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According to the ideal gas law, a 1.041 mol sample of carbon dioxide gas in a 1.016...

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Chemistry

According to the ideal gas law, a 1.041 molsample of carbon dioxide gas in a1.016 L container at 270.0 Kshould exert a pressure of 22.70 atm. By whatpercent does the pressure calculated using the van der Waals'equation differ from the ideal pressure? ForCO2 gas, a = 3.592L2atm/mol2 and b =4.267×10-2 L/mol.

%

Hint: % difference = 100×(P ideal - Pvander Waals) / P ideal

Answer & Explanation Solved by verified expert
4.3 Ratings (923 Votes)

Given n (CO2) = 1.041 mol, V (CO2) = 1.016 L and T (CO2) = 270 .0 K

Pideal = 22.70 atm

Now we will calculate pressure using van der Waals equation

(P + an2/V2) (V - nb) = nRT (Here R is gas constant)

Rearranging the equation,

Preal = (nRT/V - nb) - an2/V2

Substitute the all given values and calculate P

Preal = (1.041 x 0.08206 x 270 / 1.016 - 1.041 x 4.267×10-2) - 3.5x(1.041)2 / (1.016)2

Preal = 20.07 atm

Percentage difference = [(Pideal - Pvan der Waals) / P ideal ] x 100

                                 = (22.70 - 20.07 / 22.70) x 100

                                 = 11.58 %
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