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)

• Standard Temperature is 0oC• Standard Pressure is 1.00atm

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

– P1V1/T1= P2V2/T2

– (780.0torr)(0.350 L)/(297.2K) = (760.0torr)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= m2v2

2

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– m1v1

2= m2v22

– (32.00 g/mol)(480 m/s)2= (146.07 g/mol) v2

– v = 224 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 = P1 + P2 + P3 + ……• PT = 845.0 torr + 18.6 torr• PT = 863.6 torr