Chemistry - Could a magnet pull oxygen out of the air?
Solution 1:
I'm a physicist, so apologies if the answer below is in a foreign language; but this was too interesting of a problem to pass up. I'm going to focus on a particular question: If we have oxygen and nothing else in a box, how strong does the magnetic field need to be to concentrate the gas in a region? The TL;DR is that thermal effects are going to make this idea basically impossible.
The force on a magnetic dipole $\vec{m}$ is $\vec{F} = \vec{\nabla}(\vec{m} \cdot \vec{B})$, where $\vec{B}$ is the magnetic field. Let us assume that the dipole moment of the oxygen molecule is proportional to the magnetic field at that point: $\vec{m} = \alpha \vec{B}$, where $\alpha$ is what we might call the "molecular magnetic susceptibility." Then we have $\vec{F} = \vec{\nabla}(\alpha \vec{B} \cdot \vec{B})$. But potential energy is given by $\vec{F} = - \vec{\nabla} U$; which implies that an oxygen molecule moving in a magnetic field acts as though it has a potential energy $U(\vec{r}) = - \alpha B^2$.
Now, if we're talking about a sample of gas at a temperature $T$, then the density of the oxygen molecules in equilibrium will be proportional to the Boltzmann factor: $$ \rho(\vec{r}) \propto \mathrm e^{-U(\vec{r})/kT} = \mathrm e^{-\alpha B^2/kT} $$ In the limit where $kT \gg \alpha B^2$, this exponent will be close to zero, and the density will not vary significantly from point to point in the sample. To get a significant difference in the density of oxygen from point to point, we have to have $\alpha B^2 \gtrsim kT$; in other words, the magnetic potential energy must comparable to (or greater than) the thermal energy of the molecules, or otherwise random thermal motions will cause the oxygen to diffuse out of the region of higher magnetic field.
So how high does this have to be? The $\alpha$ we have defined above is approximately related to the molar magnetic susceptibility by $\chi_\text{mol} \approx \mu_0 N_\mathrm A \alpha$; and so we have1 $$ \chi_\text{mol} B^2 \gtrsim \mu_0 RT $$ and so we must have $$ B \gtrsim \sqrt{\frac{\mu_0 R T}{\chi_\text{mol}}}. $$ If you believe Wikipedia, the molar susceptibility of oxygen gas is $4.3 \times 10^{-8}\ \text{m}^3/\text{mol}$; and plugging in the numbers, we get a requirement for a magnetic field of $$ B \gtrsim \pu{258 T}. $$ This is over five times stronger than the strongest continuous magnetic fields ever produced, and 25–100 times stronger than most MRI machines. Even at $\pu{91 Kelvin}$ (just above the boiling point of oxygen), you would need a magnetic field of almost $\pu{150 T}$; still well out of range.
1 I'm making an assumption here that the gas is sufficiently diffuse that we can ignore the magnetic interactions between the molecules. A better approximation could be found by using a magnetic analog of the Clausius-Mossotti relation; and if the gas gets sufficiently dense, then all bets are off.
Solution 2:
Physics says yes. And at the US Patent Office, it certainly looks like the answer is yes, according to (at least) this US patent application. The abstract reads:
A process for separating O$_2$ from air, that includes the steps effecting an increase in pressure of an air stream, magnetically concentrating O$_2$ in one portion of the pressurized air stream, the one portion then being an oxygen rich stream, and there being another portion of the air stream being an oxygen lean stream, compressing the oxygen rich stream and removing water and carbon dioxide therefrom, to provide a resultant stream, and cryogenically separating said resultant stream into a concentrated oxygen stream and a waste stream.
I would say the yes is conditional in that you'd probably need a room that is sealed from communication with the atmosphere (otherwise equilibrium will be re-established with respect to oxygen pretty quickly), is vented to the outside in order to dispose of the oxygen, houses one heck of a strong magnet, and has a strongly-locked door to prevent the unfortunate organisms from leaving.
Solution 3:
No, to separate oxygen from air you need extremely high gradients of field strength. in this paper http://link.springer.com/article/10.1007%2Fs11630-007-0079-1#page-1 they used about $\pu{0.4T}$ per $\pu{mm}$, but to cause breathing problems it is enough to get the $\ce{O2}$ concentration below 17%, so lets say $\pu{0.1T/mm}$ is needed. To sustain such gradients over a whole room (lets say 4 meters), the field strength on one side of the room needs to be around $\pu{400T}$, which is very likely to kill humans (dissolved ions begin to circle due to lorentz force instead of going where they should, moving around induces huge currents…), and has never been achieved in a continuous field. (from nationalmaglab.com: …45-Tesla hybrid magnet, which offers scientists the strongest continuous magnetic field in the world…)