Chapter 10 PHYSICAL CHARACTERISTICS OF GASES
The Kinetic Molecular Theory of Matter To account for the behavior of the atoms and molecules that make up matter, scientists created the kinetic molecular theory. Underlying premise of the KMT: All particles of matter are in constant motion. KMT can describe the particles of solids, liquids, and gases.
The Kinetic Molecular Theory of Gases The KMT of gases revolves around 5 basic assumptions: 1. Gases are made up of large numbers of particles that are far apart. 2. Gas particles are involved in elastic collisions with container walls. 3. Gas particles possess kinetic energy due to their rapid, random motion.
The Kinetic Molecular Theory of Gases 4. There are no forces of attraction or repulsion between gas particles. 5. The average kinetic energy of gas particles depends on the temperature of the gas. Gases that meet all 5 assumptions of the KMT are called ideal gases. Many physical properties of gases are attributed to the KMT.
The Nature of Gases The 5 primary physical properties that can be attributed to the KMT are: 1. Expansion 2. Low Density 3. Compressibility 4. Diffusion 5. Effusion
Deviations from the KMT If a gas does not adhere to the 5 assumptions of the KMT, then the gas is classified as a real gas. Gases behave ideally typically when gas particles are far enough apart and have enough kinetic energy. 1873: Johannes van der Waals accounts for deviations from ideal behavior (creates van der Waals equation) Van der Waals figured out that particles of real gases occupy space and exert attractive forces on each other. If these gas particles are at very high pressure and low temperature, then the deviations would be very significant.
Pressure Pressure is the force per unit area on a surface. P = force/area (P = F/A) To express pressure using SI units, we use the newton. A newton is the force that will increase the speed of one kilogram mass by one meter per second each second it is applied.
Measuring Pressure Early 1600s, Italian scientist Evangelista Torricelli creates a device to measure the pressure exerted by the atmosphere, a barometer. Torricelli’s device used a capillary tube with a vacuum and a pan of mercury.
Measuring Pressure Torricelli realized that the mercury from the pan rose to a height of 760 mm. He determined that this value must be the atmospheric pressure exerted on the mercury.
Measuring Pressure We can express pressure using various units: Millimeters of mercury Torrs (torr) Atmospheres (atm) Pascals (Pa) Kilopascals (kPa) Pounds per square inch (psi) The SI unit for pressure is the pascal.
Standard Temperature and Pressure Standard conditions of exactly 1 atm pressure and 0°C are called standard temperature and pressure or STP. We can express standard pressure as: 1 atm = 760 torr = 760 mm Hg = 101.325 kPa (or 101,325 Pa)
GAS LAWS
Gas Laws There will be 6 gas laws that will be introduced: Boyle’s Law Charles’s Law Gay-Lussac’s Law Combined Gas Law Ideal Gas Law Dalton’s Law of Partial Pressures
Boyle’s Law Robert Boyle: 1662 Derives relationship between volume and pressure Uses J-tubes to gather information
Boyle’s Law Relationship between pressure and volume P1V1 = P2V2 Inverse proportionality
Boyle’s Law Sample Question A sample of oxygen gas has a volume of 150 mL when its pressure is 0.947 atm. What will the volume of the gas be at a pressure of 0.987 atm if the temperature remains constant?
Boyle’s Law Sample Question A balloon filled with helium gas has a volume of 500 mL at a pressure of 1 atm. The balloon is released and reaches an altitude of 6.5 km, where the pressure is 0.5 atm. Assuming that the temperature has remained the same, what volume does the gas occupy at this height?
Boyle’s Law Sample Question A weather balloon with a volume of 1.375 L is released from Earth’s surface at sea level. What volume will the balloon occupy at an altitude of 20 km, where the air pressure is 10 kPa?
Charles’s Law Jacques Charles : 1787 Creates relationship between volume and absolute temperature V1/T1 = V2/T2 In order to use Charles’s law, temperature values must be in Kelvin! T (in K) = T (in Celsius) + 273
Charles’s Law Sample Problem A sample of neon gas occupies a volume of 752 mL at 25°C. What volume will the gas occupy at 50°C if the pressure remains constant?
