Chapter 5Properties of the Gas

Phase

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Gases Pushing☂ Gas molecules are constantly in motion.

☂ As they move and strike a surface, they push on that surface.

♅push = force

☂ If we could measure the total amount of force exerted by gas molecules hitting the entire surface at any one instant, we would know the pressure the gas is exerting.

♅pressure = force per unit area

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Measuring Air Pressure

☂ Use a barometer.

☂ column of mercury supported by air pressure

☂ force of the air on the surface of the mercury balanced by the pull of gravity on the column of mercury

gravity

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Common Units of Pressure

UnitAverage Air Pressure at

Sea Level

pascal (Pa) 101,325

kilopascal (kPa) 101.325

atmosphere (atm) 1 (exactly)

millimeters of mercury (mmHg) 760 (exactly)

inches of mercury (inHg) 29.92

torr (torr) 760 (exactly)

pounds per square inch (psi, lbs./in2) 14.7

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Boyle’s Law

☂ Pressure of a gas is inversely proportional to its volume.

♅constant T and amount of gas

♅graph P vs. V is curve

♅graph P vs. 1/V is straight line

☂ As P increases, V decreases by the same factor.

☂ P × V = constant

☂ P1 × V1 = P2 × V2

Robert Boyle (1627–1691)

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Charles’s Law

☂ Volume is directly proportional to temperature.♅constant P and amount of gas♅graph of V vs. T is straight line

☂ As T increases, V also increases.☂ Kelvin T = Celsius T + 273☂ V = constant × T

♅if T measured in Kelvin

Jacques Charles (1746–1823)

If the lines are extrapolated back to a volume of “0,” they all show the same temperature, -273.15 °C, called absolute zero.

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Avogadro’s Principle

☂ volume directly proportional to the number of gas molecules♅V = constant × n♅while P and T remain constant♅more gas molecules = larger volume

☂ count number of gas molecules by moles☂ Equal volumes of gases contain equal numbers of molecules.

♅The gas doesn’t matter.

Amedeo Avogadro (1776–1856)

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By combing the gas laws we can write a general equation. R is called the gas constant. The value of R depends on the units of P and V.

We will use 0.08206 and convert P to atm and V to L.

♘ The other gas laws are found in the ideal gas law if two variables are kept constant.

♘ This allows us to find one of the variables if we know the other three.

Ideal Gas Law

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How many moles of helium are found in a balloon that contains 5.5 L of helium at a pressure of 1.15 atm and a temperature of 22.0 ºC?

A. 3.5

B. 0.26

C. 2.6

D. 0.35

E. 3.8

i>clicker

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The volume of O2 gas in a balloon at 1.0 atm and 305 K is 0.65 L. Calculate the volume of the gas after the temperature is lowered to 77 K while keeping the pressure and amount of O2 constant.

A. 0.16 L

B. 0.65 L

C. 2.8 × 10–5 L

D. 3.6 × 104 L

E. not enough information

i>clicker

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Standard Conditions☂ Since the volume of a gas varies with pressure and temperature,

chemists have agreed on a set of conditions to report our measurements so that comparison is easy. We call these Standard Temperature and Pressure conditions.♅STP

☂ standard pressure = 1 atm☂ standard temperature = 273 K

♅0 °C

☂ Solving the ideal gas equation for the volume of 1 mol of gas at STP gives 22.4 L. The mass depends on the gas!

☂ We call the volume of 1 mole of gas at STP the molar volume.

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Practice—A gas occupies 10.0 L at 44.1 psi and 27 °C. What volume will it occupy at standard

conditions?

Practice—How many liters of O2 at STP can be made from the decomposition of 100.0 g of PbO2?

2 PbO2(s) → 2 PbO(s) + O2(g)(PbO2 = 239.2, O2 = 32.00)

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Gas Density

☂ Density is directly proportional to molar mass.

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Practice—Calculate the density of a gas at 775 torr and 27 °C if 0.250 moles weighs 9.988 g.

Practice—What is the molar mass of a gas if 12.0 g occupies 197 L at 3.80 × 102 torr and 127

°C?

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The four most common gases in the atmosphere are N2, O2, Ar, and CO2. Assuming all gases are in containers of equal size, temperature, and pressure, which gas has the highest density?

A. All have the same density

B. N2

C. O2

D. Ar

E. CO2

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A 3.50-g sample of a diatomic gas in a 1.5-L container has a pressure of 2.42 atm at 355 K. Determine the identity of the gas.

A. H2

B. N2

C. Cl2

D. O2

E. F2

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Mixtures of Gases☂ When gases are mixed together, their molecules behave

independently of each other.♅All the gases in the mixture have the same volume.

☿ All completely fill the container each gas’s volume = the volume of the container.

♅All gases in the mixture are at the same temperature.☿ Therefore, they have the same average kinetic energy.

