The Gaseous State Chapter 5 Suggested problems to start: 19, 23-27, 29, 31, 33, 35, 39, 41, 45

Chapter 522 Copyright © by Houghton Mifflin Company. All rights reserved. Operational Skills Converting units of pressure. Using the empirical gas laws. Deriving empirical gas laws from the ideal gas law. Using the ideal gas law. Relating gas density and molecular weight. Solving stoichiometry problems involving gases. Calculating partial pressures and mole fractions. Calculating the amount of gas collected over water. Calculating the rms speed of gas molecules. Calculating the ratio of effusion rates of gases. Using the van der Waals equation.

Chapter 533 Copyright © by Houghton Mifflin Company. All rights reserved. Pressure Force exerted per unit area of surface by molecules in motion. 1 atmosphere = 14.7 psi 1 atmosphere = 760 mm Hg (see Fig. 5.2)(see Fig. 5.2) 1 atmosphere = 101,325 Pascals 1 Pascal = 1 kg/m. s 2 P = Force/unit area Force = mass x acceleration due to gravity (9.81 m/s 2 )

Chapter 544 Copyright © by Houghton Mifflin Company. All rights reserved. Figure 5.2: A mercury barometer.

Chapter 555 Copyright © by Houghton Mifflin Company. All rights reserved. P = gdh P = pressure g = acceleration due to gravity = 9.81 m/s 2 d = denisty h = height of column

Chapter 566 Copyright © by Houghton Mifflin Company. All rights reserved. Figure 5.3: Atmospheric pressure from air mass. 760 mm Hg=1 atm=101 kPa Pa = Pascal (Blaise !) units = kg/(m -s 2 ) The force of gravity on the column of air above the earth exerts a pressure at earth’s surface.

Chapter 577 Copyright © by Houghton Mifflin Company. All rights reserved. Figure 5.4: A flask equipped with a closed- tube manometer. (a device used to measure gas pressure)

Chapter 588 Copyright © by Houghton Mifflin Company. All rights reserved. Figure 5.5: Robert Boyle’s experiment (1661. Volume of gas at 1 atm 2 atm 3 atmGases are compressible!

Chapter 599 Copyright © by Houghton Mifflin Company. All rights reserved.

Chapter 510 Copyright © by Houghton Mifflin Company. All rights reserved.

Chapter 511 Copyright © by Houghton Mifflin Company. All rights reserved. Figure 5.6: Gas pressure- volume relationship.

Chapter 512 Copyright © by Houghton Mifflin Company. All rights reserved. Figure 5.6: Gas pressure- volume relationship.

Chapter 513 Copyright © by Houghton Mifflin Company. All rights reserved.

Chapter 514 Copyright © by Houghton Mifflin Company. All rights reserved. The Empirical Gas Laws Boyle’s Law: The volume of a sample of gas at a given temperature varies inversely with the applied pressure. (Figure 5.5)(Figure 5.5) V  1/P (constant moles and T) or

Chapter 515 Copyright © by Houghton Mifflin Company. All rights reserved. A Problem to Consider A sample of chlorine gas has a volume of 1.8 L at 1.0 atm. If the pressure increases to 4.0 atm (at constant temperature), what would be the new volume?

Chapter 516 Copyright © by Houghton Mifflin Company. All rights reserved. Figure 5.13: Hot-air ballooning. Jaques Alexander Charles--1787

Chapter 517 Copyright © by Houghton Mifflin Company. All rights reserved. Figure 5.7: Effect of temperature on a volume of gas. (A) N 2 (l) John Dalton (1801) & Joseph Guy Lussac (1802

Chapter 518 Copyright © by Houghton Mifflin Company. All rights reserved. Figure 5.7: Effect of temperature on a volume of gas. (B)

Chapter 519 Copyright © by Houghton Mifflin Company. All rights reserved. Figure 5.8: Linear relationship of gas volume and temperature at constant pressure.

Chapter 520 Copyright © by Houghton Mifflin Company. All rights reserved.

Chapter 521 Copyright © by Houghton Mifflin Company. All rights reserved. The Empirical Gas Laws Charles’s Law: The volume occupied by any sample of gas at constant pressure is directly proportional to its absolute temperature. V  T abs (constant moles and P) or

Chapter 522 Copyright © by Houghton Mifflin Company. All rights reserved. A Problem to Consider A sample of methane gas that has a volume of 3.8 L at 5.0 o C is heated to 86.0 o C at constant pressure. Calculate its new volume.

Chapter 523 Copyright © by Houghton Mifflin Company. All rights reserved. The Empirical Gas Laws Gay-Lussac’s Law: The pressure exerted by a gas at constant volume is directly proportional to its absolute temperature. P  T abs (constant moles and V) or

Chapter 524 Copyright © by Houghton Mifflin Company. All rights reserved. A Problem to Consider An aerosol can has a pressure of 1.4 atm at 25 o C. What pressure would it attain at 1200 o C, assuming the volume remained constant?

