Gases Chapter 5 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Elements that exist as gases at 25 0 C and 1 atmosphere 5.1

Gases assume the ______________ and ______________ of their containers. Gases are the most _______________________________ state of matter. Gases will mix _____________ and __________________ when confined to the same container. Gases have much _______________ than liquids and solids. 5.1 Physical Characteristics of Gases

Units of Pressure 1 pascal (Pa) = 1 N/m 2 1 atm = 760 mmHg = 760 torr 1 atm = 101,325 Pa (~10 5 ) 5.2 Barometer Pressure = Force Area 1.0 N is the force required to accelerate 1.0 kg 1.0 m/s 2

5.2

5.3 As P (h) increases V decreases

P  1/V P x V = constant P 1 x V 1 = P 2 x V _______________ Law Constant temperature Constant amount of gas

_______________ —constant temperature _______________ —constant pressure _______________ —constant volume

A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. What is the pressure of the gas (in mmHg) if the volume is reduced at constant temperature to 154 mL? P 1 x V 1 = P 2 x V 2 P 1 = 726 mmHg V 1 = 946 mL P 2 = ? V 2 = 154 mL P 2 = P 1 x V 1 V2V2 = = 5.3

As T ____________V ________________ 5.3

Variation of gas volume with __________________ at constant ________________. 5.3 V  TV  T V = constant x T V 1 /T 1 = V 2 /T 2 T (K) = t ( 0 C) Charles’ & Gay-Lussac’s Law Temperature must be in ____________

A sample of carbon monoxide gas occupies 3.20 L at C. At what temperature will the gas occupy a volume of 1.54 L if the pressure remains constant? V 1 = 3.20 L T 1 = K V 2 = 1.54 L T 2 = ? T 2 = V 2 x T 1 V1V1 = = 5.3 V 1 /T 1 = V 2 /T 2

__________________ Law V  number of moles (n) V = constant x n V 1 /n 1 = V 2 /n Constant _________

Ammonia burns in oxygen to form nitric oxide (NO) and water vapor. How many volumes of NO are obtained from one volume of ammonia at the same temperature and pressure? 4NH 3 + 5O 2 4NO + 6H 2 O __ mole NH 3 __ mole NO At constant T and P __ volume NH 3 __ volume NO 5.3

________________________ 5.4 Charles’ law: V  T  (at constant n and P) Avogadro’s law: V  n  (at constant P and T) Boyle’s law: V  (at constant n and T) 1 P V V  nT P V = constant x = R nT P P R is the ____________ _______ = ____________

The conditions ___ 0 C and ___ atm are called standard temperature and pressure (STP). PV = nRT R = PV nT = (1 atm)(22.414L) (1 mol)( K) R = ___________ L atm / (mol K) 5.4 Experiments show that at STP, 1 mole of an ideal gas occupies _________ L.

What is the volume (in liters) occupied by 49.8 g of HCl at STP? PV = nRT V = nRT P T = 0 0 C = K P = 1 atm n = 49.8 g x 1 mol HCl g HCl = 1.37 mol V = V = ____________ 5.4

Argon is an inert gas used in light bulbs to retard the vaporization of the filament. A certain light bulb containing argon at 1.20 atm and 18 0 C is heated to 85 0 C at constant volume. What is the final pressure of argon in the light bulb (in atm)? PV = nRT n, V and R are _________________ nR V = P T = constant P1P1 T1T1 P2P2 T2T2 = P 1 = 1.20 atm T 1 = 291 K P 2 = ? T 2 = 358 K P 2 = P 1 x T2T2 T1T1 = 1.20 atm x 358 K 291 K = _________ atm 5.4

Density (d) Calculations d = m V = PMPM RT Molar Mass ( M ) of a Gaseous Substance dRT P M = 5.4 How do we arrive at these equations?? Let’s see…

PV = nRT (1) (2) (3) (4) (5) P = nRT V Divide by V Divide by RT P RT n V = m M = = n n = number of moles m = mass in grams M = molar mass sub. (4) into (3) m MVMV P RT Multiply by M

(7) = m V (8) (9) = M dRT P Multiply by RT and divide by P in order to Solve for M (6) = m V PMPM RT Since d and = m V PMPM RT d = PMPM RT

Density (d) Calculations d = m V = PMPM RT m is the mass of the gas in g M is the molar mass of the gas Molar Mass ( M ) of a Gaseous Substance dRT P M = d is the density of the gas in g/L 5.4

Gas Stoichiometry What is the volume of CO 2 produced at 37 0 C and 1.00 atm when 5.60 g of glucose are used up in the reaction: C 6 H 12 O 6 (s) + 6O 2 (g) 6CO 2 (g) + 6H 2 O (l) g C 6 H 12 O 6 mol C 6 H 12 O 6 mol CO 2 V CO g C 6 H 12 O 6 1 mol C 6 H 12 O g C 6 H 12 O 6 x 6 mol CO 2 1 mol C 6 H 12 O 6 x = _________ mol CO 2 V = nRT P mol x x K Latm molK 1.00 atm = = __________ L 5.5

Dalton’s Law of ___________________ V and T are constant P1P1 P2P2 P total = P 1 + P 2 5.6

Consider a case in which two gases, A and B, are in a container of volume V. P A = n A RT V P B = n B RT V n A is the number of moles of A n B is the number of moles of B P T = P A + P B X A = nAnA n A + n B X B = nBnB n A + n B P A = X A P T P B = X B P T P i = X i P T 5.6 X is the mole fraction

A sample of natural gas contains 8.24 moles of CH 4, moles of C 2 H 6, and moles of C 3 H 8. If the total pressure of the gases is 1.37 atm, what is the partial pressure of propane (C 3 H 8 )? P i = X i P T X propane = P T = 1.37 atm = __________ P propane = x 1.37 atm= __________ atm 5.6

2KClO 3 (s) 2KCl (s) + 3O 2 (g) Bottle full of oxygen gas and water vapor P T = ________ + ________ 5.6

_______________________________ 1.A gas is composed of molecules that are separated from each other by distances far greater than their own dimensions. The molecules can be considered to be _____; that is, they possess mass but have negligible volume. 2.Gas molecules are in constant ______ in random directions. Collisions among molecules are perfectly elastic. 3.Gas molecules exert neither __________ nor __________ forces on one another. 4.The average kinetic energy of the molecules is proportional to the temperature of the gas in _____________________. Any two gases at the same temperature will have the same average kinetic energy. 5.7

Kinetic theory of gases and … _________________ of Gases ___________ Law P  collision rate with wall Collision rate  number density Number density  1/V P  1/V ___________ Law P  collision rate with wall Collision rate  average kinetic energy of gas molecules Average kinetic energy  T P  TP  T 5.7

Kinetic theory of gases and … ___________ Law P  collision rate with wall Collision rate  number density Number density  n P  nP  n ___________ Law of ___________ ___________ Molecules do not attract or repel one another P exerted by one type of molecule is unaffected by the presence of another gas P total =  P i 5.7

Apparatus for studying molecular speed distribution 5.7

The distribution of speeds for nitrogen gas molecules at three different temperatures The distribution of speeds of three different gases at the same temperature 5.7 u rms = 3RT M 

___________ is the gradual mixing of molecules of one gas with molecules of another by virtue of their kinetic properties. 5.7

________________________________ 1 mole of ideal gas PV = nRT n = PV RT = Repulsive Forces Attractive Forces

Effect of intermolecular forces on the pressure exerted by a gas. 5.8