Chapter 6 Gases PV=nRT is SUPER- FANTASTIC!!! 1 I. Properties of Gases A) Physical Properties B) Pressure II. The Ideal Gas Law A) Simple Calculations B) Molar Mass and Density Calculations C) Stoichiometry D) Partial Pressures and Mole Fractions III. Kinetic Molecular Theory A) Effusion and Diffusion B) Real Gases vs. Ideal Gases http://www.nasa.gov/sites/default/files/1-bluemarble_west.jpg, https://upload.wikimedia.org/wikipedia/commons/thumb/a/a3/atmosphere_composition_diagramen.svg/1024px-atmosphere_composition_diagram-en.svg.png
Stoichiometry Problems Thus Far 2 1. S 8 (s) + 8Mg(s) 8MgS(s) 2. HCl(aq) + AgNO 3 (aq) AgCl(s) + HNO 3 (aq) 3. N 2 (g) + 3H 2 (g) 2NH 3 (g) How do we quantify amounts of the gases reacted and produced?
I. Properties of Gases A. Physical Properties 3 1. gases expand to fill the container holding them - gas particles are much smaller than the container holding them V gas = Volume of free space the gas can occupy ~ Volume of the container that holds the gas 2. compressible 3. speed of gas particles directly related to temperature 4. form homogeneous mixtures - uniform composition throughout - normal temps and pressures gas particles move very fast and are far away from each other https://static.squarespace.com/static/4ff36a2b84aecc34311d0e6c/523b0fcce4b099ee151514e7/523b0fd5e4b099ee151523bf/1350328192307/1000w/red%20bull %20Stratos%203.jpg
B. Pressure (at the molecular level) 4 Pressure Meter Measures frequency of collisions and force of collisions What happens to the pressure? http://img.bleacherreport.net/img/slides/photos/003/680/493/hi-res-117182f11c7a20c6f3353a5b52b62144_crop_north.jpg?w=630&h=420&q=75
Units of pressure 5 1 atm (atmosphere) = pressure at the surface of the Earth
II. The Ideal Gas Law 6 P ~ nt V and P = nrt V or PV = nrt Units R = 0.082057 L atm / mol K P = pressure (atm) V = volume (L) n = # of moles T = temperature (K) What is an ideal gas? Assumptions 1. Molecules/gas particles are assumed to occupy an infinitesimally small volume relative to the size of the container 2. Molecules/gas particles are assumed not to interact with each other
A. Simple Calculations Example Problem Jacques Charles was the first to create a hot air balloon. However, instead of using air he used H 2 gas. His first balloon was filled with 262 g of H 2 at a temperature of 23.0 ºC, its pressure was 750.0 torr. What was the volume of the balloon? Given: 7 PV = nrt V = nrt P Need n H2 =262 g 1 mol H 2 2.01588 g H 2 = 129. 96 mol H 2 P=750.0 torr 1 atm 760 torr = 0.986 84 atm T = 23.0 + 273.15 = 296.1 5 K R = 0.082057 L atm / mol K V = 129. 96 mol 0.082057 L atm mol K 296.1 5 K 0.986 84 atm V = 320 0.29 L = 3.20x10 3 L
Example Problem Helium filled balloons are used to carry scientific instruments high into the atmosphere. Suppose a balloon is launched when the temperature is 22.5ºC and the barometric pressure is 754 mmhg. If the balloon s volume is 4.19x10 3 L (and no Helium escapes from the balloon), what will the volume be at a height of 20 miles, where the pressure is 76.0 mmhg and the temperature is 33.0ºC? 8 Same Gas 2 sets of conditions Initial Conditions Final Conditions P 1 = 754 mmhg P 2 = 76.0 mmhg V 1 = 4.19x10 3 L V 2 = n 1 (no He escapes) n 2 = n 1 = constant T 1 = 22.5ºC (295.6 5 K) T 2 = -33.0ºC (240.1 5K) P1 V1 n1rt1 P2 V2 n2rt2 PV 1 n T 1 1 1 R 2 PV 2 n T 2 2 2 2 P1 V1 PV 2 2 general gas equation n T 1 1 n T
Standard Temperature and Pressure 9 https://upload.wikimedia.org/wikipedia/en/5/57/stp_logo.png
Molar Mass and Density Calculations 10 Goal Use PV = nrt to find density and/or molar mass of a gas
Using PV=nRT to calculate 11 Molar Mass Density
Example Problem A mixture of unknown gas and oxygen was used as an anesthetic on the t.v. program LOST. The unknown gas contains 85.7% C and 14.3 % H by mass. At 50.0 C and 0.984 atm. of pressure, 1.56 g of the gas has a volume of 1.00 L. What is the molecular formula of the gas? 12 https://images2.alphacoders.com/750/750.jpg
Example Problem Calculate the density of CO 2 (g) at STP. 13
C. Gases in Stoichiometry Problems Example Problem Ammonium sulfate, an important fertilizer, can be prepared by the reaction of ammonia with sulfuric acid: NH 3 (g) + H 2 SO 4 (aq) (NH 4 ) 2 SO 4 (aq) What mass of (NH 4 ) 2 SO 4 can be produced from the reaction of 5400. L of NH 3 (g) at 42.0ºC and 8.6 atm with 1000. L of 0.8000 M H 2 SO 4 (aq). NH 3 (g) + H 2 SO 4 (aq) (NH 4 ) 2 SO 4 (aq) 14
D. Partial Pressures and Mole Fractions 15 All gases have the same volume and same T Individual Gas (O 2 )
Example Problem A mixture containing He(g) at a pressure of 1.88 atm, Ne(g) at a pressure of 1.10 atm, and Ar(g) at a pressure of 0.360 atm is confined in a 7.00 L vessel at 25 C. What is the mole fraction of He in the mixture? How many moles of gases are in the mixture? 16
Example Problem A study of the effects of certain gases on plant growth requires a synthetic atmosphere composed of 1.50 mol percent CO 2, 18.0 mol percent O 2, and 80.5 mol percent Ar. (a) Calculate the partial pressure of O 2 in the mixture if the total pressure of the synthetic atmosphere is to be 745 torr. (b) If this atmosphere is to be held in a 120 L space at 295 K, how many moles of O 2 are needed? 17
Example Problem A sample of KClO 3 partially decomposes according to the equation below. The O 2 (g) that is produced is collected in a container over water. The volume of the collected gas is 0.250 L at a temperature of 25.0ºC. If the total pressure in the container is 765.0 torr after the KClO 3 decomposes, (a) how many moles of O 2 (g) are collected, and (b) how many moles of KClO 3 were decomposed? 18 KClO 3 (s) KCl(s) + O 2 (g)