1 GASES Paul Gilletti, Ph.D. Mesa Community College

2 Gases (Vapors) Gases expand to fill any container. Therefore, gases are highly compressible.

3 Kinetic Molecular Theory (of an Ideal Gas): 1. Gases are composed of molecules or atoms whose size is negligible compared to the average distance between them. (Most of the space in the gas container is empty.) 2. Gas molecules move randomly in straight lines in all directions at various speeds. 3. The forces of attraction or repulsion between gas molecules are very weak or negligible (except during collisions) 4. Collisions between gas molecules are considered elastic. 5. The average kinetic energy of a molecule is proportional to the absolute temperature.

4 Pressure and Volume: Boyle’s Law How is the pressure applied to a gas related to its volume? Piston Gas molecules Let’s apply pressure

5 Pressure and Volume: Boyle’s Law How is the pressure applied to a gas related to its volume? Piston Gas molecules Piston Gas molecules Boyle’s Law: P 1 V 1 = P 2 V 2 Volume is inversely proportional to applied pressure.

6 The Harder we Push the smaller the gas volume gets! Boyle’s Law: P 1 V 1 = P 2 V 2

7 molecules of air Where is the pressure the greatest? We live in “sea of air” Why does a diver get the bends?

8 Pressure:force per unit area of surface Units lbs per in 2 (psi) mm of Hg (torr) atmospheres (atm) 1 atm = 760 mm of Hg =760 torr = psi = kPa Pascal (Pa) Pairs of these can be used as conversion factors.

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11 Temperature and Volume: Charles’s Law How is the volume of a gas related to its temperature? gas molecules moveable mass (constant pressure) What happens if heat is applied to the gas?

12 Temperature and Volume: Charles’s Law How is the volume of a gas related to its temperature? gas molecules moveable mass (constant pressure) Why did the volume change? What happens to the average speed of the gas molecules?.

13 Temperature and Volume: Charles’s Law How is the volume of a gas related to its temperature? gas molecules moveable mass (constant pressure) The volume of a gas is directly proportional to its Temperature (temperature must be in Kelvin) Charles’s Law: V 1 /T 1 = V 2 /T 2

14 Combined Gas Law (Boyle and Charles): T must be in Kelvin Can be rearranged to: P 1 V 1 T 2 = P 2 V 2 T 1 A combined gas law problem can be recognized by having two sets of conditions. Note: if one set of parameters is unchanged that term will cancel on each side.

15 A balloon contains helium gas with a volume of 2.60 L at 25 o C and 768 mmHg. If the balloon ascends to an altitude where the helium pressure is 590 mmHg and the temperature is 15 o C, what is the volume of the balloon? What type of problem is this? There are 2 sets of conditions.

16 A balloon contains helium gas with a volume of 2.60 L at 25 o C and 768 mmHg. If the balloon ascends to an altitude where the helium pressure is 590 mmHg and the temperature is 15 o C, what is the volume of the balloon? P 1 V 1 T 2 = P 2 V 2 T 1 P1=P1= V1=V1= T1=T1= P2=V2=T2=P2=V2=T2= 768 torr 2.60 L = 298 K 590 torr = 288 K ? = (768 torr)(2.60 L)(288 K) (590 torr)(298 K) = 3.27 L

17 Ideal Gases and the Ideal Gas Law: PV = nRT Temperature in K * gas constant Latm = Ltorr molK molK moles of gas volume in L pressure in units to match * R units Note: there is only one set of conditions.

18 Avogadro’s Law: Equal volumes of any two gases (ideal) at the same temperature and pressure contain the same number of molecules (they also occupy equal volumes). STP Pressure 1 atm (760 mm Hg) Temperature 0 o C (273 K) Standard At STP one mole of ideal gas occupies 22.4 L

19 A L cylinder contains 75.5 g of neon at 24.5 o C. Determine the pressure in the cylinder. What type of problem is this? Only one set of conditions

20 A L cylinder contains 75.5 g of neon at 24.5 o C. Determine the pressure in the cylinder. PV = nRT P = V = n = R = T = ? L 75.5 g = mol g mol Ltorr molK = K P = nRT V = (3.74 mol)(62.4Ltorr)(297.5K) (12.25 L) molK = torr = 5670 torr How many atmospheres is this?

21 What is the density of carbon dioxide gas at 25 o C and 725 mmHg pressure? Density = g/L = g  L so if we can find g and L, division will work! P = V = n = R = T = 725mmHg 62.4 L torr molK = 298 K What do we do now?

22 What is the density of carbon dioxide gas at 25 o C and 725 mmHg pressure? Density = g/L = g  L so if we can find g and L division will work! P = V = n = R = T = 725mmHg 62.4 Ltorr molK = 298 K Two variables! Let’s pick an amount for one and calculate the other! Let’s choose 1 mol of CO 2 and find the number of Liters.

