Ideal Gas Law

• Why bother with Gases?• Properties of a Gas• Animation P, V, T, n• Ideal Gas Law• Examples of Ideal Gas Law• Ideal Gas Law - #molecules version

Temperature and Gases• Gas

– Simplest material phase – all kinetic energy.– Energy “reservoir” – convert disordered KE to useful mechanical

work.

• Properties of a Gas– Pressure– Volume– Temperature– Quantity

• 4 Properties are interrelated – Animation– Ideal gas law

Ideal Gas Animation• Gas/piston animation

(Java animation) ……..……

• Gas/piston animationhttp://www.chem.ufl.edu/~itl/2045/MH_sims/ideal_nav.swf

• Other animationshttp://www.mhhe.com/physsci/chemistry/animations/chang_7e_esp/gam2s2_6.swf

idealgas.jnlp

ideal_nav.swf

gam2s2_6.swf idealGasModel.swf

Ideal Gas Observations• Observations of P, V, T, n

– Pressure vs. Volume (Boyle’s Law) P proportional to 1/V– Volume vs. Temperature (Charle’s law) V proportional to T– Pressure vs. Temperature (Gay-Lussac’s Law) P proportional to T– Pressure and volume vs. quantity PV proportional to n

Ideal Gas Law – Primary units• Ideal gas law combines Boyle’s, Charles, Gay-Lussac’s

PV = nRT

– P proportional 1/V– V proportional T– P proportional T

– P proportional n

• Units – P in pascals – V in m3 – T in K° (not C °)– n in moles– R = 8.314 J/mol-K

• Definition of Mole n = mass/molecular mass (N2=28g/mol, O2= 32g/mol, etc.)

Ideal Gas Law – Alternative units• Ideal gas law combines Boyle’s, Charles, Gay-Lussac’s

PV = nRT – P in atmospheres– V in liters– T in K° – n in moles– R = .0821 L-atm/mol-K

• Use either primary units or alternative units completely, don’t mix n’ match!

• Use primary units for First Law (Ch 15) calculations.

Celsius vs. Kelvin• Degree sizes same!

• Kelvin = Celsius with zero shifted to absolute zero.

• May use Celsius when only relative changes important.– Thermal Expansion

– Specific and Latent Heat problems

– Thermal Conduction

• Must use Kelvin when absolute temperature important.

– Ideal Gas Law

– Kinetic Theory

– Thermal Radiation

– First and Second Law Thermodynamics

Similar to Gauge vs. Absolute Pressure

Example 13-10 - volume 1 mole at STP

• STP = 0C (273K), 1 atm (101.3 kPa)

• Primary units

• Alternative units

Example 13-11 - helium balloon

• Volume of 18 cm radius sphere

• Number of moles in alternative units (just being different)

• Mass of Helium

Example 13-12 - mass of air in room

• Volume of 5 x 3 x 2.5 m room

• Number of moles

• Mass of Air @ 29 g/mol (N2 28 g/mol, O2 32 g/mol)

Example 13-13 – automobile tireAn automobile tire is filled to a gauge pressure of 200 kPa at 10°C. After a long drive the temperature as risen to 40°. What is the pressure now?

• Strategy – Put all constant quantities on same side of Ideal Gas Law

• Convert 200 kPa gauge pressure to 301 kPa absolute pressure

• Solve

Convert 333 kPa absolute pressure back to 232 kPa gauge pressure

More examples of ideal gas

• Problem 29 V2 = V1 (P1/P2) (T2/T1)

• Problem 30 T2 = T1 (P2/P1) (V2/V1)• Problem 31 ρ = 32 x 10-3/22.4 x 10-3

• Problem 32 P2 = P1 (n2/n1)• Problem 33• Problem 36 n2 = n1 (P2/P1)

• Problem 39 P2 = P1 (V1/V2)(T2/T1)

Problem 29 – V change with P, T

• First move all constant quantities to one side

• Then solve for V2

Note: Arbitrary units OK, since only ratios important

Problem 30 – T change with P, V

• Move all constant quantities to one side

• Solve for T2

(Diesel car) Note: Arbitrary units OK, since only ratios important

Problem 31 – Density of O2

• Volume of 1 mole at STP22.4 L = 0.0224 m3 (shown earlier)

• Mass of a mole O2

32 g = .032 kg (lookup in table)

• Density

Problem 32 – Gas substitution

• Calculate mole ratio for equal mass CO2 and N2

(since mass equal)

• Move all constant quantities to one side

• Solve for P2

Problem 36 – Gas substitution

• First find #moles O2

• Move all constant quantities to one side

• Solve for n2

670 moles

• Then find mass 670 moles Helium

Problem 39 – P change with V, T

• Move all constant quantities to one side

• Solve for V2

Note: Arbitrary units OK, since only ratios important

Ideal Gas Law - #molecules version

• Ideal Gas Law can also be written:

PV = NkT PV = nRT

– N = nNA (N number of molecules)

– k= R/NA (NA Avagadro’s number)– P in Pascals (no alternative units)– V in m3 – T in K°

• Boltzman’s constant– k = R/NA = 1.38e-12 J/K