Gas Laws

PROPERTIES AND LAWS OF GASES



The main difference in the three physical states is the proximity of their particles.



Solids - particles are very close together, locked in a rigid crystal lattice in which the only

movement of the particle is a rotation on its axis; have both definite shape and definite

volume



Liquids - particles are touching each other but not locked in a rigid lattice; they are allowed to

slide past each other and exhibit rotational as well as translational motion; have definite

volume but not definite shape; both solids and liquids are considered to be "condensed"

states



Gases - particles do not touch each other at all, but bump into each other constantly; have no

definite shape nor definite volume; more affected by changed in temperature and

pressure than the other physical states





Temperature is a measure of kinetic energy. (kinetic energy is not just how fast they are moving).



KE = 1/2 mv2



In this equation, m stands for mass which MUST BE IN KILOGRAMS

v stands for velocity which MUST BE IN METERS/SECOND.



If you use these two units correctly, your answer will have the label kg-m2/sec2 which is also known as a Joule. Therefore, kinetic energy is expressed in the units of Joules.





Since many of the problems will use equations which include temperature, it is important to have temperature scales which do NOT have negative values since you do not want to multiply nor divide by a negative value and get an answer which is negative. Therefore, it became obvious that we needed to find the lowest temperature possible in the universe and call it Absolute Zero and therefore all temperatures above this would have positive values. We do this with the Kelvin scale. Here is a

comparison of the 3 common temperature scales.



Fahrenheit Celsius Kelvin



boiling point of water 212o F 100o C 373 K



freezing point of water 32o F 0o C 273 K



number of degrees between 180 100 100



coldest temp in universe - 523o F -273o C 0 K









Notice that the degree mark is NOT used with Kelvin temperatures. Also, the size of the Celsius and the

Kelvin degree is the same--they just start on the number line in different places. The Fahrenheit

degree is a much smaller degree than the Celsius or the Kelvin





YOU MUST BE ABLE TO CONVERT FROM KELVIN TO CELSIUS AND VICE VERSA. You do not

need to know how to convert to nor from Fahrenheit.



To convert from Celsius to Kelvin, add 273 Co + 273 = K



To convert from Kelvin to Celsius, subtract 273 K - 273 = Co





Example 10-5 Convert -167oC to Kelvin



Convert 1100oC to Kelvin



Convert 321 Kelvins to Celsius



How much does the temperature change in Celsius if it changes from 20oC to 255 K





The term STP stands for Standard Temperature and Pressure.

Mathematically, this means 1 atmosphere pressure (or equivalent i.e. 760 mm Hg, 760 torr, etc) and 0oC (or 273 K).





PRESSURE is defined as Force/Area.

We will not be concerned with the mathematical aspect of finding pressure, but only using pressures and converting them to various other units. There are five units of pressure which are used in chemistry and you must be able to convert between all of them.



1 atmosphere = 760 mm Hg = 760 torr = 1.01325 X 105 Pascals (Pa) = 101.325 kPa.



Example 10-6 Convert a pressure of 1.55 atm to kPa,











Which is higher pressure 1.45 atm or 1.159 X 104Pa?















Gas pressure is measured in an instrument called a manometer. Atmospheric pressures are measured with a special type of manometer called a barometer which you should know how it works.



Draw it:











There are two types of manometers--(1) open-arm manometer and (2) closed-arm manometer



















Open-arm manometers determine pressures relative to atmospheric pressure (which must be known).

The difference in the mercury column is either added to or subtracted from the atmospheric pressure.



Closed-arm manometers determine pressures based on differences in height of mercury column only and

DO NOT depend in any way on atmospheric pressure





There are several laws which govern the behavior of gases as changes in temperature, pressure and volume occur. You should know these by name, by equation, by word description and know how to apply them to problems.



1. Boyle's Law - describes the relationship between pressure and volume when temperature is constant. It states that volume and pressure vary inversely when temperature is constant. This means when the pressure increases, the volume decreases and vice versa.



It can be written mathematically as P1 = V2 or arranging a different way

P2 V1



P1V1 = P2V2 (T is constant)



P1 is beginning or original pressure. It may be in any units of pressure you wish, but you must

use the same units on P2 which is final or ending pressure.



V1 is beginning or original volume. It may be expressed in any units of volume you wish, but

again, you must use the same units on V2 which is final or ending volume.



Example 10-8 A gas is known to have a volume of 7.81 liters when the pressure is 754 torr. What

would be the volume when the pressure is changed to 1.23 atm? Temperature is constant.

















