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The ideal gas law

The ideal gas law. The ideal gas law: the gas law that includes all four variables: P, V, T, and n When the pressure, volume, and temperature of a contained gas are known, you can use the ideal gas law to calculate the number of moles of the gas. Pressure (P). The (P) in PV = nRT

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The ideal gas law

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  1. The ideal gas law • The ideal gas law: the gas law that includes all four variables: P, V, T, and n • When the pressure, volume, and temperature of a contained gas are known, you can use the ideal gas law to calculate the number of moles of the gas.

  2. Pressure (P) • The (P) in PV = nRT • Force exerted over an area • Measured in: • Millimeters of mercury (mm Hg) • Kilopascals (kPa) • Atmospheres (atm) • 1 atm = 760 mmHg = 101.3 kPa

  3. Practice • 1. The pressure of a tire is measured as 29.4 kPa. What is this pressure in mmHg? • 2. What is 475 mmHg expressed in atm?

  4. Volume • The (V) in PV = nRT • How much space something takes up • Measured in liters (L) • 1 L = 1000 ml = 1000 cm3

  5. Moles • The (n) in PV = nRT • The number of gas particles • Measured in moles (mol) • 1 mol occupies 22.4 L

  6. Temperature • The (T) in PV = nRT • The average kinetic energy of the gas particles (temperature) • Measured in Kelvin (K) • Kelvin = (oC) + 273 • (oC) = (5/9) x (oF – 32) • = K - 273

  7. Practice • 3. What is 450 K in degrees Celsius? • 4. What is 27 degrees Fahrenheit in Kelvin?

  8. Gas Constant • The (R) in PV = nRT • Is a universal constant required to make the Ideal Gas Law work. • Its value depends on what pressure units you are using: • If using atm; R = 0.0821 (L)(atm)/(mol)(K) • If using kPa; R = 8.31 (L)(kPa)/(mol)(K) • If using mmHg; R = 62.4 (L)(mmHg)/(mol)(K)

  9. Standard Temperature and Pressure (STP) The volume of a gas varies with a change in temperature or a change in pressure. Due to these variations, the volume of a gas is usually measured at a standard temperature and pressure. Standard temperature and pressure (STP) means a temperature of 273 K and a pressure of 101.3 kPa/1 atm/760 mmHg. At STP, 1 mol (6.02  1023 representative particles) of any gas occupies a volume of 22.4 L. The quantity 22.4 L is called the molar volume of a gas. (contd.)

  10. Practice • 5. Assuming ideal gas behavior, calculate the number of moles of oxygen, as described by the ideal gas law, in a 12.5-L tank if the pressure is 25,325 kPa and the temperature is 22ºC. • 6. At 34ºC, the pressure inside a nitrogen-filled tennis ball with a volume of 0.148 L is 212 kPa. How many moles of nitrogen gas are in the tennis ball? (contd.)

  11. Practice • 7. What is the volume of 2.30 moles of hydrogen gas at a pressure of 122 kPa and temperature of 20.0 oC? • 8. How much N2 is required to fill a small room with a volume of 27,000 L to 0.98atm at 25 oC?

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