I balanced the equation and showed you the long way of doing it before. Here it is again.
The short way (but I think harder to understand) follows:
N2 + 3H2 ==> 2NH3
2 moles N2*(3moles H2/1 mole N2) = 6 moles H2. Do you have 6 moles H2. No, therefore, N2 (not H2) must be the limiting reagent. You can check it this way.
5 moles H2 x (1 mole N2/3 moles H2) = 1.667 moles N2. Do you have that much N2? Yes, therefore, N2 (not H2) is the limiting reagent.
Why do I like the other way.
1. I think it's easier to understand.
2. You don't really do any fewer calculations. You MUST do one, then I always feel I must do the second one to check myself so I end up doing two no matter which way I go; it really isn't any shorter for me.
Now you have both ways. Take you pick.
5 moles N2
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