Answer:
P=atm
![b=\frac{L}{mol}](https://tex.z-dn.net/?f=b%3D%5Cfrac%7BL%7D%7Bmol%7D)
Explanation:
The problem give you the Van Der Waals equation:
![(P+\frac{n^{2}a}{V^{2}})(V-nb)=nRT](https://tex.z-dn.net/?f=%28P%2B%5Cfrac%7Bn%5E%7B2%7Da%7D%7BV%5E%7B2%7D%7D%29%28V-nb%29%3DnRT)
First we are going to solve for P:
![(P+\frac{n^{2}a}{V^{2}})=\frac{nRT}{(V-nb)}](https://tex.z-dn.net/?f=%28P%2B%5Cfrac%7Bn%5E%7B2%7Da%7D%7BV%5E%7B2%7D%7D%29%3D%5Cfrac%7BnRT%7D%7B%28V-nb%29%7D)
![P=\frac{nRT}{(V-nb)}-\frac{n^{2}a}{v^{2}}](https://tex.z-dn.net/?f=P%3D%5Cfrac%7BnRT%7D%7B%28V-nb%29%7D-%5Cfrac%7Bn%5E%7B2%7Da%7D%7Bv%5E%7B2%7D%7D)
Then you should know all the units of each term of the equation, that is:
![P=atm](https://tex.z-dn.net/?f=P%3Datm)
![n=mol](https://tex.z-dn.net/?f=n%3Dmol)
![R=\frac{L.atm}{mol.K}](https://tex.z-dn.net/?f=R%3D%5Cfrac%7BL.atm%7D%7Bmol.K%7D)
![a=atm\frac{L^{2}}{mol^{2}}](https://tex.z-dn.net/?f=a%3Datm%5Cfrac%7BL%5E%7B2%7D%7D%7Bmol%5E%7B2%7D%7D)
![b=\frac{L}{mol}](https://tex.z-dn.net/?f=b%3D%5Cfrac%7BL%7D%7Bmol%7D)
![T=K](https://tex.z-dn.net/?f=T%3DK)
![V=L](https://tex.z-dn.net/?f=V%3DL)
where atm=atmosphere, L=litters, K=kelvin
Now, you should replace the units in the equation for each value:
![P=\frac{(mol)(\frac{L.atm}{mol.K})(K)}{L-(mol)(\frac{L}{mol})}-\frac{(mol^{2})(\frac{atm.L^{2}}{mol^{2}})}{L^{2}}](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B%28mol%29%28%5Cfrac%7BL.atm%7D%7Bmol.K%7D%29%28K%29%7D%7BL-%28mol%29%28%5Cfrac%7BL%7D%7Bmol%7D%29%7D-%5Cfrac%7B%28mol%5E%7B2%7D%29%28%5Cfrac%7Batm.L%5E%7B2%7D%7D%7Bmol%5E%7B2%7D%7D%29%7D%7BL%5E%7B2%7D%7D)
Then you should multiply and eliminate the same units which they are dividing each other (Please see the photo below), so you have:
![P=\frac{L.atm}{L-L}-atm](https://tex.z-dn.net/?f=P%3D%5Cfrac%7BL.atm%7D%7BL-L%7D-atm)
Then operate the fraction subtraction:
P=![P=\frac{L.atm-L.atm}{L}](https://tex.z-dn.net/?f=P%3D%5Cfrac%7BL.atm-L.atm%7D%7BL%7D)
![P=\frac{L.atm}{L}](https://tex.z-dn.net/?f=P%3D%5Cfrac%7BL.atm%7D%7BL%7D)
And finally you can find the answer:
P=atm
Now solving for b:
![(P+\frac{n^{2}a}{V^{2}})(V-nb)=nRT](https://tex.z-dn.net/?f=%28P%2B%5Cfrac%7Bn%5E%7B2%7Da%7D%7BV%5E%7B2%7D%7D%29%28V-nb%29%3DnRT)
![(V-nb)=\frac{nRT}{(P+\frac{n^{2}a}{V^{2}})}](https://tex.z-dn.net/?f=%28V-nb%29%3D%5Cfrac%7BnRT%7D%7B%28P%2B%5Cfrac%7Bn%5E%7B2%7Da%7D%7BV%5E%7B2%7D%7D%29%7D)
![nb=V-\frac{nRT}{(P+\frac{n^{2}a}{V^{2}})}](https://tex.z-dn.net/?f=nb%3DV-%5Cfrac%7BnRT%7D%7B%28P%2B%5Cfrac%7Bn%5E%7B2%7Da%7D%7BV%5E%7B2%7D%7D%29%7D)
![b=\frac{V-\frac{nRT}{(P+\frac{n^{2}a}{V^{2}})}}{n}](https://tex.z-dn.net/?f=b%3D%5Cfrac%7BV-%5Cfrac%7BnRT%7D%7B%28P%2B%5Cfrac%7Bn%5E%7B2%7Da%7D%7BV%5E%7B2%7D%7D%29%7D%7D%7Bn%7D)
Replacing units:
![b=\frac{L-\frac{(mol).(\frac{L.atm}{mol.K}).K}{(atm+\frac{mol^{2}.\frac{atm.L^{2}}{mol^{2}}}{L^{2}})}}{mol}](https://tex.z-dn.net/?f=b%3D%5Cfrac%7BL-%5Cfrac%7B%28mol%29.%28%5Cfrac%7BL.atm%7D%7Bmol.K%7D%29.K%7D%7B%28atm%2B%5Cfrac%7Bmol%5E%7B2%7D.%5Cfrac%7Batm.L%5E%7B2%7D%7D%7Bmol%5E%7B2%7D%7D%7D%7BL%5E%7B2%7D%7D%29%7D%7D%7Bmol%7D)
Multiplying and dividing units,(please see the second photo below), we have:
![b=\frac{L-\frac{L.atm}{atm}}{mol}](https://tex.z-dn.net/?f=b%3D%5Cfrac%7BL-%5Cfrac%7BL.atm%7D%7Batm%7D%7D%7Bmol%7D)
![b=\frac{L-L}{mol}](https://tex.z-dn.net/?f=b%3D%5Cfrac%7BL-L%7D%7Bmol%7D)
![b=\frac{L}{mol}](https://tex.z-dn.net/?f=b%3D%5Cfrac%7BL%7D%7Bmol%7D)