The Combined and Ideal The Combined and Ideal Gas LawsGas Laws

Honors ChemistryHonors Chemistry

The Combined Gas LawThe Combined Gas Law

PP11VV11 = P = P22VV22

TT11 T T22

Example:Example: A balloon with Helium has a volume of 50.L at A balloon with Helium has a volume of 50.L at 2525ooC and a pressure of 1.08 atm. What volume will it C and a pressure of 1.08 atm. What volume will it

have at 0.855 atm and 10have at 0.855 atm and 10ooCC??

**Convert Temps to Kelvin T1 = 25 + 273 = 298K

T2 = 10 + 273 = 283K

Plug in and Solve: (1.08atm)(50L) = (0.855atm)V2

298K 283 K

(1.08)(50)(283) = (0.855)(298) V2

V2 = 60. Liters

Standard Temperature and Standard Temperature and Pressure (STP)Pressure (STP)

Refers to a Temperature of Refers to a Temperature of 00ooCC , and a , and a pressure of pressure of 1 atm.1 atm.

Keep in mind the STP values in other Keep in mind the STP values in other units:units:Standard Temp = 0Standard Temp = 0ooC or 273 KelvinC or 273 Kelvin

Standard Pressure = 1atm = 760 mmHgStandard Pressure = 1atm = 760 mmHg = 760 torr = 760 torr = 101.325kPa = 101.325kPa

Ideal GasIdeal Gas An imaginary gas that fits all the assumptions of An imaginary gas that fits all the assumptions of

the kinetic molecular theory of gases.the kinetic molecular theory of gases.

In reality, the noble gases (He, Neon, etc) are In reality, the noble gases (He, Neon, etc) are the only gases that most closely behave like an the only gases that most closely behave like an ideal gas.ideal gas.

All gases behave like an ideal gas at All gases behave like an ideal gas at high high temperatures andtemperatures and low low pressure. This is pressure. This is because they cannot be attracted to each other because they cannot be attracted to each other if they are moving to fast and are very far apart if they are moving to fast and are very far apart from each other.from each other.

Avagadro’s LawAvagadro’s Law

Volume is directly proportional to the Volume is directly proportional to the moles of a gas at the same temperature moles of a gas at the same temperature and pressure.and pressure.

VV11 = V = V22

n = molesn = moles nn11 n n22

Remember 1 mole of a gas at STP Remember 1 mole of a gas at STP occupies 22.4Litersoccupies 22.4Liters

The Ideal Gas LawThe Ideal Gas Law Mathematical formula that relates the pressure, volume, Mathematical formula that relates the pressure, volume,

temperature and the number of particles(or moles) of a temperature and the number of particles(or moles) of a gas.gas.

PV = nRTPV = nRT

““R” is the gas constant,R” is the gas constant, R = 0.0821 R = 0.0821 atm.Latm.L

K.moleK.mole

The R value comes from using 1atm, 1 mole, 273K and The R value comes from using 1atm, 1 mole, 273K and 22.4 Liters as our comparison values.22.4 Liters as our comparison values.

Ideal gas law exampleIdeal gas law example What is the pressure in atmospheres exerted by What is the pressure in atmospheres exerted by

a 0.500gram sample of nitrogen (Na 0.500gram sample of nitrogen (N22) gas in 10. ) gas in 10.

Liter container at 25Liter container at 25ooC ?C ?

PV = nRT

P (10L) = (0.0178moles)(0.0821 L.atm/K.mole) (298K)

P = 0.044 atm

You must use Liters, atm and kelvin in this formula!!!!!

*you must convert grams to moles (and Celcius to Kelvin!!)

0.500g 1 mole = 0.0178 moles

28.02 grams

Other Derivations of the ideal gas lawOther Derivations of the ideal gas law To calculate the molar mass (M) of a gasTo calculate the molar mass (M) of a gas

PV = nRT

Moles = n = mass (m)

Molar Mass(M)

PV = m R T

M

Rearranging Molar Mass = M = m R T

PV

ExampleExample:: A 6.39 gram sample of a gas occupies a A 6.39 gram sample of a gas occupies a

2.00L container at 117kPa and 35.12.00L container at 117kPa and 35.1ooC. C. What is the molar mass of the gas?What is the molar mass of the gas?

Molar Mass = M = m R T PV

M = (6.39g)(0.0821)(308.1) (117/101.325)(2.00)

= 70.0 g/mole

To calculate the density of a gasTo calculate the density of a gasPV = nRTPV = nRT

Density = mass/volume or m/VDensity = mass/volume or m/V

PV = m R T

M

Rearrange PM = mRT V

Density = m = PM V RT

Ideal Gas law Tutorial - Online