Chpt 5 - Gases• Gas Law Development• Dalton’s Partial pressure law• Graham’s effusion• Kinetic Theory

–Root-mean-square velocity• van der Waals equation of state• HW: Chpt 5 - pg. 223-231, #s 5, 22, 23, 25,

31, 32, 35, 39, 41, 46, 55, 64, 66, 71, 75, 77, 81, 91, 95, 97, 101, 124 Due Mon 10/4

Torricelli barometer

The height in mm of mercuryabove the surface of the resevoirof mercury determines the pressure.The units are mmHg.

mmHg is also the same unit asTorr. i.e. standard pressure is 760 mmHg and 760 Torr

Pressure is? Units?

Simple Manometer

Similar to the barometer, the height difference of the Hg relates the pressure difference in the unknown gas bulb side to the current atmospheric pressure.

The higher Hg side has the _____ pressure. (higher/lower)

Boyle’s Law

• Constant temperature experiments demonstrated the PV=constant graphing this yields an inverse relationship

• Thus if the pressure of volume changes at a constant temperature

P1V1 = P2V2

Plot of PV vs. P for Several Gases

This graph shows Boyles linear relationship for the PxV. The constant depends on the gas

Charles’s Law

• Constant pressure experiments demonstrated that Volume is directly proportional to Temperature (Kelvin)

V1 = V2

T1 T2

• Several gases were used & all extrapolate to zero volume and the same temperature at negative 273oC

Plots of V vs. T(ºC)

Charles’s Law Experiment results

Demonstrates a unique absolute zero at -273.15 oC

Combined Gas Law

P1V1 = P2V2

T1 T2

Avogadro’s Law - equal volumes of gas contain equal particles of gas

V = k n

At constant temperature and pressure the volume is directly proportional to the number of moles of gas.

Ideal Gas Law

• Putting it all together, we can calculate that constant now. The universal gas constant R.

PV=R or PV=nRT

nT R =0.0821 l *atm/mol*K

=8.31 l *kpa/mol*K

Density / Molar Masswith Ideal gas law

Molar mass, MM = ? What are the units?

So, moles = ?

Density, d = ? Use L for density since gas

So, mass = ?

Combine and get expression for moles n=

N= PV = dV Thus MM = dRT volume will be in Liters

RT MM P

Dalton’s Law of Partial Pressures

The gases in a mixture act independently and thus the forces (and pressures) are additive.

Ptotal = P1 + P2 + P3 + …

Kinetic Molecular Theory

• Ideal Gas Behavior– Particles assumed to have zero volume– Particles in constant motion– Particles exert no forces on each other

– KEave is directly proportional to T (K)

• Check out Appendix 2 to see derivation of ideal gas law PV=nRT

Kinetic Theory

• also KEave = 3/2 RT

• Root square mean velocity

• urms = sqrt(3RT/M) – Where M is mass of a mole in kg – So now we can calculate ave velocities of

gases

Effusion of Gas into Evacuated Chamber

If more than one type of gas or more than one isotope, which gas effuses faster?

Lighter gas movesFaster!!

KE = 1/2 mv2

Relative Molecular Speed Distribution of H2 and UF6

Diffusion Rates of NH3 and HCl Molecules Through Air

Relative diffusion/effusion rate pg. 213 textbookrate1 = Sqrt(M2)rate2 Sqrt(M1) lighter gas is faster

Ideal vs. Real Gases

• All of the gases are real!!! They just behave “ideally” at certain temperatures and pressures.

• Think of the KMT assumptions, what conditions would gases “fail” to act ideally.

• Low temperatures (gases condense) & High pressures (force the gases together so they have to interact)

Plots of PV/nRT vs. P for Several Gases

Plot of PV/nRT vs. P for N2 Gas

This graph shows that at higher temperatures gases behave closer to ideal even at high pressures.

Recall that gases behave “ideally” at low pressures and high temperatures.

van der Waals Equation

• van der Waals equation is entire gas law relationship with corrections for real volume and molecular attractions. pg.216 textbook with Table 5.3 for some common gases

(Pobs + correction) x ( V - nb) = nRT

This formula is also given on AP exam sheet.

Values of the van der Waals Constants for Common Gases

a is a measure of intermolecular attractions (it is the correction to the pressure to account for attractions for each other)

b is a measure of size of the molecule (it is the volume correction)