Van der Waals pressure I was solving some problems and I had a doubt a problem since the resulting pressure gives me a negative value. The problem was the following:


  Could $100~\mathrm{g}$ of $\ce{N2}$ in a $200~\mathrm{mL}$ container exert a pressure of $25~\mathrm{atm}$ at $28~^\circ\mathrm{C}$ if it behave like an ideal gas? If your answer is no, what pressure would exert the gas, knowing that the van der Waals constants for $\ce{N2}$ are $3.11~\mathrm{\frac{L\,atm}{mol^2}}$ and $0.076~\mathrm{\frac{L}{mol}}$. 


I have converted the 100 grams of $\ce{N2}$ to moles of $\ce{N2}$, and with that I've replaced the data in the van der Waals formula, using $a = 3.11~\mathrm{\frac{L\,atm)}{mol^2}}$ and $b = 0.076~\mathrm{\frac{L}{mol}}$. The result was a negative pressure, and I am pretty sure that's impossible (or at least that's what my chemistry teacher said). 

This is what I did:

$$\begin{align}
P &amp;= \frac{nRT}{V-nb} -\frac{an^2}{V^2}\\
  &amp;= \frac{(3.57~\mathrm{mol})(0.082\mathrm{\frac{L\,atm}{K\,mol}})
    (301.1~\mathrm{K})}{(0.2~\mathrm{L}) 
   -(3.57 ~\mathrm{mol})(0.076\mathrm{\frac{L}{mol}})}
   -\frac{(3.11~\mathrm{\frac{L~atm}{mol^2}})
    (3.57~\mathrm{mol})^2}{(0.2~\mathrm{L})^2}
\end{align}$$

The result was: 
$-1626.19~\mathrm{atm} - 9.9075~\mathrm{atm} = -1636.0975~\mathrm{atm}$
Let's get the obvious out of the way: The answer to that exercise is yes. Hence it is completely unnecessary to do the second part. With the parameters given in the exercise I calculated a pressure of about 440 atmospheres using the ideal gas law.

But then since we're all here to learn, let's also have a look at the second part. The good news is that I can't see anything wrong with how you used the equation. The problem is already pointed out by orthocresol in the comments, which I will quote here for safekeeping (emphasis by me):


  Ok. Firstly, the constant $a$ has units of $\mathrm{L^2~atm~mol^{-2}}$ (not $\mathrm{L~atm~mol^{-2}}$), but I am guessing it is just a typo on your part. The issue seems to arise from the values given for $a$ and $b$. Wikipedia gives the constants as $1.352$ and $0.0387$ respectively (converted to the same units as yours). Using those values I get a pressure of 997.3 atm.


I would assume that nobody caught this mistake earlier since you are not actually supposed to do that part of the question.