Answer:
43.1atm is the pressure using gas law and 27.2atm using Van der Waals Law.
Explanation:
Ideal gas law is:
PV = nRT
<em>Where P is pressure in atm</em>
<em>V is volume = 4.00L</em>
<em>n are moles of the gas (For chlorine Molar Mass: 70.90g/mol):</em>
<em>500g * (1mol / 70.90g) = 7.052 moles</em>
<em>R is gas constant = 0.082atmL/molK</em>
<em>T is absolute temperature = 25°C + 273 = 298K</em>
To solve the pressure, P:
P = nRT/V
P = 7.052mol*0.082atmL/molK*298K / 4.00L
P = 43.1atm is the pressure using gas law.
Van der Waals equation is:
![P + a(\frac{n}{V})^2 * (V-nb) = nRT](https://tex.z-dn.net/?f=P%20%2B%20a%28%5Cfrac%7Bn%7D%7BV%7D%29%5E2%20%2A%20%28V-nb%29%20%3D%20nRT)
<em>Where a is 6.58L²atm*mol⁻²</em>
<em>b = 0.056Lmol⁻²</em>
Solving for pressure:
![P + a(\frac{n}{V})^2 = \frac{nRT}{(V-nb)}](https://tex.z-dn.net/?f=P%20%2B%20a%28%5Cfrac%7Bn%7D%7BV%7D%29%5E2%20%3D%20%5Cfrac%7BnRT%7D%7B%28V-nb%29%7D)
![P = \frac{nRT}{(V-nb)}-a(\frac{n}{V})^2](https://tex.z-dn.net/?f=P%20%20%3D%20%5Cfrac%7BnRT%7D%7B%28V-nb%29%7D-a%28%5Cfrac%7Bn%7D%7BV%7D%29%5E2)
![P = \frac{7.052mol*0.082atmL/molK*298K}{(4.00L-7.052mol*0.056L*mol)}-6.58L^2mol^{-2}(\frac{7.052mol}{4.00L})^2](https://tex.z-dn.net/?f=P%20%20%3D%20%5Cfrac%7B7.052mol%2A0.082atmL%2FmolK%2A298K%7D%7B%284.00L-7.052mol%2A0.056L%2Amol%29%7D-6.58L%5E2mol%5E%7B-2%7D%28%5Cfrac%7B7.052mol%7D%7B4.00L%7D%29%5E2)
P = 172.323 / 3.6051 - 20.4866
P = 27.2atm using Van der Waals Law