Chapter 10 Gases

• Characteristics of Gases

• Pressure

• The Gas Laws

• The Ideal-Gas Equation

• Applications of the Ideal-Gas Equation

• Gas mixtures and partial pressures

• Kinetic-Molecular Theory

• Real Gases: Deviations from Ideal Behavior

Gases differ from Solids and Liquids

10.1 Characteristics of Gases

These molecular properties define the physical properties of gases

Physical properties common to all gases

Pressure, P, is the force, F that acts on a given area, A.

10.2 Pressure

http://www.indiana.edu/~geog109/topics/10_Forces&Winds/GasPressWeb/PressGasLaws.html

Atmospheric Pressure

Gravity causes the atmosphere as a whole to press down on the Earth’s surface

Force, F, exerted by a column of air 1m2 in cross section extending through the entire atmosphere is given by: F = ma

Considering that the mass of air in that column is 10,000 Kg, we can calculate the force from this column in a 1 m2 surface.

Pressure exerted by our 1m2 column of air can be calculated using P = F/A

Standard Atmospheric Pressure (typical pressure at sea level)

First demonstrated using a mercury barometer

Be able to convert gas pressures from one set of units to another

Sample exercise 10.1 Remember: 1 atm = 760 mmHg = 101.325 kPa

A manometer is used to measure the pressure of enclosed gases

10.3 The Ideal Gas Laws

Physical State of a gas is defined by four variables

The gas Laws express the relationship between these variables.

Sample exercise 10.2

Boyle’s Law : The relationship between pressure and volume

If we have a certain amount of gas at a state 1 with pressure P1 and volume V1and then we move it to a state 2 with pressure P2 and volume V2 at constant temperature, we get:

Charles’s Law : The relationship between temperature and Volume

A balloon will shrink when the gas in it is cooled

A plot of Volume vs. Temperature in Kelvin (K) will be linear (ideal gas)

If we have a certain amount of gas at a state 1 with temperature T1 and volume V1and then we move it to a state 2 with temperature T2 and volume V2 at constant pressure, we get:

Always use Absolute Temperature (in Kelvin) for gas problems

Avogadro’s Hypothesis : The relationship between Quantity and Volume

Double the number of moles of an ideal gas will cause the volume to double if T and P remain constant.

Boyle’s Law V α 1/P (constant n,T)

Charles’s Law V α T (constant n,P)

Avogadro’s Law V α n (constant P,T)

Combine these to give:

10.4 The Ideal-Gas equation

This constant is called the gas constant R

Ideal gas • no interaction between molecules (only during collisions)• the volume of each molecule is negligible• obey the idea-gas equation

Combined Ideal-Gas Law

When P, V and T all change for a fixed number of moles of gas

Sample exercise 10.6

Remember always check your answer…does it seem reasonable?

10.5 Further applications of the Ideal-Gas equation

Gas Densities and Molar MassKnowing the Molar Mass, M, the Pressure and the Temperature of an ideal gas allows us to calculate its density, d

The density of a gas INCREASES with increasing pressure

The density of a gas DECREASES with increasing temperature

The Molar Mass of a gas can therefore be calculated if the density is known

Volumes of gases in chemical reactions

Useful to be able to calculate the volumes of gases consumed or produced in chemical reactions

Sample exercise 10.9

Sample exercise 10.7 and 10.8

Imagine different amounts of 3 ideal gases in 3 distinct containers with same volume (V) and same temperature (T)

What would be the total pressure (PT) if I mix all these ideal gases in the same container with volume V and temperature T?

10.6 Gas Mixtures and Partial Pressures

10.6 Gas Mixtures and Partial Pressures

The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present on its own.

At constant temperature and volume, and assuming each gas in themixture obeys the ideal-gas equation then:

If Pt is the total pressure exerted by a mixture of gases, and the partial pressure of each individual gas is P1, P2, P3 etc. then Dalton’s Law of partial pressures states:

The total pressure is determined by the total number of moles ofgas present, whether this is one gas or a mixture of gases.

Sample exercise 10.10

Partial Pressures and Mole fractions

Each gas in a mixture behaves independently. We can relate the mole fraction of a gas in a mixture to its partial pressure.

The sum of the mole fractions of a mixture MUST = 1, i.e. Σ Xi = 1

The partial pressure of a particular gas in a mixture can be calculated from its mole fraction and the Total Pressure:

Collecting Gases over water

Often the gas produced in a chemical reaction is collected over water

The total pressure Ptotal, is the sum of the pressure of gas(es) collected and the pressure exerted by the water vapor.

The pressure exerted by water vapor PH2O at various temperatures is given in a table (data sheet)

When the gas has been collected, the bottle is raised or lowered until the water levels inside and out are equal.

Sample exercise 10.12

10.7 Kinetic Molecular Theory

The ideal-gas equation describes how gases behave, but does not explain why they behave as they do.

Kinetic Molecular Theory developed to help understand the physical properties of gases.

Distribution of Molecular Speed

Root mean square (rms) speed, μ

Gas molecules have an average speed. However at any instant the molecules have a wide range of speeds.

Boltzmann Curves plot the molecular speed vs. the number of molecules.

M3RTμ =

10.9 Real Gases

All real gases fail to obey the ideal-gas equation to some degreeReal gases deviate from ideal behavior because:

Pressure deviation from ideal gas behaviour

For one mole (n =1) of ideal gas PV/RT = 1 (at all pressures)

Temperature deviation

Deviation from ideal behavior also depends on temperature

The Van der Waals equation

Introduces two constants ( a and b) into the Ideal-Gas equation to account for real gas behavior

( P + n2a/V2 ) ( V - nb ) = nRT