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The Ideal Gas law

Bringing It All Together. The Ideal Gas law. Introduction. When we use the combined gas law we allow P , V , and T to vary. we keep the amount of gas constant . If we vary the amount of gas as well as the pressure, volume, and temperature we will use the Ideal Gas Law. Introduction.

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The Ideal Gas law

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  1. Bringing It All Together The Ideal Gas law

  2. Introduction • When we use the combined gas law • we allow P, V, and T to vary. • we keep the amount of gas constant. • If we vary the amount of gas as well as the pressure, volume, and temperature • we will use the Ideal Gas Law

  3. Introduction • When we use the phrase “Ideal Gas Law,” • we are talking about an ideal gas • we are not talking about a real gas • An ideal gas obeys all of the assumptions of the kinetic theory of gases - • small particles • no attraction • moving rapidly • perfectly elastic

  4. Introduction • Under most common circumstances, real gases act like ideal gases. • Only under conditions of - • low temperature • or • high pressure • will real gases deviate from ideality.

  5. Application • Applying the kinetic theory, as we add an amount of gas to a container of gas, we are introducing additional particles to collide with the walls of the container. • Pressure goes up to keep V & T const. • Volume goes up to keep P & T const. • Temperature goes down to keep P & V const.

  6. Application • This means that the amount (number of mols) of material varies - • directly with pressure and volume • inversely with temperature • We will use the equation - • PV = nRT • P is pressure, V is volume, n is mols of gas, T is temperature, and R is the gas constant.

  7. Application • PV = nRT • P: measured in atm, kPa, or mmHg • V: measured in L • n: measured in mol • T: measured in K • R: a constant whose value depends on the units of P, V, n, and T

  8. Application • PV = nRT • If P is measured in atm: • R = 0.0821 atm-L/mol-K • If P is measured in kPa: • R = 8.31 kPa-L/mol-K • If P is measured in mm Hg: • R = 62.4 mm Hg-L/mol-K

  9. Application • PV = nRT • Remember: • The value of R is dependent on the units of pressure. • Always use the correct value of R. • All appropriate values for R will be given to you for any test or quiz.

  10. nRT (0.125)(0.0821)(430) P = = atm V (4.00) Example 1 What is the pressure, in atm, of 0.125 mols of helium in a 4.00 L container at a temperature of 153°C (430 K)? P = ? atm V = 4.00 L n = 0.125 mol R = 0.0821 atm-L/mol-K T = 430 K PV = nRT ➔ P = 1.10321875 atm = 1.10 atm

  11. nRT (2.50)(8.31)(315) V = = L P (85.0) Example 2 What is the volume of 2.50 mols of oxygen at a pressure of 85.0 kPa and a temperature of 42.0°C (315 K)? P = 85.0 kPa V = ? L n = 2.50 mol R = 8.31 kPa-L/mol-K T = 315 K PV = nRT ➔ V = 76.98970588 L = 77.0 L

  12. PV (760)(22.4) n = = mol RT (62.4)(273) Example 3 How many mols of nitrogen is contained in a volume of 22.4 L at a pressure of 760 mm Hg and a temperature of 0°C (273 K)? P = 760 mm Hg V = 22.4 L n = ? mol R = 63.4 mm Hg-L/mol-K T = 273 K PV = nRT ➔ n = 0.999342538 mol = 1.00 mol

  13. PV (1.20)(15.0) T = = K nR (1.60)(0.0821) Example 4 What is the temperature of 1.60 mols of neon contained in a volume of 15.0 L at a pressure of 1.20 atm? P = 1.20 atm V = 15.0 L n = 1.60 mol R = 0.0821 atm-L/mol-K T = ? K PV = nRT ➔ T = 137.0280146 K = 137 K

  14. We can also combine this with other equations to give us even more detailed information

  15. PV (1,640)(565) n = = mol RT (62.4)(400) Example 5 What mass of Argon (M = 40.0 g/mol) is in a volume of 565 L at a pressure of 1,640 mm Hg and a temperature of 127°C (400 K)? P = 1,640 mm Hg V = 565 L n = ? mol R = 63.4 mm Hg-L/mol-K T = 400 K PV = nRT ➔ n = 37.1 mol m = nM = (37.1)(40.0) g m = 1,480 g

  16. Summary • When we use the phrase “Ideal Gas Law,” • we are talking about an ideal gas • we are not talking about a real gas • An ideal gas obeys all of the assumptions of the kinetic theory of gases - • small particles • no attraction • moving rapidly • perfectly elastic

  17. Summary • We will use the equation - • PV = nRT • P is pressure, V is volume, n is mols of gas, T is temperature, and R is the gas constant. • The value of R is dependent on the units of pressure. • Always use the correct value of R. • All appropriate values for R will be given to you for any test or quiz.

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