I believe I now understand the question - and my earlier comment and the link for a potential duplicate does not apply.
If I'm right, you are actually asking this question:
If you take two containers - one with hydrogen, and one with oxygen -
and you weigh them separately; then allow the gases to mix, will the
mass of the mixture be different?
If the atoms react, the chemical energy releases will result in a corresponding loss of mass for the combined system; see for example this earlier question or the answer to another related question.
If the atoms did not react, there is no change in the chemical energy; but interestingly, there is a change in the entropy of the system. And entropy is closely related to energy. Speculating here - my thermodynamics is very very rusty:
In fact, if you have a perfectly reversible engine, you can do work by changing the amount of entropy: $\Delta U = T\Delta S$. This means that the small change in entropy as you mix your gases will result in a small change in energy, and this should produce a change in mass.
I'm willing to be proven wrong on this last point. As I said - thermodynamics rusty.