☂ Therefore, in certain applications, the mixture can be thought of as one gas.♅Even though air is a mixture, we can measure the pressure,

volume, and temperature of air as if it were a pure substance.♅We can calculate the total moles of molecules in an air

sample, knowing P, V, and T, even though they are different molecules.

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Partial Pressure

☂ The pressure of a single gas in a mixture of gases is called its partial pressure.

☂ We can calculate the partial pressure of a gas if

♅we know what fraction of the mixture it composes and the total pressure

♅or, we know the number of moles of the gas in a container of known volume and temperature

☂ The sum of the partial pressures of all the gases in the mixture equals the total pressure.

♅Dalton’s Law of Partial Pressures

♅because the gases behave independently

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The partial pressure of each gas in a mixture can be calculated using the ideal gas law.

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Mole Fraction

The fraction of the total pressure that a single gas contributes is equal to the fraction of the total number of moles that a single gas contributes.

The ratio of the moles of a single component to the total number of moles in the mixture is called the mole fraction, X.

for gases = volume %/100%

The partial pressure of a gas is equal to the mole fraction of that gas times the total pressure.

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Practice—Find the mole fraction and partial pressure of neon in a mixture with total pressure 3.9 atm, volume 8.7

L, temperature 598 K, and 0.17 moles Xe.

Practice—What volume of O2 at 0.750 atm and 313 K is generated by the thermolysis of 10.0 g of HgO?

2 HgO(s) 2 Hg(l) + O2(g)(MMHgO = 216.59 g/mol)

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A gas phase mixture of H2 and N2 at 298 K has a total pressure of 784 torr with an H2 partial pressure of 124 torr. What mass of N2 gas is present in 2.00 L of the mixture?

A. 0.0133 g

B. 0.0710 g

C. 0.374 g

D. 0.994 g

E. 1.99 g

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Kinetic Molecular Theory☂ The particles of the gas (either atoms or molecules) are

constantly moving.☂ The attraction between particles is negligible.☂ When the moving gas particles hit another gas particle or the

container, they bounce off (instead of sticking) and continue moving in another direction.

☂ There is a lot of empty space between the gas particles.♅compared to the size of the particles

☂ The average kinetic energy of the gas particles is directly proportional to the Kelvin temperature.♅As you raise the temperature, the average speed of the

particles increases.☿ NOTE: All the gas particles are NOT moving at the same speed!!

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Kinetic Energy and Molecular Velocities☂ Average kinetic energy of the gas molecules depends on the

average mass and average velocity (speed).♅KE = ½mu2

☂ Gases in the same container have the same temperature; therefore, they have the same average kinetic energy.

☂ If they have different masses, the only way for them to have the same kinetic energy is to have different average velocities.♅Lighter particles will have a faster average velocity than

more massive particles.

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Molecular Velocities☂ All the gas molecules in a sample can travel at different speeds.☂ However, the distribution of speeds follows a pattern called a

Boltzmann distribution.☂ We talk about the “average speed” of the molecules, but there

are different ways to take this kind of average.☂ The method of choice for our average speed is called the root-

mean-square method, where the rms average velocity, urms, is the square root of the average of the sum of the squares of all the molecule velocities.

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Temperature and Molecular Velocities

• As temperature increases, the average velocity increases.

• KEavg = ½NAmu2

NA is Avogadro’s number.• KEavg = 3/2 RT

R is the gas constant in energy units. 8.314 J/mol∙K

1 J = 1 kg∙m2/s2

• equating and solving we get: NA∙mass = molar mass in kg/mol

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Diffusion and Effusion☂ The process of a collection of molecules spreading out from high

concentration to low concentration is called diffusion.☂ The process by which a collection of molecules escapes through a

small hole into a vacuum is called effusion.☂ Both the rates of diffusion and effusion of a gas are related to its

rms average velocity.

Graham’s Law of EffusionThomas Graham (1805–1869)

☂ For two different gases at the same temperature, the ratio of their rates of effusion is given by the following equation:

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Practice—Calculate the ratio of the rate of effusion for oxygen to hydrogen.

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Ideal vs. Real Gases☂ Real gases often do not behave like ideal gases at high

pressure or low temperature.☂ Ideal gas laws assume (based on the kinetic-molecular theory)1) no attractions between gas molecules2) gas molecules do not take up space☂ At low temperatures and high pressures, these assumptions are

not valid.♅ Because real molecules take up space, the molar volume of a

real gas is larger than predicted by the ideal gas law at high pressures.

♅ Because real molecules attract each other, the molar volume of a real gas is smaller than predicted by the ideal gas law at low temperatures.

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Van der Waals Equation

☂ Combining the equations to account for molecular volume and intermolecular attractions, we get the following equation.

♅used for real gases