Gases

Gases

Since we can’t deal with matter on an atomic level, we use larger aggregates forming solids, liquids, and gases.

Why do particular substances exist as solids, liquids, and gases?

What forces exist with the states of matter?

What are the characteristic properties of a state?

Characteristics of Gases

Expand to fill container.Volume = volume of container.Highly compressible.Form homogeneous mixtures with other gases.Molecules relatively far apart, so they behave as though other molecules weren’t present.

Common Gases

Composed entirely of non-metallic elements.Low molecular masses.0.1% of total volume, rest is empty space (liquids occupy 70% of space.)

Pressure

P = F/A

The SI unit of force is the kg.m/s2 and is called the Newton (N).

The SI unit of pressure is the N/m2= Pascal (Pa)

Standard atmospheric pressure= pressure needed to support a column of mercury 760 mm high = 1.01325 x 105 Pa = 101.325 kPa.

1 atm = 760 mm Hg = 101.325 kPa

A manometer is used to measure the pressure of enclosed gases.

In manometer #1, the system is closed to the atmosphere, so the pressure of the gas equals the height measurement.

In manometer #2, the system is open to the atmosphere, so the pressure of the gas is equal to the Patm + the heightmeasurement, Pgas > Patm.

In manometer #3, open system, the pressure of the gas is equal to the Patm - the height measurement, Pgas < Patm.

The state or condition of a gas can be defined using P, V, T, and n.

Pressure-Volume Relationship: Boyle’s Law-volume of a fixed quantity of gas maintained

at constant temperature is inversely proportional to the pressure.

PV = constant PP1V1 = P2V2

V

Temperature-Volume Relationship: Charles’ Law-volume of a fixed amount of gas at constantpressure is directly proportional to its absolutetemperature.

V = constant x TV1 = V2

T1 T2 P

T

Temperature readings must be converted to K.K = oC + 273

Quantity-Volume Relationship: Avogadro’s Law-as gas is added, volume expands.-equal volumes of gas at the same temperature

and pressure contain equal numbers of particles.

-volume of a gas at constant T,P is directly proportional to the number of moles.

V = constant x n

Boyle V 1/P n, T constantCharles V T n, P constantAvogadro V n P, T constant

V nT P

PV ntPV = nRT Ideal Gas Law

R is the gas law constant and depends on PV units.R = 0.0821 atm.L/mol.K 8.314 Pa.m3/mol.K

Determine the number of moles of oxygen present at 2.3 atm, volume of 2.6 cm3 and 26oC.

http://intro.chem.okstate.edu/1314F00/Laboratory/GLP.htm

Molar Mass and Density

PV = nRT d = m/Vn = PV RT

mass/M = P n = mass/M V RT

mass = PM V RT

d = PM RT

Determine the density of CO2 at 745 mm Hg and 65oC.

Dalton’s Law of Partial Pressures

PTOT = P1 + P2 + P3 …

Determine the pressure caused by a mixture of 2.00 g H2 and 8.00 g N2 at 273K in a 10.0 L vessel.

What is the pressure of each gas?

PGas = Xgas. PTOT

X = mole fraction = moles of gastotal moles

To solve for PH use PV = nRT or PH = XH. PTOT

Other applications of Dalton’s Law:

“collected over water”

PDry Gas = PATM - PWater

Stoichiometric Relationships:Application of PV = nRT to mass-volume

equations.

4NH3(g) + 5O2 (g) 4NO(g) + 6H2O(g)

at non-STP conditions, first use PV=nRT to determine volume.

Determine the volume of NH3(g) given 1.00 mol O2 at 850oC and 5.00 atm pressure.

Kinetic-Molecular Theory

Explains why gases behave as they do.Theory of moving molecules.Gases consist of a large number of particles in continuous, random motion.Volume of gas is negligible compared to total volume of container.Attractive and repulsive forces are negligible.

•Energy transfer occurs during collisions but average kinetic energy doesn’t change, collisions are perfectly elastic.•Average kinetic energy is proportional to absolute temperature.

KM Theory explains pressure and temperature at the molecular level. Pressure = collision of particles with sides of container. Temperature = average kinetic energy of particles.

Oxygen gas at STP is placed in a container whose Volume decreases from 2L to 1L. Predict effect on:

•average kinetic energy of oxygen gas•average speed•total number of collisions with walls of container•number of collisions within a unit area

Root mean square (rms) speed, u, is the speed of a molecule possessing average kinetic energy.

Kinetic Energy = 1/2 mu2

As kinetic energy increases, so does u

How is rms speed of nitrogen gas changed by:a) an increase in temperatureb) an increase in volumec) mixing with Ar at same temperature

Molecular Effusion and Diffusion

Two gases at same temperature have same Kinetic Energy.Lighter molecules must travel faster to have same kinetic energy.

u = 3RT/M

Since M is in the denominator, the lighter the molecule’s mass, the faster the speed of the molecule.

Application of this is effusion - rate at which a gas

escapes through a holediffusion - spread of a substance

through a space or through-

out a second substance

Graham’s Law of Effusion:For two different gases under identical

conditions, the lighter gas will effuse more rapidly.

r1 = M2

r2 M1

Calculate the ratio of the effusion rates of nitrogen gas and oxygen gas.

Deviations from Ideal Behavior:

Pressure and temperature affect ideal behavior.-volume is finite-at short distances gas molecules exert attractive forces on each other

These factors become important when Pressure increasesand Temperature decreases.

The van der Waals equation corrects for real behavior.

(P + n2a) (V - nb) = nRT V2 Correction for Volume correction for molecular

attraction

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