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Gases Jespersen Chapter 11 (very loosely)

Gases Jespersen Chapter 11 (very loosely). Dr. C. Yau Spring 2014. 1. Properties of Gases: Macroscopic View. Gases can be compressed Gases exert a pressure. The pressure of a gas depends on how much gas is confined. Gases fill completely any container into which they are placed.

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Gases Jespersen Chapter 11 (very loosely)

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  1. GasesJespersen Chapter 11(very loosely) Dr. C. Yau Spring 2014 1

  2. Properties of Gases: Macroscopic View • Gases can be compressed • Gases exert a pressure. • The pressure of a gas depends on how much gas is confined. • Gases fill completely any container into which they are placed. • Gases mix freely and quickly with each other. 2

  3. Kinetic Molecular Theory (KMT) of Gases:View at the Particulate Level • A gas is made of an extremely large number of very tiny particles that are in constant, random motion. • The gas particles themselves occupy a net volume so small in relation to the volume of their container that their contribution to the total volume can be ignored. • The particles often collide in perfectly elastic collisions with themselves and with the walls of the container. 3

  4. Kinetic Molecular Theory of Gases:View at the Particulate Level (cont'd.) 4. The particles move in straight lines neither attracting nor repelling each other. 5. The pressure of a gas is due to the frequency and force of collisions of the particles with the sides of the container. 6. The particles within a sample of gas have different kinetic energy (KE), but for samples at a given temperature, the average kinetic energy is the same. It is affected only by temperature. 4

  5. The Ideal Gas Law This is the law for the ideal gas. It's the gas that is ideal, not the law. There are "real gases" that do not follow this law. KNOW THIS WELL! PV = nRT where P = pressure of gas in atm V = volume of gas in L n = # moles of gas T = temp. of gas in Kelvin R = 0.08206 atm L mol-1 K-1 or (no need to memorize R) 5

  6. Parameters of a Gas To describe a gas, one must specify the P, V and T as they are all interdependent on each other. Pressure: Units: 1 atm = 760 mmHg = 760 torr 1 mmHg = 1 torr What has P to do with mm and mercury? The barometer measures the P of the atmosphere. It is constructed with a tube of mercury, and the height of the mercury column is measured in millimeters, hence, mm Hg. 6

  7. Parameters of a Gas (cont'd.) The column of Hg is affected by the pressure of the atmosphere pressing down on the reservoir of Hg. Which day has the higher atmospheric pressure? A taller column means a higher P. Day 1 has the higher atmospheric pressure (or barometric pressure). 752 mm Hg means a higher P than 750 mm Hg. Day 1 Day 2 7

  8. Parameters of a Gas: P, V, T (cont'd.) Pressure: The manometer measures the P of a gas sample. Temperature: • The Celsius scale was arbitrarily based on the fp of water to be zero. • The behavior of gases cannot be based on something arbitrary. Instead it is based on the absolute zero being the lowest temp possible. • The Kelvin scale: TK = ToC + 273.15 KNOW THIS! • If P is not changed, V of gas decreases with T. Theoretically when V = zero, T is at lowest (zero K). • KE of gas particles decreases with T. • At 0 K, theoretically gas particles have zero KE (motionless).

  9. Parameters of a Gas: P, V, T (cont'd.) Volume: Varies with P and T. This makes it difficult to compare gases when measured at different P and T...hence the definition of STP: STP (Standard Temperature & Pressure) KNOW THIS WELL! STP means "standard temperature & pressure):0oC (273.15 K)and 1 atm (760 mm Hg) 9

  10. Molar Volume at STP For ease of comparison, we usually give the volume of a gas at STP. For example, which gas sample contains more molecules of gas? Sample A: 3.45 L of gas at 758 mmHg and 38.4oC Or Sample B: 1.22 L of gas at 798 mmHg and 17.3oC? Sample A has a larger V, but it is at a lower P and higher T. It is difficult to compare the two samples without doing some calculations. 10

  11. Molar Volume at STP "Molar volume" refers to the V of one mole of gas. Molar Volume of any ideal gas at STP = 22.4 L Do not forget this is ONLY at STP, for ideal gas. For an ideal gas, since the gas particles have negligible volume and do not sense the presence of neighboring particles (no attraction nor repulsion) the volume does NOT depend on the type of gas we have.

  12. Gas Calculations TWO types of Gas Problems dealing with PV=nRT: 1) One set of parameters given: Use PV=nRT 2) Two sets of parameters given:Rearrange equation so only R is on one side of eqn: Since R is a constant, this means that under any conditions, PV/nT must always equal to each other: 12

  13. Example 1 (from handout): What is the volume of one mole of gas at STP? First identify which type of problem it is. Example 2 What does "molar volume of a gas" refer to? Example 3 Sulfur hexafluoride SF6 is a colorless, odorless, very unreactive gas. Calculate the pressure (in atm) exerted by 1.82 moles of the gas in a steel vessel of volume 5.43 L at 69.5C.