23 What is the density of carbon dioxide gas at 25 o C and 725 mmHg pressure? Density = g/L = g  L so if we can find g and L division will work! P = V = n = R = T = 725mmHg 62.4 Ltorr molK = 298 K 1.0 mol (44.0 g) V = nRT P = (1 mol) (62.4 Ltorr) (298 K) ( molK ) (725 torr) = 25.6 L NOW: 1.72 ___________ = g L 44.0 g 25.6 L

24 A 2.50 gram sample of a solid was vaporized in a 505 mL vessel. If the vapor pressure of the solid was 755 mmHg at 155 o C, what is the molecular weight of the solid? molecular weight ~ molar mass = g/mol = g  mol..so if we can find grams and moles and divide.... P = V = n = R = T = 755 torr L...we already have grams!! We’re halfway there! 62.4 Ltorr molK = 428 K n = PV RT = 755 torr | L | molK_____ | ______ | 62.4 Ltorr | 428 K = mol NOW: 2.50 g = g mol mol 175.1

25 So Density is g/L (g ÷ L) and molar mass is g/mol (g ÷ mol).

26 Dalton’s Law of Partial Pressures: P total = P 1 + P 2 + P He H 2 N 2

27 Dalton’s Law of Partial Pressures: P total = P 1 + P 2 + P Since they are considered to be ideal gases, the attractions and repulsions between molecules are ignored.... and... PV=nRT so: PV = (n 1 + n 2 + n 3 )RT or: We also refer to mole fractions:

28 To find the gas pressure, the pressure of the water vapor must be subtracted from the total pressure.

29 A mL flask contains 1.00 mg of He and 2.00 mg of H 2 at 25.0 o C. Calculate the total gas pressure in the flask in atmospheres. The total pressure is due to the partial pressures of each of these gases. so: For He: _____________________ = mol He 1.00 x g He 4.00 g mol 2.50 x For H 2 : ______________________ = mol H x g H2H g mol 9.92 x 10 -4

30 A mL flask contains 1.00 mg of He and and 2.00 mg of H 2 at 25.0 o C. Calculate the total gas pressure in the flask in atmospheres. so: For He: _____________________ = mol He 1.00 x g He 4.00 g mol 2.50 x For H 2 : ______________________ = mol H x g H g mol 9.92 x And: P total = (2.50 x x )(RT/V) = ( mol)( Latm)( )K molK ( L) P total = atm

31 A mL flask contains 1.00 mg of He and and 2.00 mg of H 2 at 25.0 o C. Calculate the total gas pressure in the flask in atmospheres. so: For He: _____________________ = mol He 1.00 x g He 4.00 g mol 2.50 x For H 2 : ______________________ = mol H x g H g mol 9.92 x Calculate the pressure due just to He (you have 37 seconds): = atm and P hydrogen = ? = atm

32 Magnesium is an active metal that replaces hydrogen from an acid by the following reaction: Mg(s) + 2HCl(aq)  MgCl 2 (aq) + H 2 (g) How many g of Mg are needed to produce 5.0 L of H 2 at a temperature of 25 o C and a pressure of 745 mmHg? Mg(s) + 2HCl(aq)  MgCl 2 (aq) + H 2 (g) 5.0 L? g Hint: find moles of H 2 using PV = nRT then work as a stoichiometry problem. n = PV RT n = 0.20 mol =____________________________________ 745 mmHg5.0 L 62.4 LmmHg molK 298 K

33 Magnesium is an active metal that replaces hydrogen from an acid by the following reaction: Mg(s) + 2HCl(aq)  MgCl 2 (aq) + H 2 (g) How many g of Mg are needed to produce 5.0 L of H 2 at a temperature of 25 o C and a pressure of 745 mmHg? Mg(s) + 2HCl(aq)  MgCl 2 (aq) + H 2 (g) 5.0 L? g 0.20 mol ____________________________________ = g Mg 0.20 mol H2H2 1 H2H2 1 Mg mol Mg 24.3 g Mg 4.87

34 Molecular Speeds: K.E. = ½ mv 2 Average kinetic energy of a gas molecule:  = ½ m  2 Where  = the rms (root-mean-square) speed of the molecules at each temperature. From kinetic-molecular theory: At any given temperature the molecules of all gases have the same average kinetic energy. Which molecules travel faster, big or little?

35 At room temperature, the average speed of an N 2 molecule is mi/hr

36 Molecular diffusion and effusion: Diffusion: “gas molecules spreading out to fill a room are diffusing.” Its not easy since an average gas molecule at room temperature and pressure will experience about 10 billion collisions per second! It only travels about 60 nm between collisions!

37 Effusion: “A Helium filled balloon loses He by effusion.” Small hole or pore escaping molecule

38 Which molecules will effuse faster from this semiporous container? Graham’s Law of effusion: effusion rate is inversely proportional to the square root of its molar mass. For 2 gases:

39 r = rate of effusion u = root mean speed (~average speed) of molecules M = molar mass Compare the rates of effusion of He and N 2. He effuses 2.65 times as fast as N 2.

40 N 2 He Which balloon will lose pressure sooner?

41 N 2 He Which balloon will lose pressure sooner? Big molecules Little molecules (escape more easily)

42 Real Gases: When do gases become non-ideal? Temperature: low Pressure: high As they approach the liquid state, attractions between molecules increase and they become less ideal. van der Waal’s equation is one equation used to treat non-ideal gases. a and b are constants found in tables for each gas.

43 CO boiling Pt. 81K SiH 4 boiling Pt. 161K PH 3 boiling Pt. 188K C 3 H 8 boiling Pt. 231K Which gas would deviate the most from the ideal gas law at room temperature (25 o C)?

44 100K 200K 300K CO(l) boiling Pt. 81K SiH 4 (l) boiling Pt. 161K PH 3 (l) boiling Pt. 188K C 3 H 8 (l) boiling Pt K Which gas would deviate the most from the ideal gas law at room temperature (25 o C)?