Can the Coefficient b in Van der Waals Equation Be Negative

[mrawls]

solving for "b" with van der Waals

1. Homework Statement

The problem gives me "a", the temperature, volume, number of moles, and pressure. It asks me to solve for "b".

I have set up the equation to solve for b, and done it. The answer comes out with the right units but it is negative.

2. Homework Equations

Can the value of the coefficient be negative or does that mean I did it wrong?


3. The Attempt at a Solution

The equation:

p = nRT/(V-nb) - a(n/V)^2

Using that equation, I came up with:

b = (Vp + Va(n/V)^2 - nRT) / (np + na(n/V)^2)

I came up with b = -4.58x(10^-4) (m^3) (mol^-1)
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[Clever-Name]

The equation looks right. Could you provide us with the values given please?

 

[mrawls]

Yes, sorry I forgot to list them before.

a = .580(m^6)(Pa)(mol^-2)
T = 273K
P = 5,000,000 Pa
R = 8.3144 Pa(m^3)/(mol)K

I then solved for a(n/V)^2 and plugged that answer into the equation (I got 4734693.9 Pa for that)

I actually realized a huge mistake I made when posting these values. The given pressure was 5 MPa, but in my equation I plugged in only 1 MPa... I am almost certain that must have been the problem.

 

[Clever-Name]

I think you left out the Volume there.

Did plugging in the correct value for P fix your problem?

b should definitely not be negative as it is a measure of how much volume, on average, is displaced by a given particle.

 

[mrawls]

Wow I did forget to list the volume too.. Sorry I had a busy day haha I was not thinking clearly.

Using the correct pressure resulted in the right answer, with the right units!

Sadly my professor likes to give every value in non-SI unrelated units and we have to do all sorts of conversions :(