A P CHEMISTRY - Unit 5: Gases Unit 5: Gases Gases are distinguished from other forms of matter, not only by their power of indefinite expansion so as to fill any vessel, however large, and by the great effect heat has in dilating them, but by the uniformity and simplicity of the laws which regulate these changes". You should be able to: Describe Equipment Barometer Manometer Perform Conversions between units of pressure Recognize and use Basic gas Laws Boyles s Charles s Gay-Lussac s Avogadro s Combined Use Ideal gas law Perform Gas stoichiometry calculations @STP Not @ STP Partial pressures Mole fraction Gas collection problems Changing volumes Kinetic theory of gases Meaning of temperature Root square velocity Effusion Diffusion Real gases Van der Walls equation Difference between real and ideal gases Atmospheric chemistry 5. Pressure Read and outline 5. Define Barometer Mamometer
A P CHEMISTRY - Unit 5: Gases mm Hg torr Standard Atmosphere pacal What are three properties of gases according to section 5.. Explain figure 5.. What is atmospheric pressure? 5. Notes Conversions for Pressure o atm 760 torr 760 mmhg 0.3 kpa 0300 Pa 4.7 psi The barometer, which measures pressure, was invented by Torricelli. A glass tube is filled with liquid mercury and inverted in a dish of mercury. The tube standardizes itself by pushing some of the mercury out into the dish. The space on the top of the tube is a vacuum. A vacuum is a space that has no particles in it and therefore has no pressure. The open dish of mercury controls the mercury that rises in the tube. When more air (pressure) is pushing on the dish, the mercury rises in the tube. When less pressure is pushing on the dish the mercury lowers. This same principle can be applied to boiling water. At sea level (Standard condition), water boils at 00 o C. At the peak of Mt. Everest, the water will boil at a lower temperature because there is less air pressure pressing on the top of the water molecules. It is easier for the gaseous water molecules to escape the surface of the liquid water.
A P CHEMISTRY - Unit 5: Gases 3 Manometer o Used for measuring pressure of any gas o Essentially works the same way as a barometer Example: The pressure of a gas is measured as 49 torr. Represent this pressure in both atmospheres and pascals. 5. The Gas Laws of Boyle, Charles, and Avogadro Read and outline 5. Define Boyle s law Ideal Gas Charles s Law Absolute Zero Avogadro s Law Gay-Lussac s Law Combined Gas Law
5. Notes Boyle s Law Boyle found that there was a correlation between pressure and volume. Then the first type of plot, P vs. V, forms a curve called a hyperbola. If we were to plot the reaction between V vs the inverse P ( P ), then we will get a straight line. This means that pressure and volume are inversely related, or as volume goes up pressure goes down when all other variables are held constant, and the product of P x V is constant. Remember that pressure is force per area. If you increase the volume the force will be acting over a larger area decreasing the pressure of the gas. Boyle s Law: P xv P V A P CHEMISTRY - Unit 5: Gases 4 Example 5. a Sulfur dioxide, a gas that plays a central role in the formation of acid rain, is found in the exhaust of cars and power plants. Consider a.5 L sample of SO at a pressure of 5.6 x 0 3 Pa. If the pressure is changed to.5 x 0 4 Pa at a constant temperature, what will be the new volume of the gas? Charles s Law Charles found that there was a correlation between volume and temperature. If we plot the volume of a gas (at a constant pressure) vs. the temperature we will get a straight line. This means that volume and temperature are directly related. As the temperature increases so does the volume at a constant pressure. Temperature needs to be in Kelvins! Charles s Law: V T V T V T or V T or V T V T Example 5.b A sample of gas at 5 C and atm has a volume of.58 L. What volume does this gas occupy at 38 C and atm.