Charles’s Law Sample Problem A helium-filled balloon has a volume of 2.75 L at 20°C. The volume of the balloon decreases to 2.46 L after it is placed outside on a cold day. What is the outside temperature?
Charles’s Law Sample Problem A gas at 65°C occupies 4.22 L. At what Celsius temperature will the volume be 3.87 L, assuming the same pressure?
Gay-Lussac’s Law Joseph Gay-Lussac – 1802 Determines relationship between pressure and Kelvin temperature Pressure and temperature are directly proportional. P1/T1 = P2/T2
Gay-Lussac’s Law Sample Problem The gas in an aerosol can is at a pressure of 3.00 atm at 25°C. Directions on the can warn the user not to keep the can in a place where the temperature exceeds 52°C. What would the gas pressure in the can be at 52°C?
Gay-Lussac’s Law Sample Problem Before a trip from New York to Boston, the pressure in an automobile tire is 1.8 atm at 20°C. At the end of the trip, the pressure gauge reads 1.9 atm. What is the new temperature of the air inside the tire?
Gay-Lussac’s Law Sample Problem At 120°C, the pressure of a sample of nitrogen is 1.07 atm. What will the pressure be at 205°C, assuming constant volume?
Combined Gas Law Sometimes gases undergo changes in temperature, pressure, and volume all at the same time. We can used combine Boyle’s, Charles’s, and Gay-Lussac’s laws in a single expression. P1V1/T1 = P2V2/T2 We can derive each individual gas law by holding a variable (P, V, or T) constant.
Combined Gas Law Sample Problem The volume of a gas is 27.5 mL at 22.0°C and 0.974 atm. What will the volume be at 15.0°C and 0.993 atm?
Combined Gas Law Sample Problem A 700 mL sample of gas at STP is compressed to a volume of 200 mL, and the temperature is increased to 30°C. What is the new pressure of the gas in kPa?
Combined Gas Law Sample Problem A helium-filled balloon has a volume of 50 mL at 25°C and 1.08 atm. What volume will it have at 0.855 atm and 10°C?
Dalton’s Law of Partial Pressures John Dalton Proposed that the total pressure of a mixture of gases is equal to the sum of the partial pressures of each individual gas Ptotal = P1 + P2 + P3 … Sometimes, gases are collected over water. Dalton’s law allows for the determination of the partial the gas using the following equation: Ptotal = Pgas + Pwater
Dalton’s Law Sample Problem Helium gas is collected over water at 25C. What is the partial pressure of the helium, given that the barometric pressure is 750.0 mm Hg?
Dalton’s Law Sample Problem A mixture of three gases, A, B, and C, is at a total pressure of 6.11 atm. The partial pressure of gas A is 1.68 atm; that of gas B is 3.89 atm. What is the partial pressure of gas C?
Dalton’s Law Sample Problem Three of the primary components of air are carbon dioxide, nitrogen, and oxygen. In a sample containing a mixture of only these gases at exactly 1 atm, the partial pressures of carbon dioxide and nitrogen are given as 0.285 torr and 593.525 torr, respectively. What is the partial pressure of oxygen?
Ideal Gas Law Relates pressure, temperature, volume, and amount of substance (moles) P, V, n, T relationship Uses a constant = ideal gas constant, R R = 0.0821 L*atm/mol*K
Ideal Gas Law Sample Problem What is the pressure in atmospheres exerted by a 0.50 mol sample of nitrogen gas in a 10 L container at 298 K?
Ideal Gas Law Sample Problem What is the volume of 0.25 mol of oxygen gas at 20.0C and 0.974 atm pressure?
Ideal Gas Law Sample Problem A 2.07 L cylinder contains 2.88 mol of helium gas at 22C. What is the pressure in atmospheres of the gas in the cylinder?
Ideal Gas Law Sample Problem A tank of hydrogen gas has a volume of 22.9 L and holds 14.0 mol of the gas at 12C. What is the reading on the pressure gauge in atmospheres?