Physical Chemistry Deriv: P = (RTe^(-a/(RTVm)))/(Vm-b)

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aprovit

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I have to find the first and second derivatives of the Dieterici equation of state,

P = (RTe^(-a/(RTVm)))/(Vm-b)

Note: Vm is the molar volume. a and b are constants.

I came up with the following derivatives, but I don't think I did it correctly:

First derivative = (-RTe^(-a/(RTVm)))/((Vm-b)^2)

Second derivative = (2RTe^(-a/(RTVm)))/((Vm-b)^3)

Please help...
Thank you in advance!
 
Re: Physical Chemistry Derivatives

\(\displaystyle P =\frac{RTe^{-a/(RTV_{m})}}{V_{m}-b}\)

What are you differentiating in respect to? V[sub:161ypw4z]m[/sub:161ypw4z] or temperature? Kind of hard to tell with what you've got. But either way, you're going to have to take the logarithm of both sides to get rid of the exponent and implicitly differentiate.
 
the partial derivative of pressure with respect to Vm at constant Temperature
 
Re: Physical Chemistry Derivatives

\(\displaystyle P =\frac{RTe^{-a/(RTV_{m})}}{V_{m}-b}\)

You can differentiate it explicitly - if you wanted P as your dependent variable.

\(\displaystyle \frac{dP}{dT}_{v_m=constant} = \frac{R\cdot\ e^{-\frac{a}{RTV_m}}}{V_m-b}\cdot\ (1+ \frac{a}{RV_mT})\\)

and so on....
 
aprovit said:
thank you very much, but I need dp/dvm with t constant
Click to expand...

Same principle - where are you stuck? Just apply chain rule with product rule or quotient rule.
 
I'm stuck with all of them. I haven't done calculus in years. This is for a physical chemistry course.
 
So dust off those calculus books and review and show us some work.
 
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