Gases

Gases All elements that are gases at standard conditions are nonmetalsAll compounds that are gases at standard conditions are covalent compoundsGases of all elements/compounds have similar physical properties.Substances that are liquid and solid at standard condition can exist as gases – they are usually called vapors (water vapor)

Kinetic Molecular Theory

An explanation of the characteristics and properties of gases (and how they differ from liquids and solids)

Postulates (assumptions) Gases are composed of a large number of particles (atoms/molecules) that behave like hard, spherical objects in a state of constant, random motion

These particles have insignificant volume compared to the total volume of the gas. The particles are much smaller than the average distances between them. Most of the volume of a gas is empty space between the molecules.

There is no force or attraction between the gas particles or between the particles and the walls of the container.

When particles of a gas collide a small amount of energy may transfer from one particle to another but the average kinetic energy of the gas remains constant. (Energy is conserved)

The average kinetic energy of a collection of gas particles depends only on the temperature of the gas. (Samples of different gases at the same temp have the same average kinetic energy)

Properties of GasesPressure

Caused by the collision of gas particles with the walls of their container. The magnitude depends on how often and how forcefully the particles strike the walls.

Temperature (absolute - in Kelvin)A measure of the average kinetic energy of the particles. Motion increases with increasing temp.

VolumeSince a gas is mostly empty space it can be readily compressed to a smaller volume or can expand to fill any larger volume. (Takes the volume of its container)

Diffusion - The spontaneous spreading out of a gas to fill a container uniformly

DensityVery low! The mass of a gas occupies a much greater volume than an equal mass of the same liquid or solid.

MixturesAll gases that do not chemically react with each other can form homogeneous mixtures

High entropy

Ideal Gas Conforms exactly to all aspects of the kinetic theoryDoes NOT exist. Real gases have attractions between particles and the particles have volume. Real gases exhibit ideal behavior when

Temperature is high (particles have enough energy to overcome any attractions) Pressure is low (particles are so far apart their individual volume is insignificant). Real gases have near ideal behavior at room conditions.

The most ideal gases have the weakest IMFs (use molar mass as a tie-breaker when ranking)

Real Gases most ideal He no bonds

N2 nonpolar CO2 nonpolar with polar bonds

least ideal H2O polar

Pressure Exerted by Gases Pressure is due to collisions between gas molecules and the container walls Pressure = force / areaUnits are: lb/in2 (psi), g/cm2 , atmospheres (atm), mm Hg, Torr, pascals (Pa), kilopascals (kPa), barUnit relationships (used for converting units)

1.00 mm Hg = 13.6 mm H2O 1 mm Hg = 1 Torr 1 atm = 760 mm Hg

1.00 atm = 14.7 lb/in2 1.00 atm = 1.01 105 Pa

1 in2 column ofair (mass = 14.7 lb)

1 atm of pressure =14.7 lb/in2

Measuring the pressure of collected gases

Principle: Pressure on a gas = the pressure of a gas

As long as the balloon is not inflating/deflating PA = PB

Measuring EquipmentEudiometer: gas measuring tube

Manometer: instrument which allows for the determination of the pressure of a gas sample

Barometer: instrument for measuring air pressure

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Manometer - measuring the pressure of collected gases

(a) Pgas = Ph1 (b) Pgas = Patm – Ph2 (c) Pgas = Patm + Ph3

Barometer – measuring air pressure

Hg can move in and out of the tube

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Standard Temperature a reference temperature which is 0oC or 273 KNOT the same as standard state (25oC or 298 K)

Standard Pressurea reference pressure which is 1 atm or its equivalent

Molar Volume of a gasThe volume of 1 mole of a gas at standard temperature and pressure (STP)22.4 L/mole (at 273 K and 1 atm)

Boyle’s Law Gas Pressure vs. Gas Volume

As the container size decreases, the particles collide with the walls more frequently thus raising the pressure

Qualitatively: P ↑ , V ↓ or P↓ , V ↑temperature and moles held constant

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Gas Pressure vs. Gas Volume

As volume increases, pressure decreases.

PV=k (at constant temp and moles)P1V1=k and P2V2=k (*k depends on temp and moles)

thus P1V1 = P2V2

Inverse variation:

Movie

Boyle’s P-V

Increasing the temperature increases the KE of the molecules. With higher velocities, the molecules hit the walls more often and harder: more pressure (if volume held constant)

qualitatively: T ↑ , P ↑ or T↓ , P ↓ volume and moles held constant

Amonton’s Law (a.k.a. Nobody’s Law - Not in your book)

Gas Pressure vs. Gas Temperature

Amonton’s: P-T T/P = k ONLY if temp is Kelvin

T1P2 = T2P1

Represents a direct variation: graph is a straight line

P

Charles’s LawGas Volume vs. Gas Temperature

Increasing the temperature increases the KE of the molecules. The faster moving molecules will hit the walls more often and harder. If the pressure is held constant and the volume is not, the volume will increase.

