Chapter 5: Gases Dec 18 10:23 AM Gas Laws Demonstration Crushing 55 gallon drum Egg in a bottle Student in a bag Boiling Water Charles gas Law Water in a flask Ballon in a bottle Jan 1 4:11 PM 1
5.1 Pressure Define "pressure" State how pressure is different from force Convert among various units of pressure Pressure is defined as force per unit area Pressure = force / area The SI pressure unit is newtons per meter squared (N/m2) and is called Pascal (Pa) Barometer The Mercury Barometer Created by Evangelista Torricelli in 1646 it measures the pressure exerted by the Earth s atmosphere. Why use mercury instead of water? Consider the density of mercury (13.53 g/cm3) vs. the density of water (0.997 g/cm3). What would be the height of a water barometer at 1 atm of pressure? Dec 19 8:16 PM Manometer A simple manometer, a device for measuring the pressure of a gas in a container. The pressure of the gas is given by h (the difference in the mercury levels) in units of torr (b) Gas pressure = atmospheric pressure + h (a) Gas pressure = atmospheric pressure h Units of Pressure The unit mm Hg is often called torr in honor of Torricelli. 1 standard atmosphere = 101,325 Pa 1 atm = 760 mm Hg = 760 torr = 101,325 Pa Example 5.1C Interconverting the Units of Pressure The pressure exerted by a gas is measured to be 0.985 atm. Convert this pressure to torr and pascals. Nov 15 1:09 PM 2
5.2 The Gas Laws of Boyle, Charles, & Avogardo solve problems relating to the fundamental gas laws. A. Boyle's Law This law says that the pressure exerted by a gas is inversely proportional to the volume the gas occupies. Robert Boyle (1627 1691) As Pressure Increases, the Volume of SO 2 Decreases Pressure x Volume = Constant PV = k P 1 V 1 = P 2 V 2 (at constant temperature) Nov 15 1:25 PM A plot of P versus V shows that the volume doubles as the pressure is halved. A plot of v versus 1/P gives a straight line. The slope of this line equals the volume of the constant k. Boyle's law Example 5.2A Boyle's Law A gas that has a pressure of 1.3 atm occupies a volume of 27 L. What volume will the gas occupy if the pressure is increased to 3.9 atm at constant temperature? Nov 18 8:20 AM 3
B. Charles' Law This law says that at constant pressure, the volume of a gas is directly proportional to the temperature (in Kelvin) of the gas. Jacques Charles (1746 1823) Volume = Constant Temperature Chales' Law demo. Egg in a Bottle. The decomposition of sodium azide causes an airbag in an automobile to inflate. (at constant pressure) Example 5.2C Charles's Law A gas at 30.0 o C and 1.00 atm occupies a volume of 0.842 L. What volume will the gas occupy at 60.0 o C and 1.00 atm? Nov 18 8:55 AM Gay Lussac's Law This law says that at constant volume, the pressure of a gas is directly proportional to the temperature (in Kelvin) of the gas. Gay Lussac, Joseph Louis 1778 1850 Hot air Balloons The September 1804 ascension of Gay Lussac and Biot. They climbed to a record 23,000 feet. Misconceptions About Air Nov 19 8:51 AM 4
Boyle s Law Charles s Law Combined Gas Law Dec 12 5:19 PM C. Avogardo's Law Avogardo's law says that for a gas at constant temperature and pressure the volume is directly proportional to the number of moles of gas. Volume = Constant x number of moles (at constant T, P) Example 5.2D Avogardo's Law A 5.20 L sample at 18.0 o C and 2.00 atm pressure contains 0.436 moles of a gas. If we added an additional 1.27 moles of the gas at the same temperature and pressure, what will be the total volume occupied by the gas? Nov 18 8:55 AM 5
5.3 The Ideal Gas Law Solve a variety of problems relating to the ideal gas law. The ideal gas law is a combination of all the laws. It relates pressure, temperature, volume, and the number of moles, of a gas. Pressure x Volume = # of moles of the gas x a constant x temperature PV = nrt The Numerical Value for R for Ideal Gas (1.000 atm) (22.414 L) = (1.000 mol) (R) (273.15 K) Solving for R gives 0.08206 L atm / mol K, when rounded to 4 sig. figs. R = 0.08206 L atm/k mol Keep in Mind: 1. This relationship assumes that the gas behaves ideally. 2. You need to keep track of your dimensions. Many ideal gas law problems are solved using dimensional analysis. 3. Always list what you are given. You may be able to simplify the problem. Nov 19 8:51 AM The conditions assumed for an Ideal Gas: Molecules are perfectly elastic (no STICKINESS) Molecules are point masses (no SIZE) Molecules move at random Plotting the experimentally determined value of, PV/nRT, for exactly one mole of various REAL GASes as a function of pressure, P, shows a deviation from ideality Plots of PV/nRT versus P for several gases (200K). The behavior is close to ideal only at low pressures (less than 1 atm) Plots of PV/nRT versus P for nitrogen gas at three temperatures. The deviations are smaller at the higher temperatures. The deviation from ideal gas behavior is lower at low P and high T and the ideal gas law can be used to predict behavior with little error. Nov 24 8:17 AM 6
