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Home , Ideal gas law

The Ideal Law

Lecture 2 How to measure of a gas? Simple barometer

The pressure of air pushing down is vacuum strong enough to support a column of mercury that is 76 cm high. This (no air) defines the “standard atmosphere”.

Mg P = = area A M ρ ρV g ρAh g = = = ρhg (13.6 x 103 kg/m3 ) A A 1 Stnd. Atm. = 1.013 x 105 Pa Area of ≈ 100 kPa = 0.1 MPa tube A = 14.7 psi = 760 torr (1 Pa = 1 N/m2) How does P and V of gas vacuum depend on T? (no air)

P= ρgh

V ()

T ( bath); externally controlled P-V Data for Low Pressure Gas

T must be measured in ! Analysis of Data Shows

PV = Constant T

Ideal Gas Law Constant Careful experiments on low density gasses show

PV = constant = k N T N = number of

PV = N k T k = Boltzman’s Constant = 1.381 x 10-23 J/K = 8.617 x 10-5 eV/K Units?

Physics Chemistry P in P in Pascal V in m3 V in liters T in T in Kelvin N is number of molecules n is molar fraction PV = NkT PV = nRT

10 cm 1 liter = 1000 cm3 10 cm 1 is number of atoms = 0.001 m3 in 12 grams of carbon-12 10 cm Moles!

Avagadro’s hypothesis: Equal of different gasses at same pressure and contain

the same number of molecules (NA). NA is NOT a fundamental physical constant; it’s a conversion factor between microscopic mass units (amu) and macroscopic mass units (grams).

1 gm = NA x 1 amu

1 amu = 1.6605 x 10-27 kg

23 NA ≅ 6.023 x 10 Moles, Avagadro’s Number and the Universal R

Since PV=NkT=nRT and defining the

molar fraction n = N/NA

6.02 x 1023 1.381 x 10-23 J 8.314 J R = N k = x = A mole K mole K 8.314 J 1 Nm 1m2 = x x mole K J 1m2 8.314 N m3 1 liter 1 atm = x x m2 mole K 0.001 m3 1.013 x 105 N/m2 liter atm = 0.08206 mole K A Universal Law? The Law

Expect horizontal straight line Examples

1. What is the volume of 1 mole of gas at STP?

Note:

STP: 0oC (273.15 K), 1 atm (101.325 kPa) SNP: 20oC (293.15 K), 1 atm (101.325 kPa) 2. The best vacuum that can be obtained in a laboratory is about 1 x 10-13 Pa. How many molecules per cc at 273 K? 3. Fill a balloon with gas to a radius of 18 cm. The temperature of balloon is 20 C. The pressure inside is 1.05 atm. How many moles of helium gas are required? 4. A storage tank of compressed helium has a volume of 30 liters and a pressure of 30 atm at 20oC. How many balloons will the tank fill? 5. If you fill a 500 liter storage container with 25.5 moles of gas at 10C, what is the gauge pressure of the gas in the tank? Beyond the

1. (empirical): {P + a(n/V)2 } {V/n – b} = RT

P increased by long V reduced by finite range attraction size of molecules

2. Virial expansion:

B(T) is first virial coefficient, C(T) is second virial coefficient, etc.

Note: Virial is derived from the Latin word for “force”. Virial is a word commonly used to describe a function related to force.