Chapter 525 Copyright © by Houghton Mifflin Company. All rights reserved. The Empirical Gas Laws Combined Gas Law: In the event that all three parameters, P, V, and T, are changing, their combined relationship is defined as follows:

Chapter 526 Copyright © by Houghton Mifflin Company. All rights reserved. A Problem to Consider A sample of carbon dioxide occupies 4.5 L at 30 o C and 650 mm Hg. What volume would it occupy at 800 mm Hg and 200 o C?

Chapter 527 Copyright © by Houghton Mifflin Company. All rights reserved.

Chapter 528 Copyright © by Houghton Mifflin Company. All rights reserved. The volume of one mole of gas is called the molar gas volume, V m. (See figure 5.10)(See figure 5.10) Volumes of gases are often compared at standard temperature and pressure (STP), chosen to be 0 o C and 1 atm pressure. The Empirical Gas Laws Avogadro’s Law: Equal volumes of any two gases at the same temperature and pressure contain the same number of molecules.

Chapter 529 Copyright © by Houghton Mifflin Company. All rights reserved. Figure 5.10: The molar volume of a gas L

Chapter 530 Copyright © by Houghton Mifflin Company. All rights reserved. At STP, the molar volume, V m, that is, the volume occupied by one mole of any gas, is 22.4 L/mol So, the volume of a sample of gas is directly proportional to the number of moles of gas, n. The Empirical Gas Laws Avogadro’s Law

Chapter 531 Copyright © by Houghton Mifflin Company. All rights reserved.

Chapter 532 Copyright © by Houghton Mifflin Company. All rights reserved. A Problem to Consider A sample of fluorine gas has a volume of 5.80 L at o C and 10.5 atm of pressure. How many moles of fluorine gas are present? First, use the combined empirical gas law to determine the volume at STP.

Chapter 533 Copyright © by Houghton Mifflin Company. All rights reserved. A Problem to Consider Since Avogadro’s law states that at STP the molar volume is 22.4 L/mol, then

Chapter 534 Copyright © by Houghton Mifflin Company. All rights reserved. The Ideal Gas Law From the empirical gas laws, we see that volume varies in proportion to pressure, absolute temperature, and moles.

Chapter 535 Copyright © by Houghton Mifflin Company. All rights reserved. Combining the three proportionalities, we can obtain the following relationship. The Ideal Gas Law This implies that there must exist a proportionality constant governing these relationships. where “R” is the proportionality constant referred to as the ideal gas constant.

Chapter 536 Copyright © by Houghton Mifflin Company. All rights reserved. The Ideal Gas Law The numerical value of R can be derived using Avogadro’s law, which states that one mole of any gas at STP will occupy 22.4 liters.

Chapter 537 Copyright © by Houghton Mifflin Company. All rights reserved. The Ideal Gas Law Thus, the ideal gas equation, is usually expressed in the following form: P is pressure (in atm) V is volume (in liters) n is number of atoms (in moles) R is universal gas constant L. atm/K. mol T is temperature (in Kelvin)

Chapter 538 Copyright © by Houghton Mifflin Company. All rights reserved. An experiment calls for 3.50 moles of chlorine, Cl 2. What volume would this be if the gas volume is measured at 34 o C and 2.45 atm? A Problem to Consider

Chapter 539 Copyright © by Houghton Mifflin Company. All rights reserved. Figure 5.14: A gas whose density is greater than that of air.

Chapter 540 Copyright © by Houghton Mifflin Company. All rights reserved. Figure 5.15: Finding the vapor density of a substance.

Chapter 541 Copyright © by Houghton Mifflin Company. All rights reserved.

Chapter 542 Copyright © by Houghton Mifflin Company. All rights reserved. Figure 5.17: An illustration of Dalton’s law of partial pressures before mixing. Return to Slide 33

Chapter 543 Copyright © by Houghton Mifflin Company. All rights reserved. Return to Slide 33

Chapter 544 Copyright © by Houghton Mifflin Company. All rights reserved. A Problem to Consider The “real” pressure exerted by 1.00 mol of SO 2 at STP is slightly less than the “ideal” pressure.

Chapter 545 Copyright © by Houghton Mifflin Company. All rights reserved. Figure 5.22: Molecular description of Charles’s law. Return to Slide 41

Chapter 546 Copyright © by Houghton Mifflin Company. All rights reserved. Figure 5.27: The hydrogen fountain. Photo courtesy of American Color. Return to Slide 44

Chapter 547 Copyright © by Houghton Mifflin Company. All rights reserved. Figure 5.26: Model of gaseous effusion. Return to Slide 45