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Characteristics of Gases

- Vapor = term for gases of substances that are often liquids/solids under ordinary conditions
- Unique gas properties
- Highly compressible
- Inverse pressure-volume relationship
- Form homogeneous mixtures with other gases

Mullis

Pressures of Enclosed Gases and Manometers

- Barometer: Used to measure atmospheric pressure*
- Manometer: Used to measure pressures of gases not open to the atmosphere
- Manometer is a bulb of gas attached to a U-tube containing Hg.
- If U-tube is closed, pressure of gas is the difference in height of the liquid.
- If U-tube is open, add correction term:
- If Pgas < Patm then Pgas + Ph = Patm
- If Pgas > Patm then Pgas = Ph + Patm

* Alternative unit for atmospheric pressure is 1 bar = 105 Pa

Mullis

Kinetic Molecular Theory

- Number of molecules
- Temp
- Volume
- Pressure
- Number of dancers
- Beat of music
- Size of room
- Number and force of collisions

Mullis

Kinetic Molecular Theory

- Accounts for behavior of atoms and molecules
- Based on idea that particles are always moving
- Provides model for an ideal gas
- Ideal Gas = Imaginary: Fits all assumptions of the K.M theory
- Real gas = Does not fit all these assumptions

Mullis

5 assumptions of Kinetic-molecular Theory

- Gases = large numbers of tiny particles that are far apart.
- Collisions between gas particles and container walls are elastic collisions (no net loss in kinetic energy).
- Gas particles are always moving rapidly and randomly.
- There are no forces of repulsion or attraction between gas particles.
- The average kinetic energy of gas particles depends on temperature.

Mullis

Physical Properties of Gasses

- Gases have no definite shape or volume – they take shape of container.
- Gas particles glide rapidly past each other (fluid).
- Gases have low density.
- Gases are easily compressed.
- Gas molecules spread out and mix easily

Mullis

Diffusion = mixing of 2 substances due to random motion.

- Effusion = Gas particles pass through a tiny opening……..…

Mullis

Real Gases

- Real gases occupy space and exert attractive forces on each other.
- The K-M theory is more likely to hold true for particles which have little attraction for each other.
- Particles of N2 and H2 are nonpolar diatomic molecules and closely approximate ideal gas behavior.
- More polar molecules = less likely to behave like an ideal gas. Examples of polar gas molecules are HCl, ammonia and water.

Mullis

Gas Behavior

- Particles in a gas are very far apart.
- Each gas particle is largely unaffected by its neighbors.
- Gases behave similarly at different pressures and temperatures according to gas laws.
- To identify a gas that is “most” ideal, choose one that is light, nonpolar and a noble gas if possible.
- Ex: Which gas is most likely to DEVIATE from the kinetic molecular theory, or is the “least” ideal: N2, O2, He, Kr, or SO2?

Answer: sulfur dioxide due to relative polarity and mass.

Mullis

Boyle’s Law

- Pressure goes up if volume goes down.
- Volume goes down if pressure goes up.
- The more pressure increases, the smaller the change in volume.

Mullis

Boyle’s law

- Pressure is the force created by particles striking the walls of a container.
- At constant temperature, molecules strike the sides of container more often if space is smaller.

V1P1 = V2P2

- Squeeze a balloon: If reduce volume enough, balloon will pop because pressure inside is higher than the walls of balloon can tolerate.

Mullis

Charles’ Law

- As temperature goes up, volume goes up.
- Assumes constant pressure.

V1 = V2

T1 T2

T , V

Mullis

Charles’ law

- As temperature goes up volume goes up.
- Adding heat energy causes particles to move faster.
- Faster-moving molecules strike walls of container more often. The container expands if walls are flexible.
- If you cool gas in a container, it will shrink.
- Air-filled, sealed bag placed in freezer will shrink.

Mullis

Gay-Lussac’s Law

- As temperature increases, pressure increases.
- Assumes volume is held constant.

P1 = P2

T1 T2

- A can of spray paint will explode near a heat source.
- Example is a pressure cooker.

Mullis

Combined Gas Law

- In real life, more than one variable may change. If have more than one condition changing, use the combined formula.
- In solving problems, use the combined gas law if you know more than 3 variables.

