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Section 11–3: The Ideal Gas Law

Section 11–3: The Ideal Gas Law. Coach Kelsoe Chemistry Pages 383–385. Section 11–3 Objectives. State the ideal gas law. Derive the ideal gas constant and discuss its units.

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Section 11–3: The Ideal Gas Law

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  1. Section 11–3:The Ideal Gas Law Coach Kelsoe Chemistry Pages 383–385

  2. Section 11–3 Objectives • State the ideal gas law. • Derive the ideal gas constant and discuss its units. • Using the ideal gas law, calculate pressure, volume, temperature, or amount of gas when the other three quantities are known. • Using the ideal gas law, calculate the molar mass or density of a gas. • Reduce the ideal gas law to Boyle’s law, Charles’s law, and Avogadro’s law. Describe the conditions under which each applies.

  3. The Ideal Gas Law • In Chapter 10 we talked about the three quantities needed to describe a gas sample: pressure, volume, and temperature. • We can further characterize a gas sample by using a fourth quantity – the number of moles of the gas sample. • The number of molecules or moles present will always affect at least one of the other three quantities.

  4. The Ideal Gas Law • Gas pressure, volume, temperature, and the number of moles are all interrelated. There is a mathematical relationship that describes the behavior of a gas sample for any combination of these conditions. • The ideal gas law is the mathematical relationship among pressure, volume, temperature, and the number of moles of a gas. • The equation for the ideal gas law is PV = nRT.

  5. The Ideal Gas Law • PV = nRT, where • P = pressure (in atmospheres) • V = volume (in liters) • n = number of moles of gas • R = the ideal gas constant • T = temperature (in Kelvins) • Since all these values are proportional, you could actually derive the ideal gas law from Boyle’s law, Charles’s law, and Avogadro’s law.

  6. The Ideal Gas Constant • In the equation representing the ideal gas law, the constant R is known as the ideal gas constant. • The value of R depends on the units chosen for pressure, volume, and temperature. • For our calculations, we will let R be 0.0821 L·atm/mol·K. This means our measurements for pressure must be in atm, our volume must be in L, and our temperature must be in K.

  7. The Ideal Gas Constant • We can solve for R by doing R = PV/nT at STP: • P = 1 atm • V = 22.41410 L • n = 1 mol • T = 273.15 K • R = PV/nT = (1 atm)(22.41410 L)/(1 mol)(273.15 K) • R = 0.08205784 L·atm/mol·K

  8. The Ideal Gas Constant • There are other values for R when you use different units. • R = PV/nT at STP: • P = 760 mm Hg • V = 22.41410 L • n = 1 mol • T = 273.15 K • R = PV/nT = (760 mm Hg)(22.41410 L)/(1 mol)(273.15 K) • R = 62.4 L·mm Hg/mol·K

  9. The Ideal Gas Constant • There are other values for R when you use different units. • R = PV/nT at STP: • P = 101.325 kPa • V = 22.41410 L • n = 1 mol • T = 273.15 K • R = PV/nT = (101.325 kPa)(22.41410 L)/(1 mol)(273.15 K) • R = 8.314 L·kPa/mol·K

  10. Finding P, V, T, or n From the Ideal Gas Law • You can easily solve for pressure, volume, temperature, or number of moles if you have three of the other values. • The value for R is always the same, so you’ll never have to solve for it. • P = nRT/V • V = nRT/P • n = PV/RT • T = PV/nR

  11. Sample Problem 11–3 • What is the pressure in atmospheres exerted by a 0.500 mol sample of nitrogen gas in a 10.0 L container at 298 K? • Given: V = 10.0 L, n = 0.500 mol, T = 298 K • Unknown: P of N2 in atmospheres • PV = nRT P = nRT/V • P = (0.500 mol)(0.0821 L·atm/mol·K)(298 K) / 10.0 L • P = 1.22 atm

  12. Sample Problem 11–4 • What is the volume, in liters, of 0.250 mol of oxygen gas at 20.0°C and 0.974 atm pressure? • Given: P = 0.974 atm, n = 0.250 mol, T = 293.15 K • Unknown: V of O2 in liters • PV = nRT V = nRT/P • V = (0.250 mol)(0.0821 L·atm/mol·K)(293.15 K) / 0.974 atm • V = 6.17 L

  13. Sample Problem 11–5 • What mass of chlorine gas, Cl2, in grams, is contained in a 10.0 L tank at 27°C and 3.50 atm of pressure? • Given: P = 3.50 atm, V = 10.0 L, T = 300 K • Unknown: mass of Cl2 in grams • We don’t have a formula for mass, but we can find it by finding the value of n. • PV = nRT n = PV/RT • n = (3.50 atm)(10.0 L)/(0.0821 L·atm/mol·K)(300K) • n = 1.42 mol Cl2; 1.42 mol x 70.90 g/1 mol = 101 g

  14. Finding Molar Mass from the Ideal Gas Law • You can solve for molar mass once you’ve found the number of moles, but scientists have derived another form of the ideal gas law to save us time. • Since the number of moles (n) is equal to mass (m) divided by molar mass (M), we can substitute m/M for the letter n. • We can use PVM = mRT, where P is pressure, V is volume, M is molar mass (from periodic table), m is the sample mass, R is the ideal gas constant, and T is temperature.

  15. Sample Problem 11–6 • At 28°C and 0.974 atm, 1.00 L of gas has a mass of 5.16 g. What is the molar mass of this gas? • Given: P = 0.974 atm, V = 1.00 L, T = 301 K, m = 5.16 g • Unknown: M of gas in g/mol • PVM = mRT M = mRT/PV • M = (5.16 g)(0.0821 L·atm/mol·K)(301 K)/(0.974 atm)(1.00 L) • M = 131 g/mol

  16. Finding Density from the Ideal Gas Law • Density (D) is equal to mass (m) divided by (V), so therefore V = m/D. By subbing m/D for V, you can solve for density if you are given molar mass, and vice versa. • MP = DRT

  17. Vocabulary • Ideal gas constant • Ideal gas law

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