Understanding Van der Waals Equation for Ideal and Actual Gases | Homework Help

[babita]

Homework Statement

(P+ an^2/V^2)(V-nb) = nRT
I'm having some problems in understanding the above equation.

firstly, PV=nRT holds for ideal P and V , so after correction we are writing ideal P and V in terms of measured P and V right?

secondly V-nb is the actual volume not the ideal one. isn't it? if yes what is it doing in the above equation?

Homework Equations

The Attempt at a Solution

 

[babita]

please reply...i'm going mad

 

[chemisttree]

Homework Statement

(P+ an^2/V^2)(V-nb) = nRT
I'm having some problems in understanding the above equation.

firstly, PV=nRT holds for ideal P and V , so after correction we are writing ideal P and V in terms of measured P and V right?

No. This is an approximation that is somewhat better than the simple form of the IGE.

secondly V-nb is the actual volume not the ideal one. isn't it? if yes what is it doing in the above equation?

V-nb is a correction to the volume that is proportional to the number of moles of gas and has units of volume. Recall that the IGE assumes that gas molecules/atoms are non-interacting and have no "size".

 

[babita]

okkk...i was unable to understand the corrections made by van der waals in IGE...would u pls check if I'm getting it right...

in PV=nRT V is the volume that is available to the gas molecules, since at ideal gas conditions(high T and low P) the volume of particles is negligible,we can write the volume as V only...but in other cases we write V-nb taking into account the volume of particles too.
and in PV=nRT P stands for the pressure that gas particles would exert if no inter molecular forces were present...so in ideal conditions this is approximately equal to measured P...in other cases we have to add an^2/V^2
thankyou

 

[DeeNos]

The Van der Waals equation is a modification of the ideal gas law, which takes into account the intermolecular forces present in real gases. The ideal gas law assumes that gas particles have no volume and do not interact with each other, which is not true for real gases. The Van der Waals equation corrects for these deviations from ideal behavior by introducing two additional terms: (a) to account for attractive forces between particles and (b) to account for the volume occupied by the gas particles.

To answer your first question, yes, the Van der Waals equation is used to correct for the deviations from ideal behavior in measured pressure and volume. This is because real gases do not behave exactly like ideal gases, and the ideal gas law may not accurately predict their behavior.

To address your second question, V-nb is the actual volume of the gas, not the ideal volume. This term takes into account the volume that is occupied by the gas particles themselves. In an ideal gas, the particles have no volume and do not take up any space, but in reality, they do. This is why the Van der Waals equation includes this term.

Overall, the Van der Waals equation is used to better understand and predict the behavior of real gases, taking into account factors such as intermolecular forces and particle volume. It is important to note that this equation is not perfect and may still have some limitations, but it provides a more accurate representation of gas behavior than the ideal gas law.