# Chapter 5: Gases

Chapter 11: Gases Characteristics of Gases Unlike liquids and solids, gases expand to fill their containers; are highly compressible; have extremely low densities.

2009, Prentice-Hall, Inc. Pressure Pressure is the amount of force applied to an area. F P= A Atmospheric

pressure is the weight of air per unit of area. 2009, Prentice-Hall, Units of Pressure mm Hg or torr These units are literally the difference in the heights measured in mm (h) of two connected columns of mercury.

Atmosphere 1.00 atm = 760 torr 2009, Prentice-Hall, Manometer This device is used to measure the difference in pressure between atmospheric pressure and that of a gas in a vessel.

2009, Prentice-Hall, Standard Pressure Normal atmospheric pressure at sea level is referred to as standard pressure. It is equal to 1.00 atm 760 torr (760 mm Hg) 101.325 kPa

2009, Prentice-Hall, Inc. Gas Laws: Four variable are need to describe gases. Pressure (P) Volume (V) Temperature (T, Kelvin) Amount (n, mole) Understanding the interrelationship of these variables allow scientists to study properties of gases quantitatively on the molecular/atomic level.

Boyles Law The volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure. 2009, Prentice-Hall, As P and V are inversely proportional A plot of V versus P results in a curve.

Since PV = k V = k (1/P) This means a plot of V versus 1/P will be a straight line. 2009, Prentice-Hall, Charless Law When a given amount of gas is held at a constant pressure, its volume is directly proportional to the Kelvin

temperature The volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature. i.e., V T

=k A plot of V versus T will be a straight line. 2009, Prentice-Hall, The General (combined) Gas law Relates properties of P,V, T only when the amount of gas is unchanged. Sample problem: A sample of Argon gas initially at 0C occupies

2.24L and exerts 760 mm Hg. If the gas is heated to 100. C and allowed to expand to 3.00L, what is the new pressure of the gas? Answer: 775 mm Hg Avogadros Law The volume of a gas at constant temperature and pressure is directly proportional to the number of moles of the gas. Mathematically, this means

V = kn 2009, Prentice-Hall, Avogadros Law & Molar Volume Under conditions of STP (1 atm., 273K), one mole of a gas occupies 22.4L Ideal-Gas Equation So far weve seen that

V 1/P (Boyles law) V T (Charless law) V n (Avogadros law) Combining these, we get nT V P 2009, Prentice-Hall, Inc. Ideal-Gas Equation

The constant of proportionality is known as R, the gas constant. 2009, Prentice-Hall, Ideal-Gas Equation The relationship then becomes

2009, Prentice-Hall, Inc. nT V P nT V=R P or PV = nRT Sample Problem:

What pressure should 1.00g of oxygen exert if it is in a 250 mL vessel at a temperature of 15C? Answer = 2.96 atm. Densities of Gases Understanding the density of a gas at a given

temperature and pressure is useful. Likewise, knowing the density of a gas can allow us to determine the molar mass and possible identity of an unknown gas. All this can be derived from the ideal gas law. n = moles, m= mass (g), M = molar mass (g/mole) 2009, Prentice-Hall, Inc. Densities of Gases Mass volume = density So,

m P d= = V RT Note: One only needs to know the molecular mass, the pressure, and the temperature to calculate the density of a gas. 2009, Prentice-Hall, Inc.

Molecular Mass We can manipulate the density equation to enable us to find the molecular mass of a gas: P d= RT Becomes 2009, Prentice-Hall, Inc. dRT

= P Sample Density problem: Determine the density of nitrogen gas (N2) and Carbon dioxide gas (CO2) at STP Answer: N2= 1.25 g/L CO2= 1.96 g/L

Application of gas density Gas Laws & Stoichiometry The ideal gas law provides another method to calculate the number of moles of a species-useful in chemical reactions. PV = nRT Gas Stoichiometry

Incorporation of the molar quantity allows us to address gas-phase chemical reactions quantitatively. Sample Gas Law-Stoichiometry problem: Mercury can be achieved by the following reaction : __HgO(s) __ Hg(l) + __O2(g) What volume of oxygen gas can be produced from 4.10 g of mercury (II) oxide at STP?

Strategy: Balance equation Calculate moles of O2(g) Solve for volume using ideal gas law Answer: 0.212L Another problem: Given the following equation, what mass of NO is produced from 500. L of NH3 at 250.0C and 3.00 atm? 4NH3(g) + 5O2(g) 4 NO(g) + 6H2O(g) Strategy: Balance equation (done) Determine moles of NH3 (ideal gas law) Apply stoichiometry to solve for NO

Answer: 1050 g NO Daltons Law of Partial Pressures The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone. In other words, Ptotal = P1 + P2 + P3 + 2009, Prentice-Hall, Inc.

Daltons Law of Partial Pressure & Mole Fraction Daltons law states that the total pressure will be the sum of the pressure that each gas would exert if it were alone under the same condition: Pt = P1 + P2 + P3..etc. The presence of the other gases does not affect the pressure that each gas exerts because each gas molecule is moving independently.

