All the laws in science are based on common experience or common sense. The law should make sense when it is defined.

Transcription

1 he Gas Laws Ay gas ca be characterized by four basic physical properties, pressure (P), volume (), temperature (), ad amout of gas i moles (). hese properties are ot idepedet but are iterrelated; chagig the oe affects other. here are three basic laws goverig the behavi of the gas, which describe the relatio betwee oly two properties. hese are, Boyle s law describes the relatio betwee the volume () ad the pressure (P). Charles s law describes the relatio betwee the volume () ad the temperature (). Avogadro s law describes the relatio betwee the volume () ad the umber of moles () of gas. All the laws i sciece are based o commo experiece commo sese. he law should make sese whe it is defied. Boyle s Law (olume ad Pressure relatioship) his law was iveted by Robert Boyle (627-69) (the photo is take from ), which states that at a costat temperature, the volume of fixed amout of gas is iversely proptioal to the pressure. he mathematical expressio showig the above defied iverse relatioship is, P where the symbol is the mathematical symbol used to mea proptioal to. he above equatio is ot suitable i its fm f ay kid of calculatios. Hece, the proptioality sig must be removed by itroducig the equal sig as kx P where k is a proptioality costat that depeds o the ature of the gas. he above equatio ca be rearraged to yield P k costat his relatioship displays that whe the pressure is icreased, the volume decreases ad vice versa. But the product of P ad is always the same costat. F two differet sets of coditios, the above equatio takes the followig fm: P k P 2 2 P P 2 2

2 Where P ad are the iitial (coditio) pressure ad volume of the gas ad P 2 ad 2 are the fial (coditio 2) pressure ad volume of the gas. A gas occupyig the volume of 520 ml at a pressure of.5 atm is allowed to expad util it reaches the pressure of atm. What is its fial volume? Aswer First list the give quatities f two coditios as coditio coditio 2 P.05 atm P atm 520 ml 2? he substitute these values ito the equatio P P 2 2 ad solve f atm x 520 ml atm x 2 2 (.5 atm x 520 ml) / atm ml Check o your calculatio: How do you kow the aswer is crect? Boyle s says that icrease i pressure decreases volume decrease i pressure icreases volume. I this problem, the pressure is decreased from.05 atm to atm. herefe, the fial volume should be greater tha the iitial volume. he calculated volume ( ml) is ideed greater tha the iitial volume (520 ml). his tells you that, at least, you are o the right rack. But, it does ot guaratee that your aswer is crect, that depeds upo the way you etered the umbers i your calculat. Charles s Law (olume ad emperature relatioship) Charles s law iveted by Jacques Alexadre César Charles ( ) (the photo is take from ) states that, at a costat pressure, the volume of fixed amout of gas is directly proptioal to the absolute temperature. he mathematical expressio of this statemet is 2

3 α ' k k ' Accdig to this law, the volume of the gas icreases as the temperature icreases, but the ratio of volume to temperature, /, is always costat( k ). Like the Boyle s law, the Charles s law ca also be applied to two sets of coditios at a costat pressure. he equatio applicable to this situatio is k ' 2 A balloo filled with air has the volume of 250 ml at room temperature 25 0 C. What will be the volume of the balloo if it is placed i the refrigerat that operates at 8 0 C? Aswer coditio coditio ml 2? t 25 0 C t C Note that symbols t ad t 2 are used to idicate the Celsius temperatures. hese Celsius temperatures eed to be coverted ito Kelvi befe you solve f the fial volume K K Now you ca calculate the fial volume by substitutig the these values. 3

4 2 250ml K 29.5 K 250ml K x 244.3ml K Check As you ca see, the fial volume is decreased from 250 ml to ml, as it should be accdig to the Charles s law. Avogadro s Law (olume ad Amout of gas ( i moles) relatioship) Avogadro s law, iveted by Lezo Romao Amedeo Carlo Avogadro ( )(the photo is take from ), states that, at a costat pressure ad temperature, the volume of the fixed amout of gas is directly proptioal to the amout of gas expressed i moles. he mathematical equivalet of this statemet is, α where is the umber of moles of gas. Replacig the proptioality sig with a equal sig assumes the followig fm. " k k " cos ta t where k is proptioality costat. You experiece Avogadro s law whe you iflate the balloo. As you blow me air ito the balloo, the volume icreases. Me blowig meas me air iside the balloo (me umber of moles of air). less air me air still me air 4

5 Like previous two laws, the Avogadro s law ca also be exteded to two sets of coditios, f which the followig equatio is writte. k " 2 A helium filled balloo is iflated to 30.0 L with.44 moles of the gas. If a balloo eeds to be expaded further to 40.0 L, how may additioal moles of the gas are required? Aswer coditio coditio L L.44 mol 2? Substitutig these values ito above equatio leads to, 30.0L 40.0L.44 mol 2.44 mol L x.92mol 30.0L herefe, additioal moles.92 mol.44 mol 0.48 mol 5