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Understanding the Ideal Gas Equation: Factors Affecting Pressure and Density Calculations

The Ideal Gas Equation (PV = nRT) describes the relationship between pressure, volume, temperature, and the number of moles of a gas. Key factors affecting the pressure of a confined gas include the number of molecules, temperature, and volume. Increasing the number of molecules or temperature raises pressure, while expanding volume lowers it. Various forms of the gas constant (R) apply, and the equation can be used for density calculations. This guide provides insights into applying the Ideal Gas Equation effectively in gas law problems.

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Understanding the Ideal Gas Equation: Factors Affecting Pressure and Density Calculations

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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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