A P CHEMISTRY - Unit 5: Gases 5 Avogadro s Law Avogadro stated that for a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas. Therefore, as the number of gaseous moles increase in a chemical reaction the volume will increase. Avogadro s Law: V n V n V n or or Vn V n V n Example 5. c Suppose we have a.-l sample containing 0.50 mol oxygen gas at a pressure of atm and a temperature of 5 O C. If all this oxygen were converted to ozone at the same temperature, how many liters of ozone form? Gay Lussac s Law This law states that the pressure and temperature are directly related. As the temperature increases, the molecules speed up creating more collisions. In order to keep constant volume in the system the pressure will increase. The graph of pressure vs. temperature will have a straight line indicating a direct relationship. Temperature needs to be in Kelvins! Gay Lussac s Law: P T P T P T or P T or P T P T Example 5. d A sample of gas has a pressure and temperature of 5. psi and 5 O C. What is the temperature if the pressure increases to 5.5 psi? Combined gas Law Combined Gas Law: PV n T P V n T or PV T P V or P V T P V T T Temperature needs to be in Kelvins!
A P CHEMISTRY - Unit 5: Gases 6 5.3 The Ideal Gas Law Read and outline 5.3 Define Universal Gas Constant Ideal Gas Law What does an equation of state mean? What is meant by a gas acting ideally? 5.3 Notes The ideal gas law puts all of the basic gas laws together. In order to use this equation you will need to assume the gas is acting ideally. The first assumption is that the gas particles are individual, and have a negligible volume compared to the container. The second assumption is that the particles are in constant random motion and the collisions with the walls are the cause of the pressure in the container. The third assumption is that the particles are assumed to exert no forces on each other. This means that the gas does not have attractions or repulsions to any other gas particle or object. The last assumption is that the average kinetic energy of the gas particles is assumed to be directly proportional to the Kelvin temperature of the gas. atm L kpa L Ideal Gas law: PV nrt R 0. 08 or 8. 34 mol K mol K The kpa value is used when dealing with energy problems. Example 5.e A sample of hydrogen gas has a volume of 8.56 L at a temperature of 0 O C and a pressure of.5 atm. How many moles of hydrogen molecules present in this gas sample. Example 5.f A sample containing 0.35 mol of argon gas at a temperature of 3 O C and a pressure of 568 torr is heated to 56 O C and a pressure of 897 torr. Calculate the changes in volume that occur.
A P CHEMISTRY - Unit 5: Gases 7 Worksheet 5.0 Basic Gas Laws Name. A system is initially charged to a pressure of 4.8 atm. Express this pressure in each of the following units: mmhg, torr, Pa, and psi.. An aerosol can contains 400. ml of compressed gas at 5.0 atm pressure. When all the gas is sprayed into a large plastic bag, the bag inflates to a volume of.4 L. What is the pressure of gas inside the plastic bag? 3. If 0.500 mol of nitrogen gas occupies a volume of. L at 0 O C, what volume will.00 mol of nitrogen gas occupy at the same temperature and pressure? 4. A balloon has a volume of 75 cm 3 at 9 O C. At what temperature will the volume of the balloon have increased by 5%? 5. A 5.0 L flask contains 0.60 g of oxygen gas at a temperature of O C. What is the pressure inside the flask? 6. A sealed balloon is filled with.00 L helium at 3 O C and.00 atm. The balloon rises to a point in the atmosphere where the pressure is 0. torr and the temperature is -3 O C. What is the change in volume of the balloon as it ascends from.00 atm to a pressure of 0. torr.
A P CHEMISTRY - Unit 5: Gases 8 5.4 Gas Stoichiometry Read and outline 5.4 Define Molar Volume Standard Temperature and Pressure What are the conditions for STP? When is the only time you can use.4 L for the volume of a gas at one mole? 5.4 Notes The molar volume of a gas @ STP is.4 liters for every mole. You may only use this number if you are @ STP! If another temperature or pressure is listed you will need to use the ideal gas law in the problem. Example 5.4a Quicklime (CaO) is produced by the thermal decomposition of calcium carbonate. Calculate the volume of carbon dioxide at STP produced from the decomposition of 5 g of calcium carbonate. Example 5.4b A sample of methane gas having a volume of.80 L at 5.0 O C and.65 atm was mixed with a sample of oxygen gas having a volume of 35.0 L at 3.0 O C and.5 atm. The mixture was then ignited to form carbon dioxide and water. Calculate the volume of CO formed at a pressure of.50 atm and a temperature of 5 O C.
