Van der waals Definition and 144 Threads

I'm trying to follow the proof given in Box 5.3, page 235, of the MCP book regarding the Van der Waals grand potential. It seems to me that there is a missing factor (2l−1)!/(l−1)! in the last term of Equation (8). What am I doing wrong?

Ref: Van der Waals Equation @ Wikipedia The above paragraph is explains how intermolecular attraction reduces the gas pressure, assuming that there is no attraction between walls and particles. In practice, would there be a change in pressure from one kind of wall to another, if we ensure...

Hi, I am not quite sure if I have understood the second task correctly, but I proceeded as follows. It's about what happens to the isothermal compressibility when the free energy becomes minimal. In the first task there was already the equation ##\kappa_T=\frac{1}{V}\Bigl( \frac{\partial^2...

Hello, when reviewing the types of chemical bonds i was a little bit confused about van der waals interactions, in the definition we talk about momentarily disproportion of electrons that provoke a dipole , and then i read that also include hydrogen bonds . I am a bit confused about van der...

So a and b were pretty straightforward. Got stuck on part c. The question says they approximated Van der Waals in first order in a and b. So I started with that by rewriting Van der Waals eqn as ## p = \frac { N \tau } { V - Nb } - \frac {N^2a} {V^2} ## and I then Taylor approximated ## \frac...

The summary refers, for example, to the Wikipedia explanation "The force results from a transient shift in electron density. Specifically, the electron density may temporarily shift more greatly to one side of the nucleus. This generates a transient charge to which a nearby atom can be either...

<Using the hint, I tried to find the van der Waal constants in molar form. Since STP is mentioned, I used the unitary method relationship- 22.4 L=22400cm^3=1 molar V <To find a possible conversion standard between cm^3 and mol; which turned out to be 1cm^3= 4.46*10^-5 mol. <Then I used the...

Hi Everyone, can you guys please help me with the exercise attached? I knot that according to the book, van der Waals interaction is “charge fluctuations in atoms due to zero point motion.” This is correct once you understand that they are not talking about zero point motion of nuclear...

As far as I know the van der Waals constants can be expressed as functions of Pc and Tc. Why is it so? Why is it not a function of Vc/Tc, or Pc/Vc? Say for example, b = Vc/3. Why is this expressed in terms of Pc and Tc instead? Why is a also in terms of Pc and Tc, and not Vc? Is this just a...

How is surface taken into account in van der Waals equation? ( P + a n2/V2 ) ( V - nb ) = nRT The term a n2/V2 makes for a reduction of the expected pressure, due to surface effects (gas molecules near the surface sense a net attraction force towards the "inside of the volume"). But how is...

In our class, we're using Wassermann's Thermal physics as textbook. I always try to solve all question which included in Text book. But sometime when I meet a problem that look like easy but actually hard, I'm so embarrassed. This problem do also. First, in the textbook grand potential for van...

Hi, what I've done so far is solving equation 2) for ##U##, and replacing what I get in equation 1). Then, ##c_V## is equal to the partial derivative of ##S## with respect to T times T, so I've done that. The derivative is ##CNR/T##, so ##c_V=CNR## but those aren't the correct units for ##c_V##.

Van der Waals EoS is a cubic EoS that can represent the transition between gas and liquid phase. If you plot a P-V graph you end up with something like this The part I underlined in red are said to be metastable equilibria (i.e. superheated liquid and supersaturated vapor). I don't understand...

Summary:: Find the pressure using the vdw equation in reduced variables Hi everyone! I have a doubt when I try to solve this exercise. The result was very high pressure. Calculate the pressure using the reduced variable vdW equation for a sample of 74.8 grams of ethane in a ##200 cm^3##...

Diagram is here.

It is said that, for real gases at high pressure, the measured volume is higher than the calculated volume. My perception of the volume of the gas, as of now, is the following: The free space available for the gas to move. It excludes the volume of the molecules. So on increasing the pressure...

How is it proved that Van Der Waals gas is a second order phase transition? The second order derivative of the pressure (P ) with respect to volume ( V ) don't have a discontinuity ( except at point V = Nb , but the pressure is not existent for V<=Nb ). So how come Van der waals gas describes...

