1 Chapter 5 The Gas Laws

2 Example n 20.5 L of nitrogen at 25.0ºC and 742 torr are compressed to 9.80 atm at constant T. What is the new volume? Steps... n P 1 V 1 = P 2 V 2 n (20.5 L)(742 torr) = (9.80 atm x 760 torr/atm)(x) n x = 2.04 L

3 Example n What would the final volume be if 247 mL of gas at 22ºC is heated to 98ºC, if the pressure is held constant? Steps. n V 1 /T 1 = V 2 /T 2 n (247 mL)/( K) = (x mL)( K) n x = 311 ml

4 Combined Gas Law n If the moles of gas remain constant, use this formula and cancel out the other things that don’t change. n P 1 V 1 = P 2 V 2. T 1 T 2

5 Examples n A deodorant can has volume of 175 mL & pressure of 3.8 atm at 22ºC. What pressure if heated to 100.ºC? n V is constant, so (P 1 V 1 )/T 1 = (P 2 V 2 /T 2 ) n (3.8)/(295) = (x)/373 n x = 4.8 atm

6 5.3 Ideal Gas Law n PV = nRT n V = L at 1 atm, 0ºC, n = 1 mole, what is R? n R is the ideal gas constant. n R = L atm/ mol K n R also = L torr/k mol or J/k mol n Tells you about a gas is NOW. n The other laws tell you about a gas when it changes (exam hint!).

7Examples n A 47.3 L container with 1.62 mol of He heated until pressure reaches 1.85 atm. What is the temperature? Steps... n PV = nRT n T = (1.85)(47.3)/(.0821)(1.62) = 658 K or 385 ºC

8Examples n Kr gas in a 18.5 L cylinder exerts a pressure of 8.61 atm at 24.8ºC. What is the mass of Kr? Ans... n 546 g Steps... n n = PV/RT = 6.51 mol n Since M = m/mol = m/n, m = M n n Get M from periodic table n m = = 546 g

9 Examples n Can get mercury by the following: What volume oxygen gas produced from 4.10 g of mercury (II) oxide at STP? Steps. n Balance first! 2HgO  2Hg + O 2 n Since at STP can then use stoich (spider) n 4.10 g HgO 1 mol HgO/217g HgO 1 mol O 2 /2 mol HgO 22.4 L O 2 /1 mol O 2 n = L or 212 mL

10 Examples n Can get mercury by the following: What volume oxygen gas can be produced from 4.10 g of mercury (II) oxide at 400.ºC & 740. torr? (Hint: conditions are changed, so what equation do you then use?)... n 1st, find molar mass of mercury(II) oxide. n 2nd, balance reactions & spider under STP n 3rd, then use the combined law to convert. n (1)(212)/273 = (740/760)(x)/( ) n L

11 The Same reaction with some twists n What mass of H 2 O produced from 65.0 L O 2 & 75.0 L of NH 3 measured at STP?... Ans. n As before, but must find 313 g n As before, but must find LR = O 2 ans. 313 g n What volume of NO would be produced? n Above + mole ratio. Ans. = 52 L n What mass of NO is produced from 500. L of NH 3 at 250.0ºC and 3.00 atm? Ans. n non-STP so use combined gas law to get to STP (783 L), then “spider” Ans. = 895 g

12 Quick Example u What mass of ethene gas, C 2 H 4, is in a 15.0 L tank at 4.40 atm & 305 K? (steps) u PV = mRT/M and M = 28 g/mol u m = PVM/RT u m = (4.40 atm)(15.0 L)(28 g/mol) ( L atm/mol K)(305 K) u m = 73.8 g C 2 H 4

13 Another way to solve it (quick) u What mass of ethene gas, C 2 H 4, is in a 15.0 L tank at 4.40 atm & 305 K? (steps) u PV = nRT, solve for n u N = PV/RT u n = (4.40 atm)(15.0 L) ( L atm/mol K)(305 K) u n = 2.64 mol C 2 H 4 u Use spider to get g C 2 H 4 (M = 28 g/mol) u Answer is 73.8 g C 2 H 4

14 Examples u In a balloon the total pressure is 1.3 atm. What is the pressure of oxygen if the pressure of nitrogen is 720 mm Hg?... u P Total = P 1 + P 2 + P 3... u 1.3 atm = Po mm Hg u Convert to same units (we’ll use mm Hg) u 1.3 atm(760 mm Hg/1 atm) = Po mm Hg u 988 mm Hg = Po mm Hg so,... u Po 2 = 988 mm Hg mm Hg = 268 mm Hg u Can also express as 0.35 atm.

15 Mole fraction example n The partial pressure of nitrogen in air is 592 torr. Air pressure is 752 torr, what is the mole fraction of nitrogen? Steps... n  = 592 torr/752 torr = n What is the partial pressure of nitrogen if the container holding the air is compressed to 5.25 atm?... n x 5.25 atm = 4.13 atm n Note: can use mole fraction regardless of units (don’t have to convert).

16 Examples 3.50 L O L N atm n When these valves are opened, what is each partial pressure and the total pressure? Hint. n Use mole fraction to get the new partial pressures (or Boyle’s law), then add to get total pressure. Ans. n CH 4 = 1.2 atm N 2 = O 2 = Sum = L CH atm atm

17 Example n What volume of N 2 O over water at total pressure of 94 kPa & 22ºC can be produced from 2.6 g NH 4 NO 3 ? (Vp water at 22ºC is 21 torr) n Make sure reaction is balanced (it is) n M of ammonium nitrate = 80. g n Use spider to get moles of N 2 0 =.0325, then use PV = nRT, but first have to: n Convert 21 torr to 2.8 kPa (or vice versa) n = 91.2 kPa N 2 O n convert P to atm d/t R ( or use 62.4)!!! n Convert C to K n Ans. 6.6 L

18Example n Calculate the root mean square velocity of carbon dioxide at 25ºC. n Must express R using joules & M = Kg/mol (not g, d/t R) n R = J/K*Mol, M = Kg/mol ans... n 411 m/sec n If time, do for hydrogen, for chlorine. Ans... n Hydrogen is 1928 m/s; Chorine is 324 m/s n Notice that the less massive hydrogen has a higher velocity.

19 Whiteboard Examples n An element effuses through a porous cylinder 3.20 times slower than helium. What is it’s molar mass? Steps on whiteboard to get... n (Probably Argon = g/mol) n mol NH 3 effuses via a hole in 2.47 min, how much HCl would effuse in the same time? Your ans.? n mol HCl n Some N 2 effuses via a hole in 38 seconds. What is molecular weight of gas that effuses in 55 seconds under identical conditions? Your answer?... (hint: think if N 2 is faster or slower. If faster then the rate must be > 1, if slower, then the rate is a fraction. n 59 g/mol