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Gases and Moles

Gases and Moles. The Ideal Gas Equation. What factors affect the pressure of a confined gas?. Number of molecules Temperature Volume of the container. Think in terms of the number of collisions. Number of molecules.

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Gases and Moles

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  1. Gases and Moles The Ideal Gas Equation

  2. What factors affect the pressure of a confined gas? • Number of molecules • Temperature • Volume of the container Think in terms of the number of collisions.

  3. Number of molecules Increasing the number of molecules increases the number of collisions … … which increases the pressure. Where n is the number of moles of molecules P µ n

  4. Temperature Increasing the temperature makes the molecules move faster, increasing the number of collisions … … which increases the pressure. P µ T Where T is the absolute temperature

  5. Volume 1 V Increasing the volume of the container decreases the number of collisions … … which decreases the pressure. P µ Where V is the volume

  6. Sooooo… P µ 1 P µ V P µ n P µ T n T V

  7. Make it into an equation P = P µ n T V n R T V

  8. The Ideal Gas Equation P = R T n V … is usually written as … = R T P V n

  9. The Ideal Gas Equation L atm mol K P = V n R T R is the “gas constant” R = 0.0821

  10. The Ideal Gas Equation P = V n R T Can R be in units other than L atm ? mol K

  11. The Ideal Gas Equation P = V n R T R = 0.0821 L atm/mol K R = 8.314 L kPa/mol K R = 62.4 L torr/mol K

  12. The Ideal Gas Equation P = V n R T R = 0.0821 L atm/mol K R = 8.314 L kPa/mol K R = 62.4 L torr/mol K

  13. The Ideal Gas Equation P = V n R T R = 0.0821 L atm/mol K R = 8.314 L kPa/mol K R = 62.4 L torr/mol K

  14. The Ideal Gas Equation P = V n R T R = 0.0821 L atm/mol K R = 8.314 L kPa/mol K R = 62.4 L torr/mol K

  15. Ideal Gas Equation The ideal gas equation relates pressure, volume, temperature and the number of moles of a quantity of gas. PV = nRT

  16. Ideal Gas Equation Use the ideal gas equation whenever the problem gives you mass or moles, or asks for a mass or a number of moles. PV = nRT

  17. Ideal gas equation problem: Some ammonia gas (NH3) is contained in a 2.50 L flask at a temperature of 20.0 C. If there are 0.0931 moles of the gas, what is its pressure?

  18. Solution L atm (0.0821 mol K PV = nRT P = (nRT)/V )(293 K) = (0.0931 mol) 2.50 L 0.896 atm P =

  19. Here’s another one Find the volume of 1.00 mole of nitrogen gas (N2) at 0.0 C and 1.00 atm of pressure.

  20. Solution L atm (0.0821 mol K PV = nRT V = (nRT)/P )(273 K) V = (1.00 mol) 1.00 atm V = 22.4 L

  21. Ideal gas equation problem: How many grams of sulfur trioxide are in an 855 mL container at a pressure of 1585 torr and a temperature of 434 C? The answer is 2.46 g SO3

  22. The Ideal Gas Equationcan be used toderive theCombined Gas Law

  23. The Combined Gas Law Start with the ideal gas equation: PV = nRT

  24. The Combined Gas Law Suppose the volume, pressure and temperature change to give a new pressure, volume and temperature. P1V1 = nRT1 P2V2 = nRT2 and

  25. The Combined Gas Law Now, solve for what doesn’t change, the constants n and R: P1V1 = nRT1 P2V2 = nRT2 and

  26. The Combined Gas Law P1V1 = nR P2V2 T1 = nR T2 Now, solve for what doesn’t change, the constants n and R: and

  27. The Combined Gas Law P1V1 = nR P2V2 T1 = nR T2 Since both are equal to nR, we can make a new equation. and

  28. The Combined Gas Law P1V1 P2V2 T1 T2 Since both are equal to nR, we can make a new equation. =

  29. The Combined Gas Law P1V1 P2V2 T1 T2 This is the Combined Gas Law =

  30. The Combined Gas Law P1V1 P2V2 T1 T2 = It can be derived from the laws of Boyle, Amonton and Charles, or the Ideal Gas Equation

  31. The Ideal Gas Equationand Density

  32. Density calculations m n = M Start with the equation for density: m D = V And an equation for “moles”: Where m = mass and M = molar mass

  33. Density calculations m n = M mRT PV = M Now substitute into the ideal gas equation … PV = nRT and get

  34. Density calculations mRT PV = M mRT P = VM Now rearrange to get

  35. Density calculations m D = V mRT DRT P = P = VM M Recall that

  36. Density calculations DRT P = M PM D = RT Solving for density, becomes:

  37. Density calculations PM D = RT The density of a gas depends on the molar mass and the pressure and temperature.

  38. Density Problem 1. Determine the density of nitrogen, N2, gas (a) at STP (b) at a pressure of 695 torr and a temperature of 40.0 C. The answers are 1.25 g/L, and 0.996 g/L.

  39. Another Problem 2. Determine the molar mass of a gas which has a density of 8.53 g/L at a pressure of 2.50 atm and a temperature of 500.0 K? 140. g/mol The answer is

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