Qualitatively: T ↑ , V ↑ or T ↓ , V ↓pressure and moles held constant

Charles’s LawGas Temperature vs. Gas Volume

T/V = kT1V2 = T2V1 (Temp in Kelvin!!!)

Direct variation: graph is a straight line

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Charles’s Law

As temperature increases, volume increases

Absolute zero can be determined by determining T when volume is zero.

COMBINED GAS LAW This law combines Boyle’s, Amonton’s and Charles’s Laws into one law.It allows you to do calculations for situations in which only the amount of gas is constant

P1V1 = P2V2

P1T2 = P2T1 P1V1T2 = P2V2T1

V1T2 = V2T1

If you remember only this one equation – you should be able to derive all 3 of the gas laws!

Law of Combining Volumes:Gay-Lussac:

Gas volumes during a chemical reaction are proportional to the coefficients of the balanced equation.

2 H2(g) + O2(g) 2H2O(g) 2L + 1L = 2 L

Avogadro’s HypothesisAvogadro used Gay-Lussac’s work and realized:

Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. (it doesn’t matter what gas it is – H2, H2O, CO2, etc)

Ex: 22.4L of any gas at 273K and 1atm contains 6.02x1023 particles (1 mole).

Avogadro’s LawGas Volume vs. Amount of Gas Increasing number of molecules will increase collisions and will increase volume if pressure is held constant   

  qualitatively: n ↑ , V ↑ or n ↓ , V ↓ P and T held constant

   quantitatively: V/n = k

V1n2 = V2n1

Avogadro’s LawGas Volume vs. Amount of Gas Rearranging the equation:

V1n2 = V2n1

So volume and mole ratios are equivalent to one another.

Ideal Gas Lawcombines all of the above into one equation or relationship PV = nRT

o      P is pressureo      V is volumeo      n is the number of moles of gaso      T is the temperature in KELVINo      R is the universal gas constant

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Value of the Gas Constant (R)

♦

other values of R    1.987 cal/mol K   8.314 J/mol K 8.314 m3 Pa/mol K   62.36 L torr/mol K• Units must cancel when using this equation!

PV (1.00 atm)(22.4 L) L atmR = = = 0.0821 nT (1.00 mole)(273 K) mole K

 Other Applications of the Ideal

Gas Law The ideal gas equation can be stated in other ways incorporating other variables while still keeping the same general relationship

     𝐷=

𝑚𝑚𝑃𝑅𝑇𝑃𝑉=

𝑔𝑅𝑇𝑚𝑚

g = gramsD = densitymm = molar mass

van der Waals Equation (Ideal vs. Real Gases)

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2n aP + V - nb = n R TV

Corrects the ideal gas equation for the "problems" of real gases

Real gases have attractions between molecules – corrects for this.Real gas molecules have an actual volume – nb corrects for this.

    your textbook has a chart of van der Waals constants (a and b) for several common real gases on page 412

Dalton's Law of Partial Pressure Total number of collisions is based on total number of molecules. Collisions from one kind of gas molecule are based only on that kind of molecule.

The total pressure of a mixture of gases is the sum of the pressures of each individual gas (each gas is said to have a partial pressure)

Ptot = P1 + P2 + P3 + …..  

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Dalton’s Law Application #1 Dalton's Law can be stated in a slightly different way emphasizing one component of the gas mixture

      

the ratio is called the "mole fraction" of the gas and is symbolized by Xgas 1

substituting in the above equation we get: Pgas 1 = (Xgas 1) ( Ptotal )

this works because the total pressure depends on the total moles of all the gases

gas 1gas 1 total

totalP = P n

n

gas 1

total

nn

Dalton’s Law Application #2Dalton’s Law is especially useful when collecting a gas by water displacement

1. A gas collected by water displacement will have some water vapor mixed in with the gas

2. Since we want only the pressure of the gas: Ptot = Pgas + PH2O Pgas = Ptot – PH2O

3. Values for water vapor pressure are in Appendix B (page 1058) of your text

Graham's Law

Related to the rate at which gases: diffuse (spread to fill a volume) effuse (move through a small opening in their container)

Lighter particles (low MM) move faster!

most often stated as: can also use density:

gas 1 gas 2

gas 2 gas 1

rate molar mass = rate molar mass

gas 2gas 1

gas 2 gas 1

densityrate = rate density

Root-mean-square (rms) speed

The speed (velocity) of molecules with exactly the average kinetic energy

KE= ½ mv2

Some molecules in a gas sample move fasterSome molecules in a gas move slowerrms speed is close to the average speed

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Root mean square (rms) speed (symbolized by )

rms speed () decreases with increasing molar mass (heavier particles move slower!)

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2

kg m use R value of 8.314 J/mol-K (J= )s

T is in Kelvin and molar mass be in kg

3RT = molar mass

MUST