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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 40oC if 1 mole occupies 28 L, assuming that:
(i) CCl4 obeys the ideal gas equation
(ii) CCl4 obeys the van der Waals equation.
S7P3A32 (force - push)
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.
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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