The van der Waals equation for 1 mole of gas is given by (p +av-2)(v -...

90.2K

Verified Solution

Question

Chemistry

The van der Waals equation for 1 mole of gas is given by (p+av^-2)(v - b) = RT. In general, curves of p versus vforvarious values of T exhibit a maximum and a minimum at thetwopoints where (Î´p/Î´v)_T = 0. The maximum and minumumcoalesceinto a single point on that curvewhere(Î´²p/Î´v²)_T = 0 inaddition to(Î´p/Î´v)_T = 0. This point is calledthe \"critical point\"of the substance and its temperature,pressure, and molar volume aredenoted by T_c,p_c, and v_c,respectively.
Â Â Â (a) Express a and b in terms of T_candv_c.
Â Â Â (b) Express p_c in termsofT_c and v_c.
Â Â Â (c) Write the van der Waals equation in termsofthe reduced dimensionless variables T' â‰¡ T/T_c , v'â‰¡v/v_c , p' â‰¡ p/p_c
This form should involve neither a nor b.

Answer & Explanation Solved by verified expert

3.8 Ratings (615 Votes)

Answer We have the van der walls equation PaV2VbRT 1 After rearrangement we get P RTVb aV2 2 At critical Temperature dPdV 0 and d2PdV2 0 Now starting from equation See Answer

Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:

Unlimited Question Access with detailed Answers
Zin AI - 3 Million Words
10 Dall-E 3 Images
20 Plot Generations
Conversation with Dialogue Memory
No Ads, Ever!
Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!

Become a Member