1. The problem is to balance the chemical equation: \_N_2 + \_H_2 \rightarrow \_NH_3. 2. Balancing chemical equations means making sure the number of atoms of each element is the same on both sides. 3. Let the coefficients be $a$ for $N_2$, $b$ for $H_2$, and $c$ for $NH_3$. The equation is: $$aN_2 + bH_2 \rightarrow cNH_3$$ 4. Balance nitrogen atoms: $$2a = c$$ 5. Balance hydrogen atoms: $$2b = 3c$$ 6. From step 4, express $c$ as $c = 2a$. 7. Substitute $c$ into step 5: $$2b = 3(2a) = 6a$$ 8. Simplify to find $b$: $$b = 3a$$ 9. Choose the smallest integer $a=1$ to get: $$a=1, b=3, c=2$$ 10. The balanced equation is: $$1N_2 + 3H_2 \rightarrow 2NH_3$$ 11. This corresponds to the first button numbers: 1, 3, 2. Final answer: coefficients are 1, 3, 2.