Total pressure is dependent on # of molecules. It doesnt matter what the molecules are: PV = ntotalRT Partial Pressure problem: What is the pressure of 5.00L of a gas mixture consisting of: 0.30moles of N2, 0.20moles of O2 0.15 moles of CO2 The temperature is 298K. (use the Ideal gas law: ntotal) What is the partial pressure of each gas?

Answer: 3.18 atm. Mole Fraction Knowing the mole fraction (X) for each gas allows us to determine their partial pressure: XA = Moles of component A total moles PA = XA Ptotal Daltons Law: What is the total pressure in atm of a gas

mixture that contains 1.0g of H2 and 8.0 g of Ar in a 3.0 L container at 27C? What is the partial pressure of each gas? Answer: PH2 = 4.1 atm PAr = 1.6 atm Ptotal = 5.7 atm Partial Pressures When one collects a gas over water, there is water vapor mixed in with the gas.

To find only the pressure of the desired gas, one must subtract the vapor pressure of water from the total pressure. 2009, Prentice-Hall, Kinetic Molecular Theory Kinetic-Molecular Theory This is a model that aids in our

understanding of what happens to gas particles as environmental conditions change. (role of: temp (T), volume (V), amount (n) and pressure (P)) 2009, Prentice-Hall, Main Tenets of Kinetic-Molecular Theory (KMT)

Energy can be transferred between molecules during collisions, but the average kinetic energy of the molecules does not change with time, as long as the temperature of the gas remains constant. 2009, Prentice-Hall,

Main Tenets of KineticMolecular Theory Gases consist of large numbers of molecules that are in continuous, random motion. The combined volume of all the molecules of the gas is negligible relative to the total volume in which the gas is contained (more empty space than particles). Main Tenets of Kinetic-Molecular

Theory Attractive and repulsive forces between gas molecules are negligible. 2009, Prentice-Hall, The Kinetic-Molecular Theory of Gases Postulates:

Clausius (1857) A gas is a collection of a very large number of particles that remains in constant random motion. The pressure exerted by a gas is due to collisions with the container walls The particles are much smaller than the distance between them. The Kinetic-Molecular Theory

of Gases The particles move in straight lines between collisions with other particles and between collisions with the container walls. (i.e. the particles do not exert forces on one another between collisions.) The average kinetic energy ( mv2) of a collection of gas particles is proportional to its Kelvin temperature. Gas particles collide with the walls of their container and one another without a loss of energy.

The Kinetic-Molecular Theory of Gases Gas pressure at the particle level: The Kinetic-Molecular Theory of Gases The relationship between temperature (T) and velocity (u) (kinetic energy) can be found by the following: Ideal gas law nRT

P = V Setting the two equal: solving: The root mean square velocity for a gas is: KMT Nmu 2 P = 3V

and nRT V Nmu 2 = 3V 3nRT 2

u = Nm u RMS = 3RT = M wt 3RT M wt Careful for this!

J mol K kg is in mol R =8.314 M wt Kinetic-Molecular Theory

What is the RMS velocity of a nitrogen molecule in miles per hr at STP? u RMS = J 3 8.314 273.15K mol K u RMS = g N2

kg 28.01 3 mol N 2 10 g 102 cm in ft

1m 2.54cm 12in mile 3600s 5280ft hr m/s kg m recall... 1J =

s2 3RT M 2 = 1.103103 mph Kinetic-Molecular Theory At the same T, all gases have the same average KE.

As T goes up, KE also increases and so does speed. Gas law simulation and KE Kinetic Molecular Theory For a given temperature, heavier gases move slower than lighter gases. The velocities are described by a distribution.

Velocity of Gas Particles Average velocity decreases with increasing mass. Gas Diffusion & Effusion Diffusion is the process of gas migration due to the random motions and collisions of gas particles. It is diffusion that results in a gas completely filling its container. After sufficient time gas mixtures become homogeneous.

Gas Diffusion: Relation of mass to Rate of Diffusion HCl and NH3 diffuse from opposite ends of tube. Gases meet to form NH4Cl HCl heavier than NH3 Therefore, NH4Cl

forms closer to HCl end of tube. Gas Effusion EFFUSION is the movement of molecules through a small hole into an empty container. (vacuum) In this case, the H2 molecules escape more quickly due to their lower molar mass. Graham's Law:

provides a mathematical relationship of kinetic energy. KE1 = KE2 1/2 m1v12= 1/2 m2v22 m1 v22 = m2 v12 m

1 m 2 v22 = v12 = v2 v1

Grahams Law Under certain conditions, methane gas (CH4) diffuses at a rate of 12 cm/sec. Under the same conditions, an unknown gas diffuse at a rate of 8.0 cm/sec. What is the molar mass of the unknown gas? Strategy: KE1 = KE2 (M1v12 = M2v22) Solve for M2 Deviations from Ideal

Behavior The assumptions made in the kineticmolecular model (negligible volume of gas molecules themselves, no attractive forces between gas molecules, etc.) break down at high pressure and/or low temperature. 2009, Prentice-Hall, Real Gases In the real world, the behavior of gases only conforms to the ideal-gas

equation at relatively high temperature and low pressure. Even the same gas will show wildly different behavior under high pressure at different temperatures. 2009, Prentice-Hall,

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