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Chapter 13: Gases

Chapter 13: Gases. Sec. 13.2: The Ideal Gas Law. Objectives. Relate the amount of gas present to its pressure, temperature, & volume by using the ideal gas law Compare the properties of real & ideal gases. The Ideal Gas Law.

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Chapter 13: Gases

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  1. Chapter 13: Gases Sec. 13.2: The Ideal Gas Law

  2. Objectives • Relate the amount of gas present to its pressure, temperature, & volume by using the ideal gas law • Compare the properties of real & ideal gases

  3. The Ideal Gas Law • In previously covered gas laws, the principles held true for a “given amount” of gas or a “fixed mass” of gas. Why? • Changing the number of particles present will affect at least one other variable. • If V & T are held constant, the number of particles will affect the P. • If P & T are held constant, the number of particles will have an affect on the volume.

  4. The Ideal Gas Law • We can conclude P, V, T, and number of particles are interrelated. • Since the number of particles and moles are directly proportional, “n” (representing # of moles) can be used in a mathematical statement describing the relationship of the 4 variables listed above. • Keep in mind: n = moles = mass/molar mass.

  5. The Ideal Gas Law PV = nRT • The ideal gas law describes the physical behavior of an ideal gas in terms of P, V, T, and n of gas present. • R is called the ideal gas constant. Its exact value will depend on the units used for pressure.

  6. R values • 0.0821 L-atm mol-K • 8.314 L-kPa mol-K • 62.4 L-mmHg mol-K • You WILL be given the R value with a problem BUT it may not have the correct units. You may have to convert it.

  7. For example If the R value you are given is 0.0821 L-atm but pressure is given in kPa, mol-K you can convert to kPa by multiplying: 0.0821 L-atm x 101.3 kPa = 8.317 L-kPa mol-K 1 atm mol-K

  8. Practice Problems Use R values previously given. • Calculate the number of moles of gas contained in a 3.0 L vessel at 3000 K with a pressure of 1.50 atm. • Determine the Celsius temperature of 2.49 moles of gas contained in a 1.00 L vessel at a pressure of 143 kPa. • Calculate the volume that a 0.323 mol sample of a gas will occupy at 265 K and a pressure of 0.900 atm.

  9. Applying the Ideal Gas Law • The ideal gas law can be used to calculate the molar mass and density of a gas if the mass of the gas is known. • Remember, the number of moles of a gas (n) is equal to the mass (m) divided by the molar mass (M) or n = m/M • PV = nRT becomes PV = mRT; M = mRT M PV

  10. Rearrange ... • M = mRT PV • Recall that density (D) = m/V • M = DRT P • D = MP RT

  11. Practice Problems • How many grams of gas are present in a sample that has a molar mass of 70 g/mol and occupies a 2.00 L container at 117 kPa and 35.1 0C? • What is the molar mass of a pure gas that has a density of 1.40 g/L at STP? • What is the density of a gas at STP that has a molar mass of 44.0 g/mol?

  12. Real vs. Ideal Gases • An ideal gas is one whose particles take up no space, are in constant random motion, have no intermolecular attractive or repulsive forces, and have perfectly elastic collisions. • No gas is truly ideal. • All gas particles have some volume. • All gas particles have some intermolecular attractions. • Some energy is generally lost in collisions.

  13. Real vs. Ideal Gases • An ideal gas follows the gas laws under all conditions of T & P. • Most gases behave like ideal gases at most T & P levels. • If the P is extremely high, however, the particles are forced so close together that the gas will liquefy. • If the T is extremely low, the particles have slowed down so much that forces between molecules are felt & condensation occurs.

  14. Real vs. Ideal Gases • In addition, gases made up of polar molecules do not behave as ideal gases. The oppositely charged ends of polar molecules have large electrostatic forces. • Also, larger gas molecules behave less like ideal gases that smaller ones do. The particles of gases made up of large molecules, like C4H10, occupy more actual volume than particles of smaller molecules, like He.

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