Does a gas of neutrons obey the ideal gas equation much better than hydrogen gas Consider a gas of neutrons. Does it obey the ideal gas equation much better than hydrogen gas at the same temperature and pressure? 
 A: It will not be easy to establish a pure neutron gas in thermal equilibrium to test the ideal gas law.
(1) Free neutrons have a life time of only 14.7 minutes. They decay (predominantly) into a proton, an electron, and an electron antineutrino. So you will always have positive protons and electrons and thus hydrogen around.
(2) It is not easy to contain neutrons in a vessel because due to the missing electric charge they will easily escape through any walls.
The neutron-neutron scattering cross section is probably very low.
Added later: 
The above does not yet answer the question, as @JohnRennie has rightly pointed out. To come closer to an answer, I add the following reasoning based on the van der Waals equation which has two constants $a$ and $b$ which describe the deviation from the ideal gas law.
The answer depends on the question how the "molecular volume" and the "intermolecular force" of thermal neutrons compares to those of molecular hydrogen. These two effects are represented by the constants $a$ and $b$ in the van der Waals equation $$(p+a/V_m^2)(V_m-b)=R T$$ and they describe the deviation from the ideal gas law. Here $p$ is the pressure, $V_m$ the molar volume, $R$ the ideal gas constant, $T$ the absolute temperature. The constant $a$ is a measure of the inter-molecular force, the constant $b$ the actual volume of a mole of the gas molecules.
I would consider it a very rough estimate to assume that the constant $b$ describing the molecular volume of the neutrons should be much smaller (many orders of magnitude) than the corresponding molecular volume of hydrogen.  Also, the forces between hydrogen molecules expressed by the constant $b$  are probably stronger than between neutrons. But the latter is only a wild guess. Thus a neutron gas is probably closer to an ideal gas than the hydrogen gas. 
