2

Gas Properties

Four properties determine the physical behavior of any gas: Amount of gas Gas pressure Gas volume Gas temperature

3

Gas pressure Gas molecules

exert a force on the walls of their container when they collide with it

4

Atmospheric pressure Torricelli barometer

In the closed tube, the liquid falls until the pressure exerted by the column of liquid just balances the pressure exerted by the atmosphere.

Patmosphere proportional to height of liquid in tube

Standard atmospheric pressure (1 atm) is

760 mm Hg

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Units for pressure

In this course we usually convert to atm

Let’s practice…

Standard atmospheric pressure: 1 atm = 760 mmHg

Convert 625 mmHg into atm

Convert 2.5 atm into mmHg

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Gas pressure

A manometer compares the pressure of a gas in a container to the atmospheric pressure

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Mixtures of Gases Each gas

contributes to the total pressure The pressure caused

by each gas is the partial pressure of that gas

Ptotal = PA + PB

Each gas occupies the entire container volume, at its own pressure (the partial pressure of that gas)

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Mixtures of Gases

When a gas is collected over water, it is always “wet” (mixed with water vapor). Ptotal = Pbarometric = Pgas + Pwater vapor

Example: If 35.5 mL of H2 are collected over water at 26 °C and a barometric pressure of 755 mm Hg, what is the pressure of the H2 gas? The water vapor pressure at 26 °C is 25.2 mm Hg.

Relationships between gas properties: pressure, volume, and temp 1660 Robert Boyle investigates P and

V: Indirect Relationship:

Pressure Increases, Volume Decrease Pressure Decreases, Volume Increases PV = constant or P1V1 = P2V2

Let’s Practice…

A sample of gas occupies 10 L at .800 atm. What will the volume be if the pressure decreases to .750 atm?

A sample of gas occupies 25 L at 1.5 atm. What will the new pressure be, if the volume increases to 30 L?

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Gas Pressure & Temperature Gas pressure is proportional to gas

temperature:

Pressure (psi)

temperature (°C)

• relationship between pressure and temperature is always linear

• all gases reach P = 0 at same temperature, –273.15 °C

• this temperature is ABSOLUTE ZEROABSOLUTE ZERO

Let’s practice…

P

Tconstant

2

2

1

1

T

P

T

P

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Gas Laws: Charles

In 1787, Jacques Charles discovered the same relationship between gas volume and temperature:

volume (mL)

temperature (°C)

• relationship between volume and temperature is always linear

• all gases reach V = 0 at same temperature, –273.15 °C

• this temperature is ABSOLUTE ZEROABSOLUTE ZERO

Let’s Practice…

V

Tconstant

2

2

1

1

T

V

T

V

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A temperature scale for gases:the Kelvin scale

1860 English physicist, William Thomson (Lord Kelvin), suggests a relationship between kinetic energy and temperature.

A new temperature scale was invented that has zero = absolute zero

The new temperature scale was named the Kelvin or absolute temperature scale

K = °C + 273.15

Let’s Practice…

K = °C + 273.15

Convert 98.6 °C into Kelvin

Convert 125 K into °C

Temperature and Kinetic Energy The absolute (Kelvin) temperature of

a substance is directly proportional to the kinetic energy of its molecules. Kinetic energy is the energy an object

has because of its motion. KE = 1/2mv2

Temperature and Kinetic Energy Light molecules will move faster Heavy molecules will move slower All molecules at the same temp. have

the same kinetic energy. As temp. changes the velocity (speed)

changes: Increasing temp = increasing velocity Decreasing temp = decreasing velocity At absolute zero = velocity of zero (motion

stops)

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Gas laws: Avogadro Avogadro’s hypothesis is

Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules

In mathematical terms, the ratio of gas volume to moles is constant, if pressure and temperature do not change

V

nconstant

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Putting it all together:Ideal Gas Equation

Combining Boyle’s Law, Charles’ Laws, and Avogadro’s Law give one equation that includes all four gas variables:

R is the ideal or universal gas constant R = 0.08206 atm L/mol K (most useful) If P is in units of mmHg, multiply by 760 mmHg

then use 62.4 mmHg L/mol K

PV

nTR or PV nRT

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Using the Ideal Gas Equation Ideal gas equation may be expressed two

ways: One set of conditions: ideal gas law

PV = nRT Two sets of conditions: general gas equation

P1V1 = R = P2V2 n1T1 n2T2

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Examples

What is the volume occupied by 20.2 g NH3 gas at –25 °C and 752 mm Hg?

How many moles of He gas are in a 5.00 L tank at 10.5 atm pressure and 30.0 °C?

A 1.00 mL sample of N2 gas at 36.2 °C and 2.14 atm is heated to 37.8 °C while the pressure is changed to 1.02 atm. What volume does the gas occupy at this temperature and pressure?

Standard Molar volume and Stoichiometry Scientists have chosen a set of

standard conditions (standard temp. and pressure) STP: 1 atm or 760 mmHg 0°C or 273 K

Standard molar Volume (for any gas) 1 mole = 22.4 L At STP, 22.4 L of any gas contains one

mole of gas molecules (6.02 x 1023 molecules)

Let’s Practice…

Convert .5 moles of gas into L Convert 12 L into moles

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A Model for Gas Behavior The gas laws describe what gases do, but

they do not explain why. The Kinetic Molecular Theory of Gases is

the model that explains gas behavior. KMT was developed by Maxwell and Boltzmann

in the mid-1800s KMT is based on the concept of an ideal or

perfect gas

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Ideal gas

Composed of tiny particles in constant, random, straight-line motion

Gas molecules are point masses, so gas volume is just the empty space between the molecules

Molecules collide with each other and with the walls of their container

The molecules are completely independent of each other, with no attractive or repulsive forces between them.

Individual molecules may gain or lose energy during collisions, but the total energy of the gas sample depends only on the absolute temperature.