Temperature and Pressure Gay Lussac’s Law Temperature and Pressure Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings

Gay-Lussac’s Law: P and T In Gay-Lussac’s Law the pressure exerted by a gas is directly related to the Kelvin temperature. V and n are constant. P1 = P2 T1 T2

Learning Check Solve Gay-Lussac’s Law for P2. P1 = P2 T1 T2 Multiply both sides by T2 and cancel P1 x T2 = P2 x T2 T1 T2 P2 = P1 x T2 T1

Calculation with Gay-Lussac’s Law A gas has a pressure at 2.0 atm at 18°C. What is the new pressure when the temperature is 62°C? (V and n constant) 1. Set up a data table; Conditions 1 Conditions 2 P1 = 2.0 atm P2 = T1 = 18°C + 273 T2 = 62°C + 273 = 291 K = 335 K ?

Calculation with Gay-Lussac’s Law (continued) 2. Solve Gay-Lussac’s Law for P2: P1 = P2 T1 T2 P2 = P1 x T2 T1 P2 = 2.0 atm x 335 K = 2.3 atm 291 K Temperature ratio increases pressure

Try it A gas has a pressure of 645 torr at 128°C. What is the temperature in Celsius if the pressure increases to 1.50 atm (n and V remain constant)? 1. Set up a data table: Conditions 1 Conditions 2 P1 = 645 torr P2 = 1.50 atm x 760 torr = 1140 torr 1 atm T1 = 128°C + 273 T2 = K – 273 = ?°C = 401 K

Solution 2. Solve Gay-Lussac’s Law for T2: P1 = P2 T1 T2 T2 = T1 x P2 T2 = 401 K x 1140 torr = 709 K - 273 = 436°C 645 torr Pressure ratio increases temperature

Avogadro’s Law

Avogadro's Law: Volume and Moles In Avogadro’s Law the volume of a gas is directly related to the number of moles (n) of gas. T and P are constant. V1 = V2 n1 n2

Learning Check If 0.75 mole helium gas occupies a volume of 1.5 L, what volume will 1.2 moles helium occupy at the same temperature and pressure? 1) 0.94 L 2) 1.8 L 3) 2.4 L

Solution STEP 1 Conditions 1 Conditions 2 V1 = 1.5 L V2 = ??? n1 = 0.75 mole He n2 = 1.2 moles He STEP 2 Solve for unknown V2 V2 = V1 x n2 n1 STEP 3 Substitute values and solve for V2. V2 = 1.5 L x 1.2 moles He = 2.4 L 0.75 mole He

Partial Pressure (Dalton’s Law)

Partial Pressure The partial pressure of a gas is the pressure of each gas in a mixture. is the pressure that gas would exert if it were by itself in the container.

Dalton’s Law of Partial Pressures Dalton’s Law of Partial Pressures indicates that pressure depends on the total number of gas particles, not on the types of particles. the total pressure exerted by gases in a mixture is the sum of the partial pressures of those gases. PT = P1 + P2 + P3 +.....

Dalton’s Law of Partial Pressures

Illustrating Partial Pressures

Total Pressure Gas mixtures For example, at STP, one mole of a pure gas in a volume of 22.4 L will exert the same pressure as one mole of a gas mixture in 22.4 L. V = 22.4 L Gas mixtures 1.0 mole N2 0.4 mole O2 0.6 mole He 1.0 mole 0.5 mole O2 0.3 mole He 0.2 mole Ar 1.0 mole 1.0 atm 1.0 atm 1.0 atm

Scuba Diving When a scuba diver dives, the increased pressure causes N2(g) to dissolve in the blood. If a diver rises too fast, the dissolved N2 will form bubbles in the blood, a dangerous and painful condition called "the bends". Helium, which does not dissolve in the blood, is mixed with O2 to prepare breathing mixtures for deep descents.

Learning Check A scuba tank contains O2 with a pressure of 0.450 atm and He at 855 mm Hg. What is the total pressure in mm Hg in the tank?

Solution 1. Convert the pressure in atm to mm Hg 0.450 atm x 760 mm Hg = 342 mm Hg = P(O2) 1 atm 2. Calculate the sum of the partial pressures. Ptotal = P(O2) + P(He) Ptotal = 342 mm Hg + 855 mm Hg = 1197 mm Hg

Learning Check For a deep dive, a scuba diver uses a mixture of helium and oxygen with a pressure of 8.00 atm. If the oxygen has a partial pressure of 1280 mm Hg, what is the partial pressure of the helium? 1) 520 mm Hg 2) 2040 mm Hg 3) 4800 mm Hg

Solution PTotal = 8.00 atm x 760 mm Hg = 6080 mm Hg 1 atm PTotal = PO + PHe 2 PHe = PTotal - PO2 PHe = 6080 mm Hg - 1280 mm Hg = 4800 mm Hg

Gases We Breathe The air we breathe is a gas mixture. contains mostly N2 and O2 and small amounts of other gases. TABLE 6.4

Learning Check A.If the atmospheric pressure today is 745 mm Hg, what is the partial pressure (mm Hg) of O2 in the air? 1) 35.6 2) 156 3) 760 B. At an atmospheric pressure of 714, what is the partial pressure (mm Hg) N2 in the air? 1) 557 2) 9.14 3) 0.109

Blood Gases In the lungs, O2 enters the blood, while CO2 from the blood is released. In the tissues, O2 enters the cells, which release CO2 into the blood.

Partial Pressures in Blood and Tissue Blood Gases In the body, O2 flows into the tissues because the partial pressure of O2 is higher in arterial blood, and lower in the tissues. CO2 flows out of the tissues because the partial pressure of CO2 is higher in the tissues, and lower in the blood. Partial Pressures in Blood and Tissue Oxygenated Deoxygenated (arterial) (venous) Gas Blood Blood Tissues O2 100 40 30 or less CO2 40 46 50 or greater

Gas Exchange During Breathing TABLE 6.5