Example 10-9 A gas expands from a volume of 17.3 cm3 to 24.5 cm3. At the expanded volume, a

manometer was used and found the pressure to be 99.3 kPa. What was the original

pressure of the gas before it expanded (in mm Hg) if temperature is constant?









Example 10-11 The volume of a gas is 71.4 liters when the temperature is 0oC and its pressure is 1.112 X 105 Pascals. What volume would this gas occupy at STP?























2. Charles’ Law - establishes a relationship between volume and temperature when the pressure is

constant. It states that temperature and volume vary DIRECTLY when the pressure is

constant. We have found mathematically that this relationship is based on Kelvin temperature only! This means that when the temperature goes up, the volume also goes up proportionally and vice versa when the pressure is constant.



Mathematically it is expressed as a direct relationship V1 = T1K

V2 T2K



Example 10-13 A 5.2 liter sample of gas is heated from 25oC to 100oC. What is its volume at the

higher temperature if the pressure remains constant?























Example 10-14 A gas is found to have a pressure of 700 torr at a temperature of 54oC. If the volume of

the gas under these conditions is 3.21 ft3, what was its original volume when the

temperature was 20oC and pressure was 700 torr?





















Example 10-15. A gas doubles its temperature from 100oC to 200oC. Does this means that the volume

has also doubled if the pressure is constant? Explain.











3. Gay-Lussac's Law - establishes a relationship between pressure and temperature when the volume is constant (rigid container). It states that pressure and temperature Kelvin vary directly--i.e. when the pressure is doubled, the temperature Kelvin doubles and vice versa.



Mathematically, it is expressed as a direct relationship P1 = T1K

P2 T2K





Example 10-18 If the pressure on a gas in a rigid container changes from 800 torr to 0.750 atm, and at the lower pressure, the temperature is found to be 40oC, how many degrees Celsius did the

temperature CHANGE as the pressure dropped?















Example 10-19 To what temperature Celsius must a gas at 20oC and 600 torr be raised in order to cause its pressure to triple? Assume that the volume is constant in this case.



















4. Combined Gas Law - used when pressure, volume and temperature are all changing; is really a combination of all three gas laws.



P1 V1 = P2V2



T1K T2K





Example 10-20 A 3.5 cubic foot sample of nitrogen whose pressure is 79.1 kPa expands to 6.10 cubic feet while its pressure also changes to 680 torr. At the expanded volume, the temperature of the gas is found to be 28oC. What was the original temperature Celsius?

















Example 10-21 What would be the volume of a 8.90 liter sample of gas at 100oC and 113 kPa if conditions were changed to STP?









5. Dalton's Law of Partial Pressure - is used when you have a mixture (solution) of 2 or more gases which do not react chemically.



It states that the TOTAL pressure of a mixture of gases is simply the sum of the individual pressures of each of the gases (known as partial pressures).



Mathematically, it is stated Ptotal = PA + PB + PC + . . . . .



Example 10-24 A container has oxygen, xenon and helium in it. Its total pressure is

known to be 972 torr. If the pressure of the helium is 0.458 atm and the pressure of

the oxygen is 74.1 kPa, what is the pressure of the Xenon in torr?















Example 10-25 A mixture of 3 gases is known to have a pressure of 1.27 atm. If 2 of the gases have the same partial pressure and the pressure of the 3rd gas is 650 torr, what is the pressure of each of the other 2 gases in torr?

















B. Dalton's Law must also be used with problems in which gases are collected OVER WATER.

Gases that are not soluble in water are collected by water displacement and therefore what you

actually get in the collection bottle is not pure gas, but a mixture of the gas and water vapor (another gas) that was dragged along with the gas as it was collected. You must understand

that the pressure of the gas in the collection bottle is due to a mixture of gases, and you must

subtract out the water pressure by using a table of vapor pressures which lists the water pressures at all different temperatures.



AS SOON AS YOU SEE THE WORDS "OVER WATER" IN A PROBLEM, BEGIN LOOKING FOR P1 TO SUBTRACT VAPOR PRESSURE OUT OF IT AND T1 WHICH TELLS YOU THE TEMPERATURE TO LOOK UP IN THE TABLE SO YOU WILL KNOW HOW MUCH TO SUBTRACT.









Example 10-27 50.0 ml of hydrogen collected over water has a pressure of 850 torr at 27oC. What would be the volume of the dry gas at STP?











Example 10-28 A chemist collects 125.0 ml of oxygen over water and finds its pressure to be 1.24

atmospheres when the temperature is 75oC. What volume would the dry oxygen have

at STP?

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