  14. Example 4 A gas at 772 mmHg and 35.0C occupies a volume of 6.85 L. Calculate its volume at STP. Example 5 If the volume of a gas is 5.0 L at 758 torr, what is the volume when the pressure is increased to 1.23 atm. Assume the temperature remains constant.

  15. Example 6: A 2.0 L balloon filled with nitrogen at 18°C at a picnic. By noon, the temperature has gone up to 28°C. What is the volume of the balloon at that point? Assume the atmospheric pressure has not changed throughout the day. 15

  16. Example 7: Sodium azide (NaN3) is used in some automobile air bags. The impact of a collision triggers the decomposition of NaN3 as follows: 2NaN3(s) 2Na (s) + 3N2(g) The nitrogen gas produced quickly inflates the bag between the driver and the windshield. Calculate the volume of N2 generated at 80.0C and 823 mmHg by the decomposition of 60.0 g of NaN3. 16

  17. How would you rearrange PV=nRT to give you the density of the gas? How do you normally calculate the density of an object? Which part of PV = nRT would give us density? Which part of the eqn would give us molar mass (MM)? Rearrange the equation to calculate MM. 17

  18. Example 9: The volume of a gas was determined to be 200.0 mL at 99oC and 733 mmHg. It has a mass of 0.970 g. What is its molar mass? Is it chloroform (CHCl3) or carbon tetrachloride? 18

  19. Effusion & Diffusion of Gases Effusion is the gradual movement of gas particles through a very tiny hole into a vacuum. Diffusion is the spontaneous mixing of the particles of one gas with those of another. 19

  20. Graham's Law of Effusion: The rate of effusion (r) is inversely proportional to the square root of its density (d). The density of a gas is directly proportional to its molar mass. Thus, rate of effusion is inversely proportional to the square root of its molar mass.

  21. Graham's Law of Effusion Rate of effusion is inversely proportional to the square root of its molar mass. where r = rate of effusion M = molar mass The heavier gas effuses slower at a given T. Example: Which effuses faster, Ne or Xe? How much faster? 21

  22. Example: Which effuses faster, Ne or Xe?How much faster? Ne is lighter (M = 20.2 g/mol) Xe is heavier (M = 131 g/mol) Ne should effuse faster than Xe. Ans. Ne effuses _____ times faster than Xe.

  23. If a molecule B is 4 times heavier than A, how much faster would A be effusing? How does T affect the rate of effusion? Ans. A is 2X as fast.

  24. Dalton's Law of Partial Pressures This law concerns mixtures of gases that do not react with each other. Each gas exerts its own partial pressure. In a mixture of gases (such as A and B), the total pressure is the sum of the partial pressures of each gas. PTOT = p A + p B p A = and p B = Note: Since they are in the same container, T and V must be the same. R is also the same. 24

  25. Collecting Gases Over Water

  26. Example 11.10 (p. 501) A sample of oxygen is collected over water at 15oC and a pressure of 738 torr. Its volume is 316 mL. • What is the partial pressure of the oxygen? • What would be its volume when dry at STP? Ans. 725 torr, 286 mL at STP. Practice Exercises 23 and 24 p. 502

  27. Dalton's Law of Partial Pressures (cont'd.) (Partial pressure of A is a fraction of the total pressure.) Rearrangement of equation gives us… What this tells us is that the fraction in pressures is equal to the fraction in moles, the mole fraction. REMEMBER: This is only for mixtures of gases. 28

  28. Example 11.11 p. 503 Suppose a mixture of oxygen and nitrogen is prepared in which there are 0.200 mol O2 and 0.500 mol N2. If the total pressure of the mixture is 745 torr, what are the partial pressures of the two gases in the mixture? Ans. 213 torr and 532 torr Practice Exercises 25, 26, 27, p. 504.

  29. Real Gas vs. Ideal Gas A real gas differs from an ideal gas: 1) Gas particles do have volume. 2) There are interactions between particles in a gas (attraction and repulsion). These are noticeable only under these conditions: 1) At slightly higher P or VERY low T (near liquefaction) particles are closer together and can "socialize." EFFECT: Actual V smaller than ideal. P is lower than ideal. 2) At VERY high P, particles are forced VERY closely together and their volume becomes significant. EFFECT: Actual P is higher than ideal.) 30

  30. Real Gas vs. Ideal Gas Due to molecules having sig. size. Due to attraction between molecules of a real gas. You do not need to memorize this equation or do any calculations with it. Know when and how real gases deviate in the Ideal Gas Law (previous slide). 31

  31. Real vs. Ideal Gases Which factor would explain the volume being LESS than expected of an ideal gas? and which factor, for being MORE?

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