Gas Laws

Standard Temperature and Pressure (STP) Standard temperature: 0°C or 273 K Standard pressure: 1 atm, 760 mm Hg, or 101.3 kPa

Boyle’s Law The pressure of a dry gas is inversely proportional to its volume if the temperature is held constant.

Inverse Proportion two terms related so that, if one term increases, the other term decreases

Boyle’s Law P , V PV = k P1V1 = P2V2

As pressure increases, volume decreases. Chemistry textbook, p. 250

Chemistry textbook, p. 250

Sample Problem 1 A sample of gas occupies 352 mL at a pressure of 3.17 atm. If the P is reduced to 1.24 atm, what volume will result? P1V1 = P2V2 (3.17 atm)(352 mL) = (1.24 atm)V2 900 mL = V2

Question A sample of gas occupies 200 mL at a P of 2.15 atm. If the P is reduced to 1.25 atm, what is V2? 344 mL 537 mL 98 mL 89 mL

(2.15 atm)(200 mL) = (1.25 atm) V2 430 mL = 1.25 V2 344 mL = V2

Question 2,175 mm Hg 225 mm Hg 339 mm Hg 1 mm Hg A sample of gas is at a P of 700 mm Hg with a V of 300 mL. What P will increase the V to 932 mL? 2,175 mm Hg 225 mm Hg 339 mm Hg 1 mm Hg

(700 mm Hg)(300 mL) = P2(932 mL) 210,000 mm Hg = 932 P2 225 mm Hg = P2

Charles’s Law The volume and absolute temperature of a gas are directly proportional to one another if the pressure is held constant.

Direct Proportion two terms related so that, if one term increases, the other term also increases

Charles’s Law V , T = k V T V1 T1 V2 T2 =

As temperature increases, volume increases. Chemistry textbook, p. 251

Chemistry textbook, p. 251

Sample Problem 2 If a sample of gas occupies 478 mL at 126 K, what volume will result if the gas is heated to 245 K?

Sample Problem 2 V1 T1 = V2 T2 (478 mL) (126 K) = V2 (245 K) (478 mL)(245) = (126)V2 929 mL = V2

Sample Problem 3 If a sample of gas occupies 478 mL at 126°C, what volume will result if the gas is heated to 245°C?

Sample Problem 3 V1 T1 = V2 T2 (478 mL) (126°C) = V2 (245°C) NOTE: T must be in K—add 273 (478 mL)(518) = (399)V2 621 mL = V2

Question If a sample of gas occupies 232 mL at 321 K, what V will result if the gas it heated to 554 K? 134 mL 767 mL 400 mL 0.001 mL

232 mL 321 K V2 554 K = (232 mL)(554 K) = (321 K)V2 128,528 mL = (321)V2 400 mL = V2

Question If a sample of gas occupies 112 mL at 313°C, what will be the T if the V becomes 52 mL? REMEMBER KELVIN! 19 K 10 K 145 K 272 K

112 mL 586 K = 52 mL T2 (112 mL)T2 = (586 K)(52 mL) 112 T2 = 30,472 K T2 = 272 K

Gay-Lussac’s Law The pressure of a confined gas is directly proportional to its absolute temperature if the volume is held constant.

Gay-Lussac’s Law P , T = k P T P1 T1 P2 T2 =

As temperature increases, pressure increases at a constant volume. Chemistry textbook, p. 253

Chemistry textbook, p. 253

Question 18 psi 33 psi 37 psi 68 psi If a the P of a tire is 35 psi at 21°C, what will the P be if the T is raised to 41°C? 18 psi 33 psi 37 psi 68 psi

35 psi 294 K = 314 K P2 (35 psi)(314 K) = (294 K)P2 10,990 psi = 294 P2 37.4 psi = P2

Combines Boyle’s law, Charles’s law, and Gay-Lussac’s law Combined Gas Law Combines Boyle’s law, Charles’s law, and Gay-Lussac’s law

Combined Gas Law Boyle’s PV V T Charles’s P T Gay-Lussac’s

Combined Gas Law P1V1 T1 P2V2 T2 =

Sample Problem 4 = P1V1 T1 P2V2 T2 If a gas occupies 1050 L at a P of 720 mm Hg and a T of 250 K, what V will it occupy at a P of 600 mm Hg and a T of 800 K? P1V1 T1 P2V2 T2 =

( ) ( ) Sample Problem 4 (250 K) 720 (1050 L) (800 K) (V2) 600 = If a gas occupies 1050 L at a P of 720 mm Hg and a T of 250 K, what V will it occupy at a P of 600 mm Hg and a T of 800 K? (250 K) 720 mm Hg ( ) (1050 L) (800 K) (V2) 600 mm Hg ( ) = (720)(1050)(800) = (250)(600)V2

Sample Problem 4 If a gas occupies 1050 L at a P of 720 mm Hg and a T of 250 K, what V will it occupy at a P of 600 mm Hg and a T of 800 K? V2 = 4,032 L

Sample Problem 5 If a gas with V of 45 L at 700 mm Hg and 300 K changes to STP, what is its new V? (300 K) 700 mm Hg ( ) (45 L) (273 K) (V2) 760 mm Hg ( ) = (700)(45 L)(273) = (760)(300)V2

Sample Problem 5 If a gas with V of 45 L at 700 mm Hg and 300 K changes to STP, what is its new V? 37.7 L = V2

Question If a gas occupies 324 mL at a P of 526 torr and a T of 322 K, what V will it have at 433 torr and 221 K? 270 mL 1,037 mL 389 mL 1,024 mL

(433 torr)V2 = (221 K) (526 torr)(324 mL) (322 K) 37,663,704 mL = 139,426 V2 270 mL = V2

Dalton’s Law of Partial Pressures The total pressure of a mixture of gases equals the sum of the partial pressures.

Dalton’s Law of Partial Pressures PT = P1 + P2 + P3 + …

= + + Chemistry textbook, p. 255

the pressure exerted by the vapor emitted by a liquid or a solid Vapor Pressure the pressure exerted by the vapor emitted by a liquid or a solid

Vapor Pressure Patm = Pgas + H2O P Patm − H2O P = Pgas

Question 32 mm Hg 780 mm Hg 716 mm Hg A gas is collected over water. The P is 748 mm Hg. The T is 30°C. What is the partial P of the gas? 32 mm Hg 780 mm Hg 716 mm Hg Not enough information

Patm − H2O P = Pgas 748 torr – 32 torr = 716 torr