Question

Problem 7.24

A sample containing 42.1 g of Ar is enclosed in a container of volume 8.77×10⁻² L at 375 K.

Part A

Calculate P using the ideal gas equation of state.

Express your answer with the appropriate units.

Part B

Calculate P using the van der Waals equation of state.

Express your answer with the appropriate units.

Part C

Calculate P using the Redlich-Kwong equation of state.

Express your answer with the appropriate units.

Answer 1

A)

for Pressure, apply ideal gas law

PV = nRT

P = nRT/V

calculate moles

n = mass/MW

MW of AR = 39.99 g/mol

n = 42.1/39.99 = 1.0527 mol

so

P = 1.0527*(0.082)(375)/(8.77*10^-2) = 369.10 atm

B)

Pusing van der waals

a = 1.355 (bar)

b = 0.03201

Calculate V/n = v

v = (8.77*10^-2)/(1.0527 ) = 0.08330 L/mol

so:

(P + a/v^2 ) *(v-b) = RT

P = RT/(v-b) - a/(v^2)

P = RT/(v-b) - a/(v^2)

P = 0.0831 barL/molK

P = 0.0831 *375/(0.08330 -0.03201) -1.355 /(0.08330 ^2)

P = 412.29 bar = 406.898594 atm

c)

Redlich kwong

P = RT/(V-b) - a/(sqrt(T) * V(V+b))

P = 0.0831 *375 /(0.0831 -0.03201) - 1.355 /(sqrt(375) * 0.08330 (0.08330 +0.03201))

P = 602.6683 bar = 594.78736738 atm