Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Q. 5.51 (page 185)

When plotting graphs and performing numerical calculations, it is convenient to work in terms of reduced variables, Rewrite the van der Waals equation in terms of these variables, and notice that the constants a and b disappear.

Short Answer

Expert verified

p=8t3v-1-3v2

Step by step solution

01

Given information 

P=pPcT=tTcV=vVc

and

role="math" localid="1646979368068" P=NkT(V-Nb)-aN2V2 (van der Waal's equation)

02

 Substituting the values of P, V and T in the van der Waal equation.

P=NkT(V-Nb)-aN2V2pPc=NktTc(vVc-Nb)-aN2(vVc)2

03

 Substituting the values of Pc, Vc and Tc in equation. 

p127ab2=N(3Nbv-Nb)827abt-aN2(3Nbv)2

further solving the equation we get

p=8t3v-1-3v2

The van der Waal's equation is independent of constants a and b when represented in reduced variables

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

How can diamond ever be more stable than graphite, when it has

less entropy? Explain how at high pressures the conversion of graphite to diamond

can increase the total entropy of the carbon plus its environment.

Go through the arithmetic to verify that diamond becomes more stable than graphite at approximately 15 kbar.

Osmotic pressure measurements can be used to determine the molecular weights of large molecules such as proteins. For a solution of large molecules to qualify as "dilute," its molar concentration must be very low and hence the osmotic pressure can be too small to measure accurately. For this reason, the usual procedure is to measure the osmotic pressure at a variety of concentrations, then extrapolate the results to the limit of zero concentration. Here are some data for the protein hemoglobin dissolved in water at 3oC:

Concentration (grams/liter)∆h (cm)
5.62.0
16.66.5
32.512.8
43.417.6
54.022.6

The quantity ∆his the equilibrium difference in fluid level between the solution and the pure solvent,. From these measurements, determine the approximate molecular weight of hemoglobin (in grams per mole).

An experimental arrangement for measuring osmotic pressure. Solvent flows across the membrane from left to right until the difference in fluid level,∆h, is just enough to supply the osmotic pressure.

The formula for CP-CV derived in the previous problem can also be derived starting with the definitions of these quantities in terms of U and H. Do so. Most of the derivation is very similar, but at one point you need to use the relation P=-(∂F/∂V)T.

Write down the equilibrium condition for each of the following reactions:

(a)2H↔H2(b)2CO+O2↔2CO2(c)CH4+2O2↔2H2O+CO2(d)H2SO4↔2H++SO42-(e)2p+2n↔He4
See all solutions

Recommended explanations on Physics Textbooks

Geometrical and Physical Optics

Read Explanation

Wave Optics

Read Explanation

Electric Charge Field and Potential

Read Explanation

Radiation

Read Explanation

Linear Momentum

Read Explanation

Waves Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free