Example 5.3A Ideal Gas Law A sample containing 0.614 moles of gas at 12.0oC occupies a volume of 12.9 L. What pressure does the gas exert? Example 5.3B Practice with Gas Laws A sample of methane gas (CH 4 ) at 0.848 atm and 4.0oC occupies a volume of 7.0 L. What volume will the gas occupy if the pressure is increased to 1.52 atm and the temperature increased to 11.0oC? Example 5.3C More Practice with Gas Laws How many moles of a gas at 104 o C would occupy a volume of 6.8 L at a pressure of 270 mmhg? Nov 19 10:22 AM 5.4 Gas Stoichiometry Define STP conditions Do a variety of calculations regarding molar mass, density, and stoichiometry of gasses. STP Standard Temperature and Pressure One mole of an ideal gas at 0 o C (standard temperature) and 1.00 atm (standard pressure) will occupy 22.4 liters STP Means 0 o C (273 K) and 1.000 atm Example 5.4A The Ideal Gas Law and STP What volume will 1.18 moles of O 2 occupy at STP? 1 mole 22.4L at STP 32 g of oxygen at STP Example 5.4B Reactions and the Gas Laws A sample containing 15.0 g of dry ice, CO 2 (s), is put into a balloon and allowed to sublime according to the follow equation: CO 2 (s) CO 2 (g) What is the volume of the balloon at 22.0 o C and 1.04 atm after all the dry ice has sublimed? Example 5.4C Practice with the Ideal Gas Laws 0.500 L of H 2 (g) are reacted with 0.600 L of O 2 (g) at STP according to the equation: 2H 2 (g) + O 2 (g) 2H 2 O(g) What volume will H 2 O occupy at 1.00 atm and 350 o C? Nov 24 8:01 AM 7
Molar Mass of a Gas One very important use of the ideal gas law is the calculation of molar mass of a gas from its measured density. Example 5.4D Density and Molar Mass A gas at 34.0 o C and 1.75 atm has a density of 3.40 g/l. Calculate the molar mass of the gas. Nov 19 10:22 AM 5.5 Dalton's Law of Partial Pressures Solve a variety of problems relating to partial pressure, mole fraction and total pressure. Dalton's law of partial pressures states that for a mixture of gases in a container, the total pressure is the sum of the pressures that each gas would exert if it were alone. John Dalton (1766 1844) P total = P 1 + P 2 +... + P n = (n 1 + n 2 +... + n n )[RT/V] because RT/V will be the same for each of the different gases in the same container. Nov 24 9:35 AM 8
The key problem solving strategy with regard to partial pressure problem is to use the ideal gas law to interconvert between pressure and moles of each gas. Example 5.5A Partial Pressures A volume of 2.0 L of He at 46oC and 1.2 atm pressure was added to a vessel that contained 4.5 L of N 2 at STP. What is the total pressure and partial pressure of each gas after the He is added? Nov 24 9:35 AM Collecting Gases Over Water Sometimes gases are collected over water. The gas produced in a reaction is bubbled through a trough of water and into an upturned gas jar filled with water. The bubbles of gas collect in the top of the gas jar and push the water out of the bottom. The production of oxygen by thermal decomposition of KCIO 3. The MnO 2 is mixed with KClO 3 to make the reaction faster. P Total = P O 2 + P H 2 O Example Oxygen gas was collected over water at 28oC. The vapor pressure of water in air at 28oC is 28.3 torr. Calculate the partial pressure of the oxygen gas in a sample of air at 28oC and 1.03 atm pressure. Nov 26 6:29 PM 9
5.7 Effusion and Diffusion Calculate relative rates of effusion from molar masses and vise versa. Diffusion is the movement of molecules from a high concentration to a low concentration. Relates to the mixing of gases. NH3 +HCl Diffusion Movie Let gas 1 be H 2 and gas 2 be O 2. Therefore, hydrogen molecules effuse four times as fast as those of oxygen Nov 26 6:29 PM Effusion is the term used to describe the passage of a gas through a tiny orifice into an evacuated chamber The rate of effusion measures the speed at which the gas travels through the tiny hole into a vacuum. Graham s Law of Effusion Graham s law states that the rates of effusion of two gases are inversely proportional to the square roots of their molar masses at the same temperature and pressure Example 5.7 Graham's Law of Effusion How many times faster He gas would effuse than NO 2 gas? With regard to diffusion, the important idea is that even though gases travel very rapidly, their motions are in all directions, so mixing is relatively slow. In this case of diffusion, the basic structure of Graham's law holds. Distance traveled 1 Distance traveled 2 Nov 26 7:10 PM 10
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