Given that 3.50 moles of NH3 occupy 5.20 L at 47°C, calculate the pressure of the gas (in atm) using (a) the ideal gas equation and (b) the van der Waals equation. Strategy To calculate the pressure of NH3 using the ideal gas equation, we proceed as in Example 5.3 (Section 5.4). What corrections

Question

Given that 3.50 moles of [latex]NH_{3}[/latex] occupy 5.20 L at 47°C, calculate the pressure of the gas (in atm) using (a) the ideal gas equation and (b) the van der Waals equation.

Strategy To calculate the pressure of [latex]NH_{3}[/latex] using the ideal gas equation, we proceed as in Example 5.3 (Section 5.4). What corrections are made to the pressure and volume terms in the van der Waals equation?

Accepted Answer

(a) We have the following data:

V=5.20 L

T=(47+273) K=320 K

n=3.50 mol

R=0.0821 L . atm/K . mol

Substituting these values in the ideal gas equation, we write

[latex] P=\frac{nRT}{V} [/latex]

[latex]=\frac{(3.50 mol)(0.0821 L . atm/K . mol)(320 K)}{5.20 L} [/latex]

=17.7 atm

(b) We need Equation (5.18). It is convenient to first calculate the correction terms in- Equation (5.18) separately. From Table 5.4, we have

Gas	[latex]a(\frac{atm. L^{2} }{mol^{2} } )[/latex]	[latex]b(\frac{atm. L }{mol} )[/latex]
He	0.034	0.0237
Ne	0.211	0.0171
Ar	1.34	0.0322
Kr	2.32	0.0398
Xe	4.19	0.0266
[latex]H_{2}[/latex]	0.244	0.0266
[latex]N_{2}[/latex]	1.39	0.0391
[latex]O_{2}[/latex]	1.36	0.0318
[latex]Cl_{2}[/latex]	6.49	0.0562
[latex]CO_{2}[/latex]	3.59	0.0427
[latex]CH_{4}[/latex]	2.25	0.0428
[latex]CCl_{4}[/latex]	20.4	0.138
[latex]NH_{3}[/latex]	4.17	0.0371
[latex]H_{2}O[/latex]	5.46	0.0305

a = 4.17 atm · L²/mol²

b = 0.0371 L/mol

so that the correction terms for pressure and volume are

[latex]\frac{an^{2} }{V^{2} }=\frac{(4.17 atm . L²/mol²)(3.50 mol)²}{(5.20 L)²} =1.89 atm[/latex]

nb=(3.50 mol)(0.0371 L/mol)=0.130 L

Finally, substituting these values in the van der Waals equation, we have

(P + 1.89 atm)(5.20 L − 0.130 L) = (3.50 mol)(0.0821 L · atm/K · mol)(320 K)

P = 16.2 atm

Check Based on your understanding of nonideal gas behavior, is it reasonable that the pressure calculated using the van der Waals equation should be smaller than that using the ideal gas equation? Why?

Question 5.18: Given that 3.50 moles of NH3 occupy 5.20 L at 47°C, calculat...

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