Chapter 11: Behavior of Gases

Particles of Ideal vs Real GasIdeal Real

have no volume have their own volume

don’t attract or repel each other

attract each other

have elastic collisions have collisions that are not elastic

How gases behave

•Gas behavior is most ideal…–at low pressures–at high temperatures–in nonpolar atoms/molecules

**Always use Kelvin temperatures when working with gases

•pressure of a gas is caused by the collisions of the particles in the gas on the walls of their container.

Defining Gas Pressure

The more often gas particles collide with the walls of their container, the greater the pressure

Defining Gas Pressure

•more air particles inside the ball mean more mass inside.

•pressure of a gas is directly proportional to its mass.

•P α M

•If m then p

•If m then p

How are number of particles and gas pressure related?

• At higher temperatures, the particles in a gas have greater kinetic energy.

How are temperature and pressure related?

• move faster and collide with the walls of the container more often and with greater force, so the pressure rises.

• If the volume of the container stays constant &

• # of particles of gas stays constant

• Then pressure increases in direct proportion to the Kelvin temperature.

How are temperature and pressure related?

•pressure of a gas is directly proportional to its Kelvin temperature.

•P α T

•If t then p

•If t then p

How are temperature and pressure related?

Devices to Measure Pressure

• barometer - instrument that measures the pressure exerted by the atmosphere.

• The height of the mercury column measures the pressure exerted by the atmosphere

The Barometer

****remember atmospheric pressure decreases with altitude because the depth of air above you is less

• The standard atmosphere (atm) is defined as the pressure that supports a 760-mm column of mercury.

Pressure Units

• Atmospheric pressure is the force per unit area that the gases in the atmosphere exert on the surface of Earth.

• The SI unit for measuring pressure is the pascal (Pa),

Pressure Units

• Because the pascal is a small pressure unit, it is more convenient to use the kilopascal. 1 kilopascal (kPa) is equivalent to 1000 pascals.

1 atm = 101.3 kPa

The Gas Laws

•The gas laws apply to ideal gases, which are described by the kinetic theory

Boyle’s Law: Pressure and Volume• After performing many experiments

with gases. Boyle had four findings.

at constant temperatures,

1) If pressure increases

then volume decreases

2) If pressure decreases

then volume increases

Boyle’s Law: Pressure and Volume

• Boyle’s law states that the pressure and volume of a gas at constant temperature are indirectly proportional.

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Boyle’s Law

• In mathematical terms, this law is expressed as follows.

P1 = initial pressureV1 = initial volume

P2 = ending pressureV2 = ending volume

Kinetic explanation of Boyle’s Law

• At a constant temperature, the pressure exerted by a gas depends on the frequency of collisions between gas particles and the container.

• If the same number of particles is squeezed into a smaller space (decreased volume), the frequency of collisions increases, thereby increasing the pressure.

Graph of Boyle’s Lawpressure vs volume

Applying Boyle’s Law

• A sample of compressed methane has a volume of 648 mL at a pressure of 503 kPa.

• To what pressure would the methane have to be compressed in order to have a volume of 216 mL?

• Examine the Boyle’s law equation. You need to find P2, the new pressure, so solve the equation for P2.

Applying Boyle’s Law

• Substitute known values and solve.

Charles’s Law: Temperature and Volume • At constant pressure

• If the temperature is increased,

• if the volume is free to change, then

• The volume increases

Charles’s Law

Charles’s law states that the volume and temperature of a gas at constant pressure are directly proportional

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Kinetic explanation of Charles’s Law

• If the temperature is increased, average kinetic energy and particle movement increases and if volume is free to change it increases too

Graph of Charles’s Lawvolume vs temperature

Applying Charles’s Law

• A weather balloon contains 5.30 kL of helium gas when the temperature is 12°C.

• At what temperature will the balloon’s volume have increased to 6.00 kL?

• Start by converting the given temperature to kelvins.

Applying Charles’s Law

• Next, solve the Charles’s law equation for the new temperature, T2.

Applying Charles’s Law

• Then, substitute the known values and compute the result.

• Finally, convert the Kelvin temperature back to Celsius.

New Temperature = 323 – 273 = 50oC

GAY-LUSSAC’S LAW – pressure and temperature

• At constant volume

• If the temperature is increased,

• Then pressure increases

P1 = P2

T1 T2

GAY-LUSSAC’S LAW

• Gay- Lussac’s law states that the temperature and pressure of a gas at constant volume are directly proportional

Kinetic explanation of Gay-Lussac’s Law

• If the temperature is increased, average kinetic energy and particle movement increases and collisions occur more frequently, thereby increasing pressure

P1 = P2

T1 T2

Boyle’s Law

Charles’s Law

Gay-Lussac’s Law

• “Potato Chips are Very Good To Bite.”

• Pressure constant – Charles • Volume constant – Gay-Lussac• Temperature constant – Boyle

The Combined Gas Law

• The gas laws may be combined into a single law, called the combined gas law, that relates two sets of conditions of pressure, volume, and temperature by the following equation.

• With this equation, you can find the value of any one of the variables if you know the other five.

Applying the Combined Gas Law

• A sample of nitrogen monoxide has a volume of 72.6 mL at a temperature of 16°C and a pressure of 104.1 kPa.

• What volume will the sample occupy at 24°C and 99.3 kPa?

• Start by converting the temperatures to kelvins.

Applying the Combined Gas Law

• Next, solve the combined gas law equation for the quantity to be determined, the new volume, V2.

Applying the Combined Gas Law

• Substitute the known quantities and compute V2.

STP = Standard Temperature & STP = Standard Temperature & PressurePressure

0°C and

1 atm

STP

Avogadro’s Principle

• Avogadro’s principle - equal volumes of gases at the same temperature and pressure contain the same number of particles.

• An extension of Avogadro’s principle is that one mole (6.02 x 1023 particles) of any gas at STP (standard temperature and pressure -0°C and 1.00 atm pressure) occupies a volume of 22.4 L.

Applying Avogadro’s Principle

• What is the volume of 7.17 g of neon gas at 24°C and 1.05 atm?

• Start by converting the mass of neon to moles.

• The periodic table tells you that the atomic mass of neon is 20.18 amu. Therefore, the molar mass of neon is 20.18 g.

Applying Avogadro’s Principle

• Next, determine the volume at STP of 0.355 mol Ne.

• If you needed only the volume at STP, you could stop here.

• Finally, use the combined gas law equation to determine the volume of the neon at 24°C and 1.05 atm pressure.

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Applying Avogadro’s Principle

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Question 4

What pressure will be needed to reduce the volume of 77.4 L of helium at 98.0 kPa to a volume of 60.0 L?

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Answer

126 kPa

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Question 5

A sample of SO2 gas has a volume of 1.16 L at a temperature of 23°C. At what temperature will the gas have a volume of 1.25 L?

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Answer

46°C or 31.9 K

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The End!