V1P1 = V2P2

T1 T2

Mullis

Using Gas Laws

- Convert temperatures to Kelvin!
- Ensure volumes and/or pressures are in the same units on both sides of equation.
- STP = 0° C and 1 atm.
- Use proper equation to solve for desired value using given information.

V1P1 = V2P2 V1 = V2 P1 = P2 V1P1 = V2P2

T1 T2 T1 T2 T1 T2

Mullis

Gay Lussac’s law of combining volumes of gases

- When gases combine, they combine in simple whole number ratios.
- These simple numbers are the coefficients of the balanced equation.

N2 + 3H2 2NH3

- 3 volumes of hydrogen will produce 2 volumes of ammonia

Mullis

Avogadro’s Law and Molar Volume of Gases

- Equal volumes of gases (at the same temp and pressure) contain an equal number of molecules.

In the equation for ammonia formation,

1 volume N2 = 1 molecule N2 = 1 mole N2

- One mole of any gas will occupy the same volume as one mole of any other gas
- Standard molar volume of a gas is the volume occupied by one mole of a gas at STP.

Standard molar volume of a gas is 22.4 L.

Mullis

Sample molar volume problem

- A chemical reaction produces 98.0 mL of sulfur dioxide gas at STP. What was the mass, in grams, of the gas produced?

***Turn mL to L first! (This way, you can can use 22.4 L)

98 mL 1 L 1 mol SO2 64.07g SO2 = 0.280g SO2

1000 mL 22.4 L 1 mol SO2

Mullis

Sample molar volume problem 2

What is the volume of 77.0 g of nitrogen dioxide gas at STP?

77.0 g NO2 1 mol NO2 22.4 L = 37.5 L NO2

46.01g NO2 1 mol NO2

Mullis

Ideal Gas Law

- Mathematical relationship for PVT and number of moles of gas

PV = nRT n = number of moles

R = ideal gas constant

P = pressure

V = volume in L

T = Temperature in K

R = 0.0821 if pressure is in atm

R = 8.314 if pressure is in kPa

R = 62.4 if pressure is in mm Hg

Mullis

Sample Ideal Gas Law Problem

- What pressure in atm will 1.36 kg of N2O gas exert when it is compressed in a 25.0 L cylinder and is stored in an outdoor shed where the temperature can reach 59°C in summer?

V = 25.0 L T = 59+273 = 332 K P = ?

R = 0.0821L-atm n = 1.36 kg converted to moles mol-K

- 1.36 kg N2O 1000 g 1 mol N2O = 30.90 mol N2O

1 kg 44.02 g N2O

- PV = nRT
- P = 30.90 mol x 0.0821 L-atm x 332 K = 33.7 atm

25.0 L mol-K

Mullis

Volume-Volume Calculations

- Volume ratios for gases are expressed the same way as mole ratios we used in other stoichiometry problems.

N2 + 3H2 2NH3

Volume ratios are:

2 volumes NH33 volumes H2 2 volumes NH3

3 volumes H2 1 volume N2 1 volume N2

Mullis

Sample Volume-Volume Problem

- How many liters of oxygen are needed to burn 100 L of carbon monoxide?

2CO + O2 2CO2

100 L CO 1 volume O2 = 50 L O2

2 volume CO

Mullis

Sample Volume-Volume Problem 2

Ethanol burns according to the equation below. At 2.26 atm and 40° C, 55.8 mL of oxygen are used. What volume of CO2 is produced when measured at STP?

C2H5OH + 3O2 2CO2 + 3H2O

Number moles oxygen under these conditions is?

PV = nRT: 2.26 atm(.0558L) = n = 0.0049 mol O2

(0.0821 L-atm)(313K)

mol-K

0.0049 mol O2 2 mol CO2 22.4 L =0.073 L CO 2

3 mol O2 1 mol CO2

Mullis

Gas Densities and Molar Mass

- Need units of mass over volume for density (d)
- Let M = molar mass (g/mol, or mass/mol)

PV = nRT

MPV = MnRT

MP/RT = nM/V

MP/RT = mol(mass/mol)/V

MP/RT = density

M = dRT

P

Mullis

Sample Problem: Density

1.00 mole of gas occupies 27.0 L with a density of 1.41 g/L at a particular temperature and pressure. What is its molecular weight and what is its density at STP?