You can also use the ideal gas law to find density and molar mass of a compound. Solving for Molar mass and density A P CHEMISTRY - Unit 5: Gases 9 Example The density of a gas was measured at.50 atm and 7 O C and found to be.95 g/l. Calculate the molar mass of the gas.
A P CHEMISTRY - Unit 5: Gases 0 Worksheet 5.0 Gas Stoichiometry Name CH 4 + O CO + H O. How many liters of carbon dioxide are made from 6.55 L of methane at STP?. How many grams of water are formed from 9.5 L of oxygen at a pressure of 563 torr at 5 O C? 3. How many liters of carbon dioxide are formed at a pressure of 8. atm and 4 O C? The reaction is started from the same amounts of methane and oxygen added together (6.5 L,.5 atm, at 85 O C). 4. How many grams of water are formed from 7.5 ml of methane at a pressure of 53 psi at 85 O C?
A P CHEMISTRY - Unit 5: Gases 5.5 Dalton s Law of Partial Pressures Read and outline 5.5 Define Dalton s Law of Partial Pressures Partial Pressures Mole Fraction 5.5 Notes For a mixture of gases in a container, the total pressure exerted is the sum of the all the pressures each individual gas exerts. RT Daltons Law of Partial Pressures: P T P + P + P 3... OR P T n Total ( ) ) V Example 5.5a Mixtures of helium and oxygen are used in scuba diving tanks to help prevent the bends. For a particular dive, 46 L He at 5 O C at atm and L of O at 5 O C at atm were pumped in to a tank with a volume of 5.0 L. Calculate the partial pressure of each gas and the total pressure in the tank at 5 O C.
A P CHEMISTRY - Unit 5: Gases Mole Fraction Mole fraction is the ratio of the number of moles of a given component in a mixture to the total number of moles in the mixture. Mole Fraction: n n χ or Total χ P P Total Example 5.5b The partial pressure of oxygen gas was observed to be 56 torr in air with a total atmospheric pressure of 743 torr. Calculate the mole fraction of O present. Example 5.5c The mole fraction of nitrogen in the air is 0.7808. Calculate the partial pressure of N in air when the atmospheric pressure is 760. torr. Example 5.5d A sample of potassium chlorate was heated in a test tube and reacted upon by the following reaction. The oxygen produced was collected by displacement of water at O C at a total pressure of 754 torr. The volume of the gas collected was 0.650 L, and the vapor pressure of water at O C is torr. Calculate the partial pressure of oxygen in the gas collected and the mass of potassium chlorate in the sample that was decomposed.
A P CHEMISTRY - Unit 5: Gases 3 5.6 The Kinetic Theory of Gases Read and outline 5.6 Define Kinetic molecular Theory Joule Velocity Root Mean Square Why can a model never be proved? List the 4 postulates of the Kinetic Theory of Gases... 3. 4. What is the meaning of temperature?
5.6 Notes As we learned in section 5.3 the kinetic theory of gases describe ideal gases. A P CHEMISTRY - Unit 5: Gases 4 The meaning of Temperature Kelvin temperature indicates the average kinetic energy of all the particles in a sample. The Kelvin temperature is an index of the random motion of the gas particles, with higher temperature meaning greater motion. PV n KEavg 3RT RT or KE 3 avg Root Mean Square (rms) Velocity The average velocity of all the particles in a sample of a gas is a special kind of average. 3RT ν rms Where M is the molar mass of the sample. For all calculations related to rms we need to use M kpa L the temperature in Kelvin and the R value of 8. 34. mol K The rms speeds as well as the entire distribution of speeds of gas molecules are a function of temperature. On the graph on the left, the blue line(higher) is a gas sample at a lower temperature and the red line (lower line) is that of a hotter gas sample. Note that the rms speed, u as well as the entire speed distribution changes with temperature for a given gas. The rms speed for a given speed distribution (which is determined by the temperature and molecular weight of the gas) is greater in magnitude than the most probable speed or the mean speed. Example 5.6a Calculate the root mean square velocity for the atoms in a sample of helium gas at 5 O C.
