In school, I've learned that we can only get an ortho hydrogen content upto 75%. Why is that we can obtain a pure sample of para hydrogen, but not ortho hydrogen? What prevents us from isolating ortho hydrogen?
Ortho and para hydrogen differ in the alignment of their nuclear spins. The two hydrogen atoms each have a nuclear spin of 1/2 which results in a total nuclear spin of 0 or 1. The states with zero spin are called para and those with 1 ortho. The combination of the nuclear spins also results in the formation of a new spin wave function. There are 3 possibilities to get a nuclear spin of one with an even wave function and there is one possibilitie to get a spin of zero with an odd wave function. The overall wave function of the hydrogen molecule is given by the product of the electronic, vibrational, rotational and spin wave functions and should we antisymmetric with respect to exchange of the fermionic hydrogen nuclei. Because the electronic ground state of molecular hydrogen is even and the vibrational wave function of a diatomic molecule is always even, the wave function of para hydrogen has to be combined with the even rotational states and ortho with the odd rotational states. The absolute ground state of molecular hydrogen is thus the rotational state with zero rotation and is therefore para. The next state, with one quantum of rotation, is ortho.
You can only convert ortho and para hydrogen into each other using collisions or chemical reactions. To make pure para hydrogen, people use a catalyst at very low temperature. Because of the low temperature, all produced hydrogen will eventually end up in the absolute ground state, that is, para hydrogen. You cannot make ortho hydrogen this way because it does not represent the absolute ground state of the system. The 75% comes from the degeneracy of the Boltzmann factor: at low temperature (with no reaction catalyst) there are three times more ortho molecules with a spin of 1 than para molecules of zero spin.
Although you cannot make pure ortho hydrogen, you can study it by using narrow lasers that only excite odd rotational states.