Chapter 10 Gases Conditions of ideal gases: Ideal gases have no attractive forces between the molecules. the atoms volume taken into account when looking at the volume a gas occupies. Low pressure and high temperature conditions Measurement of pressure: Barometer Manometer Units Relationship of pressure and volume (Boyle s Law) Relationship of Temperature and Volume (Charles Law) Relationship of Quantity and Volume (Avogadro s Law) Derivation of the Ideal Gas Law and the R constant Values for the R constant:
Applications of the Ideal Gas Law Gas Densities and Molar Masses Volumes of Gases in Chemical Reactions (Stoichiometric relationships) STP and same pressure/ temperature Example1: The industrial synthesis of nitric acid involves reaction of nitrogen dioxide gas with water. (Nitrogen monoxide gas is also produced) How many liters of nitrogen dioxide can be produced if 5 liters of nitrogen dioxide react at STP Example 2: The industrial synthesis of nitric acid involves reaction of nitrogen dioxide gas with water. (Nitrogen monoxide gas is also produced) How many liters of nitrogen dioxide can be produced if 5 liters of nitrogen dioxide react at 5.00 atm and 298 K?
Varying temperature and pressure Example 3: Ammonia reacts with oxygen at 850C and 5.00 atm. The nitrogen monoxide produced is sent across a collection tube to a container at a temperature of 25C and 1atm. (NO remains a gas). How many liters of NO will be produced if 2 liters of ammonia gas is used? (water is also a product in this reaction) Dalton s Law of Partial Pressures Example 4: Collecting gas over water A sample of KClO 3 is partially decomposed producing oxygen gas that is collected over water. The volume of the gas collected is 0.250L at 26 and 765 torr. a. How many moles of O 2 are collected? b. How many grams KClO 3 were decomposed? c. When dry, what volume would the collected oxygen gas occupy at the same temperature and pressure?
Example 5: Mixing gases Consider the arrangement of bulbs as shown in the figure below. Each of the bulbs contain a gas at the pressure shown. What is the pressure of the system when all the stopcocks are opened, assuming the temperature remains constant. We can neglect the volume of the capillary tubes connecting the bulbs. Kinetic Molecular Theory Gases consist of molecules in continuous random motion. The volume of the molecule negligible compared to the total volume the gas occupies. Attractive and repulsive forces negligible. Energy can be transferred between molecules during collisions, but the average KE doesn t change. The average KE is proportional to temperature.
Molecular effusion and diffusion (Graham s Law) Average kinetic energy of any molecule can be found by ½ mu 2 where m = mass of particle and u is the speed. If a particle is light, its rms should be high. Therefore the KE should be relatively the same. Rms can be calculated using the expression Example 6: Cory releases methane gas in class. Calculate the rms of these gas particles. Diffusion (spread of gas across a room) Effusion (gas out of a small opening) Graham s Law of Effusion: (Derive from rms of two gases) Example 7: An unknown gas of a homonuclear diatomic molecule effuses at arate that is 0.355 times that of oxygen at the same temperature. What is the identity of the unknown gas?
Real Gases: The Van der Waals equation. Real gases have finite volumes and they do have attractions. We need to add corrections to the ideal gas law to account for the volume of molecules AND molecular attractions. Since each gas has a different molecular size and different intermolecular attractions, each gas needs its own correction factor. a and b are constants that vary for each gas. (Table 10.3 on page 373 gives van der Waals constants for gas molecules.) P = nrt n 2 a ----- - ----- V nb V 2 Example 8: Consider a sample of 1.00 mol of CO 2 confined to a volume of 3.00 L at 0.0 C. Calculate the pressure of the gas using (a) ideal gas law (b) van der Waals equation