To understand the Ideal Gas Law and use it in calculations Objectives To understand the Ideal Gas Law and use it in calculations To understand the relationship between the partial and total pressure of a gas mixture To do calculations involving Dalton’s Law of partial pressures To prepare for the Universal Gas Constant lab

So far we have considered “what happens,” but not “why.” In science, “what” always comes before “why.”

Postulates of the Kinetic Molecular Theory 1) The particles are so small compared with the distances between them that the volume of the individual particles can be assumed to be negligible (zero).

Postulates of the Kinetic Molecular Theory 2) The particles are in constant motion. The collisions of the particles with the walls of the container are the cause of the pressure exerted by the gas.

Kinetic Molecular Theory

Postulates of the Kinetic Molecular Theory 3) The particles are assumed to exert no forces on each other; they are assumed neither to attract nor to repel each other.

Postulates of the Kinetic Molecular Theory The average internal kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas. PHet gas behavior

A. The Kinetic Molecular Theory of Gases (IDEAL)

P1V1 = P2V2 n1T1 n2T2 Boyle’s Law V = k (at constant T and n) P A. The Ideal Gas Law Boyle’s Law V = k (at constant T and n) P Charles’s Law V = bT (at constant P and n) Avogadro’s Law V = an (at constant T and P) We can combine these equations to get the Combined Gas Law P1V1 = P2V2 n1T1 n2T2

PV = R (a constant) nT R = 0.08206 L atm **Found mol K Experimentally A. The Ideal Gas Law PV = R (a constant) nT Rearranging the equation gives the Ideal Gas Law PV = nRT R = 0.08206 L atm **Found mol K Experimentally

A sample of hydrogen gas, H2, has a volume of 8 A sample of hydrogen gas, H2, has a volume of 8.56 L at a temperature of 0 oC and a pressure of 1.5 atm. Calculate the number of moles of H2 present in this gas sample. Assume that the gas behaves ideally. PV=nRT P= V= n= R= T=

PV=nRT P= 1.5 atm **UNITS** V= 8.56 L n= ? R= 0.08206 Latm/molK T= 0 oC + 273 = 273 K n = PV RT n = (1.5 atm)(8.56 L) = 0.57 mol (0.08206 Latm/molK)(273 K)

What volume is occupied by 0.250 mol of CO2 gas at 25 oC and 371 torr? PV=nRT P= V= n= R= T=

What volume is occupied by 0. 250 mol of CO2 gas at 25 oC and 371 torr What volume is occupied by 0.250 mol of CO2 gas at 25 oC and 371 torr? *(1 atm = 760 torr) PV=nRT P= 371 torr V= ? n= 0.250 mol R= 0.08206 Latm/molK T= 25 oC + 273 = 298 K V = nRT P

What volume is occupied by 0. 250 mol of CO2 gas at 25 oC and 371 torr What volume is occupied by 0.250 mol of CO2 gas at 25 oC and 371 torr? *(1 atm = 760 torr) V = nRT = 0.250 mol)(0.08206 Latm/molK)(298K) P 371 torr V = 0.016 L ?? 371 torr 1 atm = 0.488 atm 760 torr V = nRT =(0.250 mol)(0.08206 Latm/molK)(298K) P 0.488 atm V = 12.5 L ****Watch the units!!!****

n1T1 n2T2 Derive Boyle’s Law (P1V1 = P2V2) from IGL PV=nRT PV = R = constant (LAB) nT P1V1 = P2V2 n1T1 n2T2 IGL Video, fire syringe

B. Dalton’s Law of Partial Pressures What happens to the pressure of a gas as we mix different gases in the container? Dalton’s Law of Partial Pressures For a mixtures of gases in a container, the total pressure exerted is the sum of the partial pressures of the gases present. Ptotal = P1 + P2 + P3

B. Dalton’s Law of Partial Pressures The pressure of the gas is affected by the number of particles but not the type of particles.

B. Dalton’s Law of Partial Pressures Two crucial things we learn from this are: The volume of the individual particles is not very important. The forces among the particles must not be very important.

B. Dalton’s Law of Partial Pressures A container holds a mixture of three gases that exhibit a total pressure of 1.8 atm. If gas A exerts 0.9 atm and gas B exerts 0.4 atm, what is the partial pressure of gas C? Ptotal = P1 + P2 + P3 Ptotal = P1 = P2 = P3 = ?