M.W. = 1.41 g |27.0 L = 38.1 g___

L |1.0 mol mol

M = dRT d= M P = 38.1 g (1 atm)______________ = 1.70 g/L

P RT mol (0.0821 L-atm )(273K)

( mol-K )

OR…AT STP: 38.1 g | 1 mol = 1.70 g/L

mol | 22.4 L

Mullis

Example: Molecular Weight

A 0.371 g sample of a pure gaseous compound occupies 310. mL at 100. º C and 750. torr. What is this compound’s molecular weight?

n=PV = (750 torr)(.360L) = 0.0116 mole

RT 62.4 L-torr(373 K)

mole-K

MW = x g_= 0.371 g = 32.0 g/mol

mol 0.0116 mol

Mullis

Partial Pressures

- Gas molecules are far apart, so assume they behave independently.
- Dalton: Total pressure of a mixture of gases is sum of the pressures that each exerts if it is present alone.

Pt = P1 + P2 + P3 + …. + Pn

Pt = (n1 + n2 + n3 +…)RT/V = ni RT/V

- Let ni = number of moles of gas 1 exerting partial pressure P1:

P1 = X1P1 where X1 is the mole fraction (n1/nt)

Mullis

Collecting Gases Over Water

- It is common to synthesize gases and collect them by displacing a volume of water.
- To calculate the amount of a gas produced, correct for the partial pressure of water:
- Ptotal = Pgas + Pwater
- The vapor pressure of water varies with temperature. Use a reference table to find.

Mullis

Kinetic energy

- The absolute temperature of a gas is a measure of the average* kinetic energy.
- As temperature increases, the average kinetic energy of the gas molecules increases.
- As kinetic energy increases, the velocity of the gas molecules increases.
- Root-mean square (rms) speed of a gas molecule is u.
- Average kinetic energy, ε ,is related to rms speed:

ε = ½ mu 2 where m = mass of molecule

*Average is of the energies of individual gas molecules.

Mullis

Maxwell-Boltzmann Distribution

- Shows molecular speed vs. fraction of molecules at a given speed
- No molecules at zero energy
- Few molecules at high energy
- No maximum energy value (graph is slightly misleading: curves approach zero as velocity increases)
- At higher temperatures, many more molecules are moving at higher speeds than at lower temperatures (but you already guessed that)

Just for fun: Link to mathematical details: http://user.mc.net/~buckeroo/MXDF.html

Source: http://www.tannerm.com/maxwell_boltzmann.htm

Mullis

Molecular Effusion and Diffusion

- Kinetic energy ε = ½ mu 2
- u = 3RT Lower molar mass M, higher rms speed u

M

Lighter gases have higher speeds than heavier ones, so diffusion and effusion are faster for lighter gases.

Mullis

Graham’s Law of Effusion

- To quantify effusion rate for two gases with molar masses M1 and M2:

r1 = M2

r2M1

- Only those molecules that hit the small hole will escape thru it.
- Higher speed, more likely to hit hole, so

r1/r2 = u1/u2

Mullis

Sample Problem: Molecular Speed

Find the root-mean square speed of hydrogen molecules in m/s at 20º C.

1 J = 1 kg-m2/s2 R = 8.314 J/mol-K

R = 8.314 kg-m2/mol-K-s2

u2= 3RT = 3(8.314 kg-m2/mol-K-s2)293K

M2.016 g |1 kg___

mol |1000g

u2= 3.62 x 106 m2/s2

u = 1.90 x 103 m/s

Mullis

Example: Using Graham’s Law

An unknown gas composed of homonuclear diatomic molecules effuses at a rate that is only 0.355 times that of O2 at the same temperature. What is the unknown gas?

rx = MO2 0.355 = 32.0 g/mol

rO2Mx 1 Mx

Square both sides: 0.3552 = 32.0 g/mol

Mx

Mx = 32.0 g/mol = 254 g/mol Each atom is 127 g,

0.3552 so gas is I2

Mullis

The van der Waals equation

- Add 2 terms to the ideal-gas equation to correct for
- The volume of molecules (V-nb)
- Molecular attractions (n2a/V2)

Where a and b are empirical constants.

P + n2a (V – nb) = nRT

V2

- The effect of these forces—If a striking gas molecule is attracted to its neighbors, its impact on the wall of its container is lessened.

Mullis

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