The Combined“Gas Law”

Various Gas Laws• Boyles Law:

– initial pressure equals final pressure times final volume P1V1 P2V2

• Charles Law:

– the ratio of volume to temperature of a given gas at fixed pressure is constant V1/T1 = V2/T2

• Gay-Lussac’s Law:

– the ratio of pressure to temperature of a given gas at fixed volume is constant P1/T1 = P2/ T2

• Avogadro's Law:

– at fixed pressure and temperature, the ratio of volume to moles (n) of a gas is constant V1/n1 V2/n2

• The Ideal Gas Law: – relates the amount of gas produced in a reaction

PV=nRT where • n= moles

• R= 8.31 L X kPa/mol x K – This is a constant number

• Dalton’s Law of Partial Pressures: – the total pressure of a mixture of gases equals the

sum of the pressures Ptotal= P1+P2 etc.

• Combined Gas Law: – the combined law incorporates all of the laws:

Boyles, Charles, Avogadro's, and Lussac’s P1V1/n1T1 = P2V2/n2T2 n= moles

Combining the gas laws

Jacques CharlesRobert Boyle

P1V1 = P2V2V1

T1

=V2

T2These are all subsets of a more encompassing law:

the combined gas law

P1

T1

=P2

T2

P1V1 P2V2

T1 T2

=

Joseph Louis Gay-Lussac

•P1V1 P2V2

• T1 T2

P1V1 T2 = P2V2T1

P1V1 T2 = P2V2T1

V1 T2 V1T2

P1 = P2V2T1

V1T2

Manipulating Variables in Equations

Combined Gas Law Equations

P1 =P2V2T1

V1T2

V1 =P2V2T1

P1T2

T2 =P2V2T1

P1V1

T1 =P1V1T2

P2V2

P2 =P1V1T2

V2T1

V2 =P1V1T2

P2T1

P1V1 T2 = P2V2T1

P1V1 P2V2

T1 T2

=

• What is the initial pressure of a system if the final volume is 250 ml.

• Initial pressure (P1)= 101 Kpa

• Initial volume was 500 ml

• All temperatures are at STP= 273 OK

• P1= ?

• V1= 250 mls

• P2= 101kPa

• V2= 500 ml

*T1 and T2 are similar

P1 =P2V2T1

V1T2

P1V1 P2V2

T1 T2P1V1 T2 = P2V2T1

P1 =P2V2

V1

P1 =(101kPa)(250mls)

500 mls= 50.5 kPa

P1 = 150 kPa, T1 = 308 K

P2 = 250 kPa, T2 = ? V1 = V2

P1V1

T1

=P2V2

T2

(250 kPa)(V2)(308 K)(150 kPa)(V1)

=(T2) = 513 K= 240 °C

Notice that V cancels out if V1 = V2

T2 =P2V2T1

P1V1

P1V1 T2 = P2V2T1

K at STP= 273, therefore, 513 K- 273= 240OC

P1 = 100 kPa, V1 = 5.00 L, T1 = 293 K

P2 = 90 kPa, V2 = ?, T2 = 308 K

P1V1

T1

=P2V2

T2

(100 kPa)(5.00 L)(308 K)(90 kPa)(293 K)

=(V2) = 5.84 L

Note: although kPa is used here, any unit for pressure will work, provided the same units are used throughout. The only unit that MUST be used is K for temperature.

P1V1 T2 = P2V2T1

V2 =P1V1T2

P2T1

P1 = 800 kPa, V1 = 1.0 L, T1 = 303 K

P2 = 100 kPa, V2 = ?, T2 = 298 K

P1V1

T1

=P2V2

T2

(800 kPa)(1.0 L)(298 K)(100 kPa)(303 K)

=(V2) = 7.9 L

V2 =P1V1T2

P2T1

P1 = 6.5 atm, V1 = 2.0 mL, T1 = 283 K

P2 = 0.95 atm, V2 = ?, T2 = 297 K

P1V1

T1

=P2V2

T2

(6.5 atm)(2.0 mL)(297 K)(0.95 atm)(283 K)

=(V2) = 14 mL

The amount of gas (i.e. number of moles of gas) does not change.

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V2 =P1V1T2

P2T1