A P CHEMISTRY - Unit 5: Gases 5 Worksheet 5.03 Kinetic Molecular Theory and Partial Pressures Name. What are the final pressures of.00 L of hydrogen gas at 475 torr, and.00l of nitrogen gas at 0.00 atm after they are evacuated into a container that is equal to the total volume (3.00 L)? (all temperatures are equal). Mixtures of helium and oxygen are used in scuba diving tanks to help prevent the bends. For a particular dive, 5 L He at 5 O C and atm 30 L of O at 5 O C and atm were pumped into a tank with a volume of 5.5 L. Calculate the partial pressure of each gas and the total pressure in the tank at 0 O C. 3. The partial pressure of methane is 0.75 atm and that of oxygen is 0.50 atm in a mixture of the two gases. What is the mole fraction of each gas in the mixture? If the mixture occupies a volume of 0.5 L at 65 O C, calculate the total number of moles of gas in the mixture? 4. Helium is collected over water at 5 O C and.00 atm total pressure. What total volume of gas must be collected to obtain 0.568 g of helium? (The vapor pressure of water at 5 O C is 5 torr)
A P CHEMISTRY - Unit 5: Gases 6 5.7 Effusion and Diffusion Read and outline 5.7 Define Diffusion Effusion Graham s Law of effusion What makes certain gases move faster? 5.7 Notes Diffusion is the mixing of gases. Gases as well as liquids will move from a high to low concentration. Gases that are lighter will move faster than heavier gases. Effusion is the passage of gas though a tiny hole into an evacuated chamber. Once again the lighter the gas the faster it will move. Graham s Law of Effusion: Rate Rate M M Example 5.7 a Calculate the ratio of the effusion rates of hydrogen gas and uranium hexafluoride, a gas used in the enrichment process to produce fuel for nuclear reactors.
A P CHEMISTRY - Unit 5: Gases 7 5.8 Real Gases Read and outline 5.8 Define Real Gases 5.8 Real Gases All this time we have been talking about ideal gases. We know that there is no such thing as an ideal gas. Real gases have a volume and attract and repel one another. Real gases also have less space to move because the actual gas takes up space. When gas particles are close together attractive forces take over. This causes the particles to hit the wall slightly less often than they would in the absence of these forces. This means that the observed pressure is less than the actual pressure we assume. The more gas particles there are in a container the more attractions the particles can have for each other. This means that the observed pressure will be less than the actual pressure calculated. Since the gas particles have a volume the volume (of the space to move) of a real gas is less than the observed volume. Van der Waal accounted for pressure and volume in a sample of a real gas to be less than the observed gas in his equation.
A P CHEMISTRY - Unit 5: Gases 8 Worksheet 5.04 Effusion and Diffusion Name. Calculate the average kinetic energy of the CH 4 molecules in a sample of methane gas at 73 K and 546K.. Calculate the root mean squared velocity of the methane molecules at the same temperatures as above. 3. At a certain temperature, Oxygen has a rate of effusion of 30.50 ml/min. The rate of effusion of an unknown gas is measured at the same temperature and was found to be 3.50 ml/min. If the choices are methane, carbon monoxide, nitrogen oxide, carbon dioxide, and nitrogen dioxide, what is the identity of the unknown gas? 4. The rate of effusion of a particular gas was measured and found to be 4.0 ml/min. Under the same conditions, the rate of effusion of pure methane gas is 47.8 ml/min. What is the molar mass of the unknown gas? 5. Calculate the pressure exerted by 0.5000 mole of nitrogen gas in a.0000 L container at 5 O C using: the ideal gas atml L law, van der Waals equation, compare the results. (a.39 and b 0.039 mol mol