Not sure where to actually start. Do I need to do a virial expansion? Any tips on on where to start would be greatly appreciated.

When two atoms or molecules are brought within hailing distance of each other, their average internal charge distributions get modified because the electrons' state in molecule A is now a function of the field coming from molecule B, and vice versa. If, on an average, the electron distributions...

Doesn't volume of ideal gas include volume of the molecules? What I was taught in school is that, when two molecules collide, no other molecule can come around it (inside the green part in the figure) and that volume is excluded volume? Is it correct? If yes, why?

According to QFT, are there hydrogen bonds or Van der Waals force? Or this an outdated concept of classical physics?

I've got a question that requires me to use the Van der Waals equation in the form: p(V-b)=nRT The process is isobaric, the volume changes from 1m3 to 2m3, and there is 1 mole of the unidentified gas. Ultimately, I need to find initial and final values of T. So I rearranged the formula...

Homework Statement I'm taking an online PChem course where the instructor throws out Z = 3Vr/(3Vr – 1) – 9/(8 VrTr); where Vr is the reduced molar volume. 2. Homework Equations {P + a/Vm^2}{Vm – b} = RT; where Vm is the molar volume Tc = 8a/27Rb ; Vc = 3b ; Pc = a/27b^2 3. The Attempt...

The title, basically. I am aware of the mixing rule for the two-component form: aP = a1z12 + 2z1z2sqrt(a1a2) + a2z22 Where do I find its extension on three or more cases? SVNA does not tell anything about this.

Homework Statement Find the expression for c_p - c_v for a van-der-waals gas, with the equation of state \Bigg{(}p+\dfrac{a}{V^2}\Bigg{)}(V-b)=RT Homework EquationsThe Attempt at a Solution Basically I've proved c_p - c_v = \Bigg{[} p + \Bigg{(}\dfrac{\partial E}{\partial V}\Bigg{)}_T...

Homework Statement The question is: What happened with the entropy in a free expansion? The system is isolated and the state equation is: $$p=AT/V+B/V^2$$ Homework Equations $$dU=TdS-pdV$$ The Attempt at a Solution My attempt is: Because the system is isolated and corresponding to an free...

I know that the two are different thing, that vdW appears in inert gas crystals and alike while hydrogen bond bonds molecules of water. My question is, how does the potential look for hydrogen bond? For vdWaals we have the two terms proportional to 1/R^6 that describes attraction and 1/R^12...

Hi, I know that if you put a dipole and a neutral molecule at a certain distance, there is the Debye's force that attract them. If you put the same molecules in the first position, they will attract another time. I know this can be a stupid answers, but what's the font of that energy? The...

Hello. What I know about the Van der Waals force is that it comes from an instantaneous electronic cloud flucutation of the netural atom. This instantaneous electric dipole of the atom attracts electrons in nearby neutral atoms so other electric dipoles are induced on those atoms. As a result...

I was watching the following TED Talks video about using carbon nanotubes to build a space elevator: After the 12-13 minute point the speaker starts describing how very short carbon nanotubes can be pulled from a "nanotube forest" and spun together to create a very long thread. However the...

The question I'm stuck on is: P = NKBT/(V-Nb) - aN2/(V2) -----> (1) Re-arrange variables in the Van Der Waals equation of state, Eq. (1), so that V always appears in the equation as V/(3Nb) and P appears as 27b2P/a. Then T should appear in the combination 27b kBT/(8a). Call these...

I was researching the relationship between magnetic dipoles and chemical bonding and I came across a very interesting paper. I'm hoping some of you can shed some light on how magnetic fields are making dissociation of a molecule possible and how to measure it...

When I plot the isenthalpic curves in T-P plane, I see isenthalpic curves are not well defined in the lower temperature region in T-P plane. Inside the inversion curve Joule-Thomson coefficient is positive so gas cools and outside of the inversion curve Joule-Thomson coefficent is negative so...

Homework Statement Hi, I have the following task: Translated into English, that means: " For Cpm and Cvm of gases the following relationship is true: (1) a) Show with the relationship (1), that for an ideal gas Cpm - Cvm = R is valid b) Deduce from equation (1) and the tripple product rule...

