1. The problem is to balance the chemical equation: $$\mathrm{N_2 + O_2 \rightarrow NO}$$ by finding the correct coefficient for $$\mathrm{NO}$$. 2. The rule for balancing chemical equations is that the number of atoms of each element must be the same on both sides of the equation. 3. Write the unbalanced equation with coefficients: $$\mathrm{N_2 + O_2 \rightarrow x \ NO}$$ where $$x$$ is the coefficient to find. 4. Balance nitrogen atoms: On the left, there are 2 nitrogen atoms in $$\mathrm{N_2}$$. On the right, each $$\mathrm{NO}$$ molecule has 1 nitrogen atom, so $$x$$ molecules have $$x$$ nitrogen atoms. Set $$2 = x$$, so $$x = 2$$. 5. Balance oxygen atoms: On the left, there are 2 oxygen atoms in $$\mathrm{O_2}$$. On the right, each $$\mathrm{NO}$$ molecule has 1 oxygen atom, so $$x = 2$$ molecules have 2 oxygen atoms. Both sides have 2 oxygen atoms, so oxygen is balanced. 6. The balanced equation is: $$\mathrm{N_2 + O_2 \rightarrow 2 \ NO}$$. 7. Among the options 4, 3, 2, 1, the coefficient to balance the equation is 2.