Questions tagged [equation-of-state]
Questions related to a thermodynamic equation describing the state of matter under a given set of physical conditions.
46
questions
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Virial expansion of real gas equation and volume work
Hi I am currently working on a thermodynamics problem, and it asks me to first find the volume work done on a gas that behaves like the simplified Dieterici equation (see below) predicts on isothermal ...
0
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0answers
118 views
Is a/b > 1 mol/L for a and b in the van der Waals equation?
We know that the van der Waals equation for real gases is
$$\left(p + \frac{an^2}{V^2}\right)(V-nb) = nRT.$$
Is $a > b$ always in this equation?
In my textbook $a > b$ for gases like $\ce{He},$ $...
3
votes
2answers
123 views
Why does van der Waals' equation of state give only one P, V pair for a particular temperature here?
I came across this question which I initially ignored believing that the data was insufficient:
Calculate the pressure exerted by one mole of $\ce{CO2}$ gas at $\pu{273 K}$ if the van der Waals' ...
3
votes
1answer
110 views
Meaning of 'constant T and p'
In chemical thermodynamics, the condition "constant temperature and pressure" appears almost everywhere. However, I felt a small ambiguity in the phrase so I wanted to clear my doubts. When ...
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0answers
24 views
At what pressure is the triple point of ethane?
Depending on source there are two givens for the triple point of ethane: 0.8 Pa or 1.1 Pa. Only one of them can be correct, which one is?
1
vote
1answer
118 views
Ideal gas equation derivation proportionality [duplicate]
While deriving the Ideal gas Equation using Boyle's, Charles', and Avogadro Laws,
how are each of the laws, which have different proportionality constants and different quantities as constant combined?...
6
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1answer
259 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 ...
0
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1answer
96 views
Why did they ‘split’ this H2+ ion in the ionic equation?
I am asked this chemistry question in my textbook:
Write an ionic equation for this reaction:
$$\ce{Mg(s) + H2SO4(aq) -> MgSO4(aq) + H2(g)}$$
This is my thought process and answer:
$\require{...
0
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1answer
2k 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 ...
0
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1answer
94 views
What is the chemical equation, along with the change in heat of the crystallization process of Sodium Acetate
This is the reaction found in chemical hand warmers, and I can't figure out the equation and the change in heat. Any help would be greatly appreciated
2
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0answers
271 views
Calculating phase diagram of mixed component natural gases (Bubble and Dew points)
I'm developing a piece of software which calculates and plots the Phase diagram (PT) for a mixed component natural gas.
For reference I have a common used natural gas plotted using a commercial ...
3
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1answer
952 views
Calculating dew point and bubble point of gas mixtures
How do you calculate approximately the triple point and critical point of any given CH-based gas mixture?
I have developed a software which uses iterations to find bubble point and dew point of any ...
5
votes
2answers
375 views
How to solve constants out of the internal energy equation?
Imagine we deal with a new kind of matter, whose state is described by:
$$PV = AT^3$$
Its internal energy is given by
$$U = BT^n \ln\left(\frac{V}{V_0}\right) + f(T)$$
where $A$, $B$ and $V_0$ is a ...
2
votes
1answer
111 views
Simple alternative to UNIFAC to prove that a mixture containing 1ml of x and 5 litres of propylene glycol is not flammable?
Section 2.6.1 of the REGULATION (EC) No 1272/2008 (CLP) defines a flammable liquid as:
Flammable liquid means a liquid having a flash point of not more than
$60 ^{\circ}$C.
So data on flash ...
2
votes
1answer
315 views
Reaction energy of oxygen and hydrogen
From the bonding energy of following bonds that I found in a Wikipedia article, I calculated the reaction energy that would be released when oxygen and hydrogen are reacted to produce water. The phase ...
1
vote
1answer
394 views
Why is excluded volume in van der Waals equation divided by 2?
Source: Physics Stack Exchange
The excluded volume calculated based on the diagram is 8 times the volume of a molecule. The volume is then divided by 2 to give the so-called excluded volume per ...
4
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2answers
281 views
Is there an intuitive reason for the proportionality constant 2/3 in pv=nRT=(2/3)U?
Why is there a $\frac23$ term?
I fully understand that it makes sense for pressure to be the volume weighted average kinetic energy. And the equation above shows that this is so (for an ideal gas). I ...
2
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0answers
86 views
Calculating the number of energy states in a particular momentum direction
Given is a 2D scenario of a particle within a container:
The circumference shows all the possible 2D spatial directions for a given momentum value of the particle. One of those momentum directions is ...
2
votes
1answer
517 views
Why is the pressure correction constant 'a' independent of temperature?
In the van der Waals equation of state, 'a' which is the correction value is based on inter-molecular forces of attraction? Then should inter-molecular forces decrease when temperature increases, and ...
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votes
1answer
60 views
How to determine if pressure surpasses capacity with the van der Waals equation of state?
I have to decide whether a $\pu{20 L}$ container with $\pu{0.8 kg}$ ethane can withstand the pressure at $\pu{373.15 K}$. The following information is given:
\begin{align}
b &= \pu{6.448x10^-2 ...
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1answer
2k views
How to use a modified Peng-Robinson equation to calculate a density?
I'm trying to use the Peng-Robinson-Stryjek-Vera 2 (PRSV2) Equation of State to calculate the density of a compound, in this example: methanol. At ambient temperature and pressure, shouldn't I be able ...
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3answers
22k 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 ...
