Questions tagged [equation-of-state]

Questions related to a thermodynamic equation describing the state of matter under a given set of physical conditions.

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9
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1answer
2k views

Does the van der Waals equation remain valid when repulsive intermolecular forces dominate?

The van der Waals equation for a real gas is: $$RT =\left(p+\frac{a}{V_\mathrm{m}^2}\right)(V_\mathrm{m}-b)$$ We have understood this formula by saying that $a$ is the term which is for force of ...
8
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3answers
18k views

Why is the pressure correction in the van der Waals equation proportional to (n/V)^2?

The van der Waals equation for real gases is stated as follows: $$\left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT$$ For the coefficient $b$, we can reason out that more the number of molecules, the ...
13
votes
1answer
2k views

Why do some gases have lower value of Z for a particular pressure?

In the above graph,the minima of the curve for methane is more than that of nitrogen. Also, for a given value of pressure, the value of $Z$ for methane is less than that of nitrogen. They seem to meet ...
6
votes
1answer
238 views

Clarification of textbook concepts relating to “perfect”, “ideal”, and “real” gases

My textbook, Atkins' Physical Chemistry, 11th edition, by Atkins, de Paula, and Keeler, says the following: The resulting expression $$pV = nRT \tag{1A.4}$$ is the perfect gas law (or ...
25
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6answers
1k views

Why are equations of state for a non-ideal gas so elusive?

The ideal gas equation (daresay "law") is a fascinating combination of the work of dozens of scientists over a long period of time. I encountered Van der Waals interpretation for non-ideal gases ...
19
votes
2answers
4k views

What is a rigorous definition of gas volume, and how is the Van der Waals equation derived?

I am confused about the justification for the corrections to the ideal gas law in the Van der Waals equation: $$p=\frac{nRT}{V-nb}-a\left(\frac{n}{V}\right)^2$$ I understand that the equation ...
16
votes
2answers
17k views

Why is the van der Waals coefficient b equal to four times the volume of the particle?

In the van der Waals equation of state $$\left[p + a\left(\frac{n}{V}\right)^2\right](V-nb) = nRT$$ the coefficient $b$ is supposed to represent the volume occupied by the particles. Why then is it ...
0
votes
1answer
764 views

Why is the pressure correction added in the Van der Waals equation?

Since real gas particles experience attraction to each other, that means the pressure must be less from what we would expect. So why do we have to add a term to correct it? For example, in the ...
6
votes
1answer
14k views

Relation between the virial coefficients and van der Waals constants

I don't know where to begin with this question. A function $f(x)$ can be expressed as a special power series called the Taylor expansion. The common expansion is $(1-x)^{-1}=1+x+x^2$ Note that the ...
2
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1answer
2k views

How much pressure is needed to make dry ice?

By compressing $\ce{CO2 (g)}$ the gas gains a lot of heat. When the hot compressed carbon dioxide is left to cool, it attains the temperature of the surrounding material. When it is released into the ...