Homework Statement [/B] You are asked to calculate changes in internal energy, entropy, heat transferred and work done for each of the following process. Also you are asked to calculate "the latent heat for the isotherm in the figure". We know the a and b parameters which characterize the VdW...

1. For a van der Waals gas πT=a/Vm2. Calculate ΔUm for the isothermal expansion of nitrogen gas from an initial volume of 1.00 dm3 to 24.8 dm3at 298K. What are values for q and w?Homework Equations I looked up a for N2 gas to be 1.352 atm*dm6/mol2 dU(V,T)=(∂U/∂V)TdV+(∂U/∂T)VdT (∂U/∂V)T=πT...

I may be as wrong as an alchemist, but according to what I know, many substance stay together because of vander vaal's forces (I forgot how it's spelt) which is essentially the temporary dipoles that form around molecules, some times, the dipoles line up such that two neighbouring molecules have...

Induced dipoles result in Van der Waals' forces and permanent dipoles in hydrogen bonds, right? But how do you know is a compound has formed hydrogen bonds or Van der Waals' forces? For example, HF forms hydrogen bonds while HCl forms Van der Waals' forces and not hydrogen bonds. But in HCl, H...

Hi all,If there is activation energy for chemisorption, then an atom with insufficient energy to overcome that barrier will remain physisorbed to the surface via van der Waals forces. I would like to further understand this activation energy in terms of, for example, the overlap of electron...

What does the following statement below mean? "The excluded volume is not just equal to the volume occupied by the solid, finite-sized particles, but actually four times that volume. To see this, we must realize that a particle is surrounded by a sphere of radius 2r (two times the original...

the equation (P+a(n/V)^2)(V-nb)=nRT was derived in this manner: The pressure of a real gas is affected by intermolecular forces and so the a(n/V)^2 term must be added to the measured pressure to obtain the ideal pressure where Pmeasured+a(n/V)^2=Pideal On the other hand when they explained...

So i want to understand how concepts like van der waals, electronegavity and covalent bonds were discovered, measured and derived back in the days. I'm looking for a good book to explain this. So far I've looked at a book by Jacob.Intermolecular and Surface Forces, Revised Third Edition -...

Homework Statement Calculate the molecular diameter of hydrogen, assuming the spherical shape on the basis of van der Waals coefficients. Van der Waals Coefficients for hydrogen a = 0.244 atm L2.mol-2 b*103 = 26.6 L.mol-1 Homework...

Homework Statement Try to estimate the latent heat of vaporization of water and nitrogen using the Van der Waals model. What happens? Homework Equations $$\Delta Q = T\Delta S=L$$ $$S=nR\left[ \ln\left(\frac{(V-nb)T^{3/2}}{n\Phi}\right)+\frac{5}{2} \right]$$ The Attempt at a Solution I...

Homework Statement Obtain the chemical potential of water as a function of temperature and volume using the Van der Waals model. Homework Equations μ=∂U∂N The Attempt at a Solution I don't really understand how to do this at all. Any help would be greatly appreciated.

Homework Statement The bulb of a constant volume gas thermometer is immersed in an ice/water/water vapour mixture at equilibrium and the recorded pressure is 0.400 atm. It is then immersed in a boiling liquid and the pressure is 0.844 atm. Sufficient gas is then removed from the bulb such that...

The pressure exerted on the walls of the container by a real gas is less compared to an ideal gas. This is due to the attractive forces of the gas pulling the molecules back towards the rest of the gas molecules. However, there is also a relationship whereby at lower temperatures, the z is even...

Homework Statement Consider ##n## moles of gas, initially confined within a volume ##V## and held at temperature ##T##. The gas is expanded to a total volume ##\alpha V##, where ##\alpha## is a constant, by a reversible isothermal expansion. Assume that the gas obeys the van der Waals equation...

Homework Statement Solve for the work done during water electrolysis using the Van Der Waals equation.[/B] Solving for work using Ideal Gas Law: This is the system work for the electrolysis of water using the Ideal Gas Law: W = PΔV = (101.3 x 103 Pa)(1.5 moles)(22.4 x 10-3...