2
votes
1answer
11k views
dU/dV in van der Waals equation of state derivation
Previous, I proved that
$$\frac{T_2}{T_1}^{C_V/(C_p-C_V)}=\frac{V_1}{V_2}$$
I've been asked to derive a similar expression for a gas that obeys the equation of state
$$p=\frac{RT}{(\overline{V}-b)}$...
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1answer
5k views
What is the relation between universal gas constant R and amount of substance n?
I have found it mentioned in various sources that the value of R depends on the amount of substance $n$ in the ideal gas equation: $PV=nRT$
If this is true, it would imply that $R$ is a function of $n$...
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1answer
1k views
Using Mathematica to Plot an Isotherm at its Critical Temperature
Hello I'm new to mathematica and I have been trying to plot an isotherm for a substance at its critical temperature, using Van der Waals equation of state. I have done all the work except I do not ...
2
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0answers
101 views
understanding redox reaction
I am a total noob in chemistry, so sorry in advance if this is a very stupid question... I am trying to solve this redox reaction:
$$\ce{KClO3 + FeSO4 + H2SO4 -> Fe2(SO4)3 + KCl}$$
$$\ce{K^{+1}Cl^{...
8
votes
1answer
325 views
Is this equation of state original?
I created this equation of state as a personal undergraduate summer project (here is the link) seven years ago:
$$\frac{PV}{nRT}-1 \propto \left(\frac{nRT}{PV}\right)^2 \left[\left(\frac{nRT}{PV}\...
12
votes
3answers
728 views
Why can't equations of state be replaced by machine learning models?
The Peng-Robinson equation of state, for example, has no underlying physical meaning, and is just a model that was fit to data. Computer scientists have developed much, much better models for data ...
13
votes
2answers
3k views
Why do some gases have lower value of Z for a particular pressure?
In the above graph,the minima of the curve for methane is more than that of nitrogen. Also, for a given value of pressure, the value of $Z$ for methane is less than that of nitrogen. They seem to meet ...
9
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1answer
3k views
Does the van der Waals equation remain valid when repulsive intermolecular forces dominate?
The van der Waals equation for a real gas is:
$$RT =\left(p+\frac{a}{V_\mathrm{m}^2}\right)(V_\mathrm{m}-b)$$
We have understood this formula by saying that $a$ is the term which is for force of ...
3
votes
2answers
110 views
How can a sample that is in two different states be at a uniform temperature?
In my chemistry course, the professor has discussed how a sample that contains both solid and liquid water would be at 0 degrees Celsius no matter what the proportion of solid to liquid water is. I ...
15
votes
3answers
3k views
PV=nRT approximation on other planets?
In Chemistry class yesterday, I learned that real gases with low atomic masses behave like an ideal gas at high temperatures and low pressure. Since on earth at sea level the pressure is close to $1\ \...
2
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0answers
63 views
Determining the equation of state when given thermodynamic relations [closed]
Empirical observations of a thermodynamic system have shown that:
$$\begin{align}C_{\mathrm m,V} &\neq C_{\mathrm m,V}(T) \\[6pt]
\left(\frac{\partial U}{\partial V_\mathrm m}\right)_{T} &...
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2answers
19k 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 ...
5
votes
1answer
1k views
Why is the ideal gas law so ubiquitous?
Why is the ideal gas law usable in most gas problems?
For example, in a problem like this: "Suppose you have $1.00\: \mathrm{mol}$ of a gas at $0\:^\circ \mathrm{C}$, occupying a container which is $...
1
vote
1answer
253 views
What are analytical expressions for the isothermal change of Gibbs energy?
The change of Gibbs energy at constant temperature and species numbers, $\Delta G$, is given by an integral $\int_{p_1}^{p_2}V\,{\mathrm d}p$. For the ideal gas law, $p\,V=n\,RT$, this comes down to
$$...
3
votes
1answer
53 views
Getting the pressure using the equation of states - will the answer be the same?
When I get the pressure using the different equations of state (e.g. van der Waals, Redlich-Kwong, etc.), will the answer still be the same?
2
votes
1answer
2k views
Determining the boiling point of a substance given the triple point and critical point
If I have the pressure and temperature of a substance in its triple point, as well as its pressure and temperature in the critical point, how can I determine the boiling point of the substance at 1 ...
4
votes
1answer
687 views
Theoretical versus empirical equations
I'm familiar with the fact that theoretical formulae are based on already known theory and are very frequently simplified (some equations don't include interactions between molecules for example) ...
1
vote
2answers
308 views
Cohesive Energy Density table request
Quick question: Any one knows a resource for Cohesive Energy Density of some organic materials ?
I am not looking for any specific molecule, actually I want to plan my project based on available ...
13
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3answers
41k views
Why does small value of van der Waals gas constant "b" ensure easier liquefication?
Larger value of b signifies that the size of the molecules is larger and hence the forces acting should become larger due to increased surface area.This should ensure easier liquefication. But my book ...
6
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1answer
15k 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 ...
3
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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 ...
6
votes
2answers
620 views
What meaning do multiple real solutions of a truncated virial equation have, if any?
Let's say I truncate the virial equation after the third term for use as my equation of state:
$${P\over\rho RT}=1+B\rho+C\rho^2$$
I have tabulated values for $B(T)$ and $C(T)$. I know $P$ and $T$ ...
21
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2answers
5k views
What is a rigorous definition of gas volume, and how is the Van der Waals equation derived?
I am confused about the justification for the corrections to the ideal gas law in the Van der Waals equation: $$p=\frac{nRT}{V-nb}-a\left(\frac{n}{V}\right)^2$$
I understand that the equation ...
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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 ...