B. Dalton’s Law of Partial Pressures Ptotal = P1 + P2 + P3 Ptotal = 1.8 atm P1 = 0.9 atm P2 = 0.4 atm P3 = ? P3 = Ptotal - P1 - P2 P3 = 1.8 atm – 0.9 atm – 0.4 atm = 0.5 atm

P He = P O2 = V = V = n = n = R = R = T = T = Mixtures of helium and oxygen can be used in scuba tanks to prevent “the bends.” For a particular dive, 46 L He at 25 oC and 1.0 atm and 12 L of O2 at 25oC and 1 atm were pumped into a tank with a volume of 5.0 L Calculate the partial pressure of each gas and the total pressure in the tank at 25 oC. For each gas… P He = P O2 = V = V = n = n = R = R = T = T = For oxygen: P1V1=P2V2 (1.30 atm)(27.4 L) = (P2)(5.81 L) P2 = 6.13 atm For helium: (2.00 atm)(8.50 L) = (P2)(5.81 L) P2 = 2.93 atm The total pressure is therefore 6.13 + 2.93 = 9.06 atm.

P He = 1 atm P O2 = 1 atm V = 46 L V = 12 L n = ? n = ? R = 0.08206 Latm/mol K R = 0.08206 T = 25 oC T = 25 oC n = PV/RT n = PV/RT 1.9 mol He 0.49 mol O2 This quantifies how many moles of each gas is contained in the sample…pressure for each gas in the 5 L tank? PV = nRT… For oxygen: P1V1=P2V2 (1.30 atm)(27.4 L) = (P2)(5.81 L) P2 = 6.13 atm For helium: (2.00 atm)(8.50 L) = (P2)(5.81 L) P2 = 2.93 atm The total pressure is therefore 6.13 + 2.93 = 9.06 atm.

Pt =9.3 atm + 2.4 atm = 11.7 atm total pressure P He = ? P O2 = ? V = 5 L V = 5 L n = 1.9 mol n = 0.49 mol R = 0.08206 Latm/mol K R = 0.08206 T = 25 oC T = 25 oC P = nRT/V P = nRT/V 9.3 atm 2.4 atm Pt = P1 + P2 Pt =9.3 atm + 2.4 atm = 11.7 atm total pressure For oxygen: P1V1=P2V2 (1.30 atm)(27.4 L) = (P2)(5.81 L) P2 = 6.13 atm For helium: (2.00 atm)(8.50 L) = (P2)(5.81 L) P2 = 2.93 atm The total pressure is therefore 6.13 + 2.93 = 9.06 atm.

Exercise 27.4 L of oxygen gas at 25.0°C and 1.30 atm, and 8.50 L of helium gas at 25.0°C and 2.00 atm were pumped into a tank with a volume of 5.81 L at 25°C. Calculate the new partial pressure of oxygen. 6.13 atm Calculate the new partial pressure of helium. 2.93 atm Calculate the new total pressure of both gases. 9.06 atm For oxygen: P1V1=P2V2 (1.30 atm)(27.4 L) = (P2)(5.81 L) P2 = 6.13 atm For helium: (2.00 atm)(8.50 L) = (P2)(5.81 L) P2 = 2.93 atm The total pressure is therefore 6.13 + 2.93 = 9.06 atm.

B. Dalton’s Law of Partial Pressures Collecting a gas over water Total pressure is the pressure of the gas + the vapor pressure of the water.

B. Dalton’s Law of Partial Pressures Collecting a gas over water How can we find the pressure of the gas collected alone? Ptotal = P1 + P2 Ptotal = atmospheric P1 = PH2O (from chart) P2 = P (gas collected)

To understand the ideal gas law and use it in calculations Objectives Review To understand the ideal gas law and use it in calculations To understand the relationship between the partial and total pressure of a gas mixture To do calculations involving Dalton’s law of partial pressures To prepare for the Universal Gas Constant lab Work Session: 459 Practice Problem 13.8 460 Practice Problem 13.9 469 Practice Problem 13.13 – PH2O ONLY 481 # 35, 36 PO2 ONLY 473 13.2 Review # 3

To convert between pressure units using the unit analysis approach Objectives To double check for unit agreement when working the 5-Step Problem Solving Method To convert between pressure units using the unit analysis approach To remember how to convert from gmol!!

Convert 5.2 atmospheres to mm Hg. 5.2 atm = Pressure Unit Conversions, Unit Analysis Approach 1 atm = 760 mm Hg 760 mm Hg = 760 torr 1 atm = 101, 325 Pa Convert 5.2 atmospheres to mm Hg. 5.2 atm = Convert 5.2 atmospheres to torrs.

