1. State the problem: Balance the chemical equation for the reaction between sulfuric acid and sodium hydroxide. 2. Write the unbalanced skeleton equation: $$H_2SO_4 + NaOH \rightarrow Na_2SO_4 + H_2O$$ 3. Assign coefficients $a$, $b$, $c$, $d$ to each species and write atom-balance equations. $$a H_2SO_4 + b NaOH \rightarrow c Na_2SO_4 + d H_2O$$ H: $2a + b = 2d$ Na: $b = 