Deviations from the Ideal Gas Equation

[doggieslover]

The derivation of the ideal gas equation employs two assumptions that are invalid for real gas molecules. First, the equation assumes that the molecules of the gas have no volume, which is not true for real molecules. Since the molecules will have some physical volume, the volume that the gas molecules occupy will be increased by the volume that the molecules occupy at rest. In addition, the equation ignores any interactions among the molecules. However, such interactions were first observed in the 19th century by J. D. van der Waals. He realized that, because of the intermolecular forces in the gas, there is a small but measurable attraction among the molecules, which will reduce the pressure of the gas on the walls of the container. To correct for these two deviations from an ideal gas, the van der Waals equation gives

(p+\frac{an^{2}}{V^{2}})(V-nb)=nRT,
where a and b are empirical constants, which are different for different gasses.

For carbon dioxide gas (\rm{CO_{2}}), the constants in the van der Waals equation are a=0.364\;{\rm J \cdot m^{3}/mol^{2}} and b=4.27 \times 10^{-5}\;{\rm m^{3}/mol}.
Part A
If 1.00 {\rm mol} of \rm{CO_{2}} gas at 350 {\rm K} is confined to a volume of 400 {\rm cm^{3}}, find the pressure p_ideal of the gas using the ideal gas equation.
Express your answer numerically in pascals.

Okay I set up the problem as p= [nRT/(V-nb)] - [(an^2)/V^2], using R = 8.314472m^3Pa/Kmol, V= 4*10^-4 I plugged everything in, and I got 8.14*10^6Pa, but it's incorrect, I'm not sure what I did wrong.

Part B
Find the pressure p_vdW of the gas using the van der Waals equation.
Express your answer numerically in pascals.

 

[alphysicist]

Hi doggieslover,

The derivation of the ideal gas equation employs two assumptions that are invalid for real gas molecules. First, the equation assumes that the molecules of the gas have no volume, which is not true for real molecules. Since the molecules will have some physical volume, the volume that the gas molecules occupy will be increased by the volume that the molecules occupy at rest. In addition, the equation ignores any interactions among the molecules. However, such interactions were first observed in the 19th century by J. D. van der Waals. He realized that, because of the intermolecular forces in the gas, there is a small but measurable attraction among the molecules, which will reduce the pressure of the gas on the walls of the container. To correct for these two deviations from an ideal gas, the van der Waals equation gives

(p+\frac{an^{2}}{V^{2}})(V-nb)=nRT,
where a and b are empirical constants, which are different for different gasses.

For carbon dioxide gas (\rm{CO_{2}}), the constants in the van der Waals equation are a=0.364\;{\rm J \cdot m^{3}/mol^{2}} and b=4.27 \times 10^{-5}\;{\rm m^{3}/mol}.
Part A
If 1.00 {\rm mol} of \rm{CO_{2}} gas at 350 {\rm K} is confined to a volume of 400 {\rm cm^{3}}, find the pressure p_ideal of the gas using the ideal gas equation.
Express your answer numerically in pascals.

Okay I set up the problem as p= [nRT/(V-nb)] - [(an^2)/V^2], using R = 8.314472m^3Pa/Kmol, V= 4*10^-4 I plugged everything in, and I got 8.14*10^6Pa, but it's incorrect, I'm not sure what I did wrong.

For part A they are asking for the pressure if the gas were an ideal gas; so you need to use the ideal gas equation, not the van der Waals gas equation. (In part B they ask for the pressure assuming it's a van der Waals gas.)

 

[doggieslover]

Oh yeah I read the question wrong, I got it now, thanks.