Chemistry 141 Friday, October 13, 2017 Lecture 17 Ideal Gases Chemistry 11 - Lecture 11 9/30/2009 Chemistry 141 Friday, October 13, 2017 Lecture 17 Ideal Gases

Concept Question What will happen to the volume of an inflated balloon when it is placed in liquid nitrogen (77 K)? goes up goes down stays constant

Charles’s Law The volume of a gas is proportional to its temperature decrease in T decrease in V V = bT + C Copyright © 2002 by Houghton Mifflin Company. All rights reserved.

Absolute Temperature V = bT + C V = bT We can define a new scale of temperature such that the zero of temperature is the point where the gases have zero volume. This temperature is called absolute zero. Absolute zero = -273.15 °C T(K) = T(°C) + 273.15 Copyright © 2002 by Houghton Mifflin Company. All rights reserved.

Avogadro’s Hypothesis Gay-Lussac noted that the volumes of gases at same T and P that react together are in the ratio of small whole numbers Avogadro concluded that equal volumes of gases contain equal numbers of particles (at same T and P) The volume a gas occupies is proportional to the number of particles n = # of particles in 1 volume a = a constant V = an 2V = a(2n)

Combining the gas laws Boyle’s Law: Charles’s Law: Avogadro’s Law: combine constants into R The ideal gas law

Using the Ideal Gas Law An ideal gas is in a cylinder with a volume of 5.0×102 ml at a temperature of 30. °C and a pressure of 710 torr. The gas is compressed to a volume of 25 ml, and the temperature is raised to 820 °C. What is the new pressure?

The gas constant The gas constant tells us how much P or V will change if n or T changes Standard temperature and pressure (STP) P = 1 atm T = 0 °C (=273.15 K) What volume is occupied by 1 mole of an ideal gas at STP?

Gas stoichiometry example Metallic molybdenum can be produced from the mineral molybdenite, MoS2. The mineral is first oxidized in air to MoO3 and SO2. MoO3 is then reduced to metallic Mo using hydrogen gas. The balanced equations are: MoS2 (s) + O2 (g)  MoO3 (s) + 2SO2 (g) MoO3 (s) + 3H2 (g)  Mo (s) + 3H2O (l) Calculate the volume of oxygen gas at 17 °C and 1.00 atm that is needed to produce 1.00×103 kg of pure Mo from MoS2.

Concept question You have two containers of gas at the same temperature and pressure. One contains ammonia gas, and the other air. Which is lighter, and why?

Gas density The density of a gas is related to its pressure, temperature, and volume (density = d or ρ) m = mass Mx = molar mass of X the density of a gas depends on its molar mass

Questions The amount of CO2 in the atmosphere is changing with time. How much CO2 is there and how big is the change? Do increases in CO2 lead to changes in air properties, such as density?

Gas mixtures Dalton’s Law of Partial Pressures What happens when two different gases are mixed together? Consider equal volumes at constant T: Remember: P, V, and T are independent of the identity of the gas – they depend only on the total n how do the pressures of these samples relate to each other? + = ni + nj = ntotal pressures add! Dalton’s Law of Partial Pressures

Mole fraction We define a new measure of concentration for gas mixtures, the mole fraction: since