The balanced chemical reaction for the synthesis of ammonia (NH₃) from nitrogen gas (N₂) and hydrogen gas (H₂) is:
\[ N_2(g) + 3H_2(g) \rightarrow 2NH_3(g) \]
From the equation, we see that 1 mole of nitrogen gas reacts with 3 moles of hydrogen gas to produce 2 moles of ammonia.
Therefore, when 1 mole of nitrogen gas reacts with 3 moles of hydrogen gas, 2 moles of ammonia (NH₃) are produced.
Thus, the correct answer is 2 moles.