Chapter 11 Gases Four factors that can affect the behavior of a gas. Amount of gas (n) = moles Volume (V), 1000 cm3 = 1000mL = 1L Temperature (T), Celsius and Kelvins Kelvins = oC + 273 Pressure(P), atmospheres(atm), mmHg, or kPa

Nature of Gases 1 mole of any gas at STP equals 22.4L of volume. STP is defined at sea level. Standard Temperature = 0oC = 273K Standard Pressure = 1 atm = 101.3 kPa = 760mmHg = 760 torrs Normal boiling point of water is 100oC at sea level. Higher elevation lower boiling points. Less Pressure above the surface of water.

Pressure and Force Pressure = Force / Area P = F/A Reduce the area - Increase the Pressure Increase the force - Increase the Pressure S.I Unit for Force - N (Newton) S.I Unit for Area - m2 S.I Unit for Pressure - Pa (Pascal) = 1 N/ m2

Standard Temperature & Pressure The volume of a gas depends upon Pressure Temperature In order to do a comparison of the volumes of various gases the gases must have the same temperature and pressure. Scientist agreed upon; STP - Temp. = 0 °C , Press. = 1 atm = 101.3kPa = 760mm Hg

Dalton’s Law of Partial Pressure The total pressure of a mixture of gases is equal to the sum of all the partial pressures. Partial pressure - pressure of one gas in a mixture of gases PT = P1 + P2 + P3 + …

Sample Problem Determine the pressure of oxygen gas in a container that is under 1 atm of pressure and contains carbon dioxide and nitrogen. Note: PCO2 = .285mmHg, PN2 = 594mmHg 760 mmHg = PO2 + .285mmHg + 594mmHg PO2 = 165.715 mmHg

Water Displacement page 859 A-8 Gases are collected through water displacement. Water vapor particles are trapped with the gas being collected. Corrected pressure of the gas is determined through the following equation. Patm = Pgas + PH2O

Boyle’s Law: Pressure-Volume Relationship 2 Conditions P1V1 = k (600) P2V2 = k (600) Then P1V1 = P2V2 If you know 3 you can find the 4th Boyle’s Law - the volume of a fixed gas varies inversely with the pressure at constant temperature. V = k 1/P or PV = k

Sample Problem A sample of gas collected occupies a volume of 150.mL when its pressure is 720. mmHg. What volume will it occupy if its pressure is changed to 750. mmHg?

Charles’ Law: Temperature-Volume Relationship The volume of a fixed amount of gas varies directly with the Kelvin temperature at constant pressure. V1 / T1 = V2 / T2 V1 T2 = V2 T1

Charles’ Law Temperature must be in Kelvin! Absolute Zero - lowest possible temperature, all kinetic energy ceases. -273.15 °C

Sample Problem A sample of neon gas occupies a volume of 752 mL at 25 °C. What volume will it occupy at 50.°C. P, n are constant.

Gay-Lussac’s Law The pressure of a fixed gas varies directly with the temperature at constant volume. Mathematically P = k T or P / T = k P1T2 = P2T1

Sample Problem The gaseous contents in an aerosol can are under a pressure of 3.00 atm at 25 °C. If the temperature is increased to 52 °C, what would the pressure of the can be?

The Combined Gas Law Expresses the relationship between P,T, & V of a fixed amount of gas. Mathematically PV/T = k P1V1 = P2V2 T1 T2 P1V1T2 = P2V2T1

Sample Problem A helium-filled balloon has a volume of 50.0 L at 25°C and 820. mmHg. What volume will it occupy at 650. mmHg and 10. °C?

Water Displacement A sample of methane gas that was collected through water displacement had a volume of 350mL at 27.0oC and 720.mmHg. What is the pressure at 2.0oC and 250.mL?

Avogadro’s Law Equal volumes of gases at the same temperature and pressure contains an equal number of gas particles. At STP, 22.4L = 1 mol V1n2 = V2n1

Sample Problem Determine the number of moles of helium that are held in a 250.mL container. Consider that 2.00 moles can be held in a 3.00L container.

11-3 : Ideal Gas Law Describes the physical behavior of an ideal gas in terms of pressure, volume, temperature and number of moles. The combination of all 4 gas laws from the previous section.

Derived Equation for the Ideal Gas Law Needed an Ideal Gas Law Constant (R). The second conditions were set at STP to equal the ideal behavior.

Ideal Gas Constant

Practice Problem A camping stove uses a propane tank that holds 4.0 moles of liquid C3H8. How many liters will be needed to hold the same amount of propane at 25oC and 3atm?

Gas Density at STP The density of a gas at STP is constant, due to the standard molar volume of a gas. Non-STP: However the density of a gas changes with temperature and pressure, due to the volume in the equation. (must use ideal gas law)

Gas Density Problems Determine the density of CO2 at STP. What is the molar mass of gas that has a density of 1.28g/L at STP?

Molar Mass and Ideal Gas Law Considering that moles are in the Ideal Gas Law equation, we can substitute the equivalent of moles(n) into the equation.

Density and the Ideal Gas Law Now that mass(m) is in the equation we can substitute density(d) into the equation.

Molar Mass not at STP Using the previous equations : Example: A 1.25g sample of gas was found to have a volume of 350mL at 20oC and 750mmHg. What is the molar mass of this gas?

Ratm = .0821 RmmHg = 62.4 RkPa = 8.314

Classwork What is the molar mass of a gas that has a density of 2.08g/L at STP? What is the density at STP of NO2? What is the molar mass of a gas, if it has a density of 3.71g/L at 22oC and 755mmHg?

11-4 Graham’s Law Diffusion – Tendency of gas particles to travel toward areas of lower concentration. Effusion – Gas escapes a tiny opening in a container. (one way diffusion) Graham’s Law Rate of effusion of a gas is inversely proportional to the square root of its molar mass. Less mass = faster gas

Graham’s Law Problems Which gas will diffuse into a container faster? CO2 or NH3? Why? Compare the rates of effusion for F2 and Cl2.

Graham’s Law Problems At a certain temperature and pressure, Cl2 has a velocity of .038m/s. What is the velocity of SO2 at the same condition?

Determining the Molar Mass An unknown gas was placed into a container with nitrogen gas. The N2 was found to travel 1.2 times faster than the unknown gas. What is the molar mass of this unknown gas?