Non-Ideal Gas Behavior

Non-Ideal Gas Behavior
TECTechnics Classroom TECTechnics Overview

Given that volume = V liters; pressure = P atmosphere; temperature = T Kelvin; Numuber of Moles = n.

Boyle's Law: V α 1/P (constant n, T)

Charle's Law: V α T (constant n, P)

Avogadro's Law: V α n (constant P, T)

Ideal Gas Equation: V α nT/P ; V = nRT/p (R is proportionality constant = 0.0821 L-atm/mol-K

Graham's Law Of Effusion: the effusion rate of a gas is inversely proportional to the square root of its molar mass.

van der Waals Equation: (P + n²a/V²)(V - nb) = nRT
Where a and b are van der Waals constants. The constant b L/mol corrects for the intrinsic volume of 1 mole of a gas molecules while the constant a L²-atm/mol² reflects the degree of attractive forces between the gas molecules.

(ai) What is the basic premise of the non-ideal gas behavior?
(ii) Identify two reasons why gases behave non-ideally
(iii) How does the ratio PV/RT help to reveal non-ideal behavior of gases?

(b) Consider Ar (argon) and CO₂ (carbon dioxide) at high pressures. Which of the two gases will behave closer to ideal gas behavior?

(c) Calculate the pressure that CCl₄ will exert at 40^oC if 1 mole occupies 28 L, assuming that:
(i) CCl₄ obeys the ideal gas equation
(ii) CCl₄ obeys the van der Waals equation.

The strings: S₇P₃A₃₂ (force - push)

The math:
The Pj problem of interest is of type force (force - push)

(ai) The basic premise of the non-ideal behavior of gases is that at high pressures and low temperatures the ideal gas equation becomes a less accurate determinant of the behavior of gases.

(aii) The intrinsic volume of a mole of gas molecules and the attractive forces between the molecules are two reasons why gases deviate from ideal behavior.

(aiii) The ratio PV/RT should be constant for a given sample of gas at all combinations of pressure, volume, and temperature. If this is not the case, then the gas sample is behaving non-ideally.

(b) van der Waals equation: (P + n²a/V²)(V - nb) = nRT
For Ar: a =1.344, b = 0.0322
For CO₂: a = 3.57, b = 0.427
So, we expect Ar to behave closer to ideal gas behavior.

(ci) Ideal gas equation: PV = nRT
So, CCl₄ at ideal behavior: P = (1x0.08206x313)/28 = 0.917 atm

(cii) van der Waals equation:(P + n²a/V²)(V - nb) = nRT
So P = nRT/(V-nb) - n²a/V² = (1x0.08206x313)/(28-0.1383) - 20.4/784
So, P = 25.685/27.862 - 0260 = 0.922 - 0260 = 0.896 atm.

Math

The point . is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.
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