Convert 5.2 atmospheres to Pa. 5.2 atm = Convert 748 torrs to Pa Pressure Unit Conversions, Unit Analysis Approach 1 atm = 760 mm Hg 760 mm Hg = 760 torr 1 atm = 101, 325 Pa Convert 5.2 atmospheres to Pa. 5.2 atm = Convert 748 torrs to Pa 748 torr =

Convert 7.48 g nitrogen gas to mol 7.48 g = g  mol Conversions, Unit Analysis Approach Convert 5.2 g CH4 to mol CH4 5.2 g CH4 = Convert 7.48 g nitrogen gas to mol 7.48 g =

A sample of hydrogen gas, H2, has a volume of 9 A sample of hydrogen gas, H2, has a volume of 9.46 L at a temperature of 0 oC and a pressure of 988 torr. Calculate the number of grams of H2 present in this gas sample. PV=nRT P= V= n= R= T=

A sample of hydrogen gas, H2, has a volume of 9 A sample of hydrogen gas, H2, has a volume of 9.46 L at a temperature of 0 oC and a pressure of 988 torr. Calculate the number of grams of H2 present in this gas sample. PV=nRT P= 988 torr V= 9.46 L n= ? R= 0.08206 Latm/molK T= 0 oC + 273 = 273 K

A sample of hydrogen gas, H2, has a volume of 9 A sample of hydrogen gas, H2, has a volume of 9.46 L at a temperature of 0 oC and a pressure of 988 torr. Calculate the number of grams of H2 present in this gas sample. n = PV RT n = PV = (1.3 atm)(9.46 L) = 0.55mol RT (0.08206 Latm/molK) (273 K) n = 0.55 mol H2

To convert between pressure units using the unit analysis approach Objectives Review To double check for unit agreement when working the 5-Step Problem Solving Method To convert between pressure units using the unit analysis approach To remember how to convert from gmol!! Work Session: Page 480 # 4 473 13.2 Review # 2 (g mol)

To understand the molar volume of an ideal gas Objectives To understand the molar volume of an ideal gas To learn the definition of STP To understand the relationship between laws and models (theories) To understand the postulates of the kinetic molecular theory To understand temperature To learn how the kinetic molecular theory explains the gas laws To describe the properties of real gases

Standard temperature and pressure (STP) 0oC and 1 atm A1. Gas Stoichiometry Molar Volume Standard temperature and pressure (STP) 0oC and 1 atm For one mole of a gas at STP Molar volume of an ideal gas at STP 22.4 L

PV=nRT P= V= n= R= T= 0.078 moles N2 A sample of nitrogen gas has a volume of 1.75 L at STP. How many moles of N2 are present? PV=nRT P= V= n= R= T= 0.078 moles N2

Exercise A sample of oxygen gas has a volume of 2.50 L at STP. How many grams of O2 are present? 3.57 g 3.57 g of O2 are present. (1.00 atm)(2.50 L) = n(0.08206)(273) n = 0.112 mol O2 × 32.00 g/mol = 3.57 g O2

A. Laws and Models (Theories) : A Review A model (theory) is an approximation and is destined to be modified as we understand more or are able to better measure phenomena occurring around us. A model (theory) can never be proved absolutely true.

B. The Kinetic Molecular Theory of Gases

C. The Implications of the Kinetic Molecular Theory Meaning of temperature – Kelvin temperature is directly proportional to the average kinetic energy of the gas particles Relationship between Pressure and Temperature – gas pressure increases as the temperature increases because the particles speed up Relationship between Volume and Temperature – volume of a gas increases with temperature because the particles speed up

D. Real Gases Gases do not behave ideally under conditions of high pressure and low temperature. Why?

The particles are so small compared with the distances between them that the volume of the individual particles can be assumed to be negligible (zero). The particles are in constant motion. The collisions of the particles with the walls of the container are the cause of the pressure exerted by the gas. 3) The particles are assumed to exert no forces on each other; they are assumed neither to attract nor to repel each other. The average internal kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas.

B. The Kinetic Molecular Theory of Gases

At high pressure the volume is decreased D. Real Gases At high pressure the volume is decreased Molecule volumes become important Attractions become important

Math Laws are still approximations….. PV = nRT ……. …..or does it? D. Real Gases Math Laws are still approximations….. PV = nRT ……. …..or does it?

Calculate the pressure exerted by 0. 75 mol of He in a 1 Calculate the pressure exerted by 0.75 mol of He in a 1.0 L container at standard temperature. Use vdW… P= nRT – a(n/V)2 (V-nb) P = 17.074 atm vs 16.79 atm

To understand the molar volume of an ideal gas Objectives Review To understand the molar volume of an ideal gas To learn the definition of STP To understand the relationship between laws and models (theories) To understand the postulates of the kinetic molecular theory To understand temperature To learn how the kinetic molecular theory explains the gas laws To describe the properties of real gases (PHet) Work session: Page 478 13.3 Review # 1 - 5