same units (761torr)(1.00atm/760torr)=1.00atm P1V1=P2V2 (1.00atm)(456mL)=(3.3atm)V2 V2=138mL=140mL

Charles’ Law Charles’ Law discusses the relationship between Temperature and Volume This shows that as the temperature increases, the volume increases This is a direct relationship V/T=k2 At a constant pressure and number of particles, if either temperature or volume change we have: V1/T1=V2/T2

Charles’ Law A sample of neon gas has a volume of 752mL at 25.0oC. What is the volume at 50.0oC if the pressure remains constant? Change the degrees in to Kelvin 25.0oC + 273 = 298 K; 50.0oC + 273 = 323 K V1/T1=V2/T2 (752 mL)/(298 K)=V2/(323K) V2 = 815 mL

Gay-Lussac’s Law Gay-Lussac’s Law discusses the relationship between temperature and pressure This shows that as the temperature increases, the pressure increases. P = k3T where k3 is the temperature-pressure constant P/T = k3 At a constant volume and number of particles, if either the temperature or pressure changes, we use this equation: P1/T1=P2/T2

Gay-Lussac’s Law At 122oC, the pressure of a sample of nitrogen is 1.07atm. What will be the pressure at 205oC, assuming constant volume? First change temperature to Kelvin 122oC + 273 = 395 K; 205oC + 273 = 478 K P1/T1=P2/T2 (1.07 atm)/(395 K)=P2/(478 K) P2= 1.29 atm

Combined Gas Law When the three different laws just discussed are analyzed, what would they be if they are all combined? PV = k1 V/T=k2 P/T = k3

Combined Gas Law PV/T = k4 If the number of moles remains constant, we can solve for any of the other variables P1V1/T1= P2V2/T2 Also used is Standard Temperature and Pressure (STP)

Combined Gas Law At a pressure of 780.0 torr and 24.2oC, Xenon has a volume of 0.350L. What will the volume be at STP? First change temperature to Kelvin 24.2oC + 273 = 297.2 K Change the pressure to atmospheres (780.0 torr)(1.00 atm/760 torr) = 1.03 atm P1V1/T1= P2V2/T2 (1.03atm)(0.350 L)/(297.2K) = (1.00atm)V2/(273K) V2 = 0.330 L

Diffusion and Effusion Diffusion is the movement of particles from high density to low density Popping a balloon Effusion is the passage of gas molecules under pressure through a tiny opening Nail in a tire

Graham’s Law of Diffusion In Graham’s Law of Diffusion, we will analyze the kinetic energy of two different gases Kinetic energy formula is 1/2mv2 m is the mass (in this case molar mass) v is the velocity of the molecule Graham’s Law states that the kinetic energy of the first gas will equal the kinetic energy of the second gas m1v12= m2v22

Graham’s Law of Diffusion Oxygen molecules have an average speed of 480 m/s at room temperature. At the same temperature, what is the average speed of molecules of sulfur hexafluoride? Molar mass of Oxygen is 32.00 g/mol (O2) Molar mass of SF6 is 146.07 g/mol m1v12= m2v22 (32.00 g/mol)(480 m/s)2= (146.07 g/mol) v2 v = 220 m/s

Dalton’s Law of Partial Pressures Dalton’s law of partial pressures states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of each gas PT = P1 + P2 + P3 + …… A 42.0 mL sample of hydrogen is collected over water at 30.0oC. What is the total pressure if the pressure of the dry gas 845.0 torr and the vapor pressure of water at 30.0oC is 18.6 torr? PT = 845.0 torr + 18.6 torr PT = 863.6 torr

Essential Information 1.00 atm=101.325 kPa=760 torr=760 mm Hg STP: 273 K and 1.00 atm Dalton’s Law: PT = P1 + P2 + P3 + …… Combined Gas Law: P1V1/T1= P2V2/T2 Gay-Lussac’s Law: P1/T1=P2/T2 Charles’ Law: V1/T1=V2/T2 Gramham’s Law: m1v12= m2v22 Boyle’s Law: P1V1=P2V2 Ideal Gas Law: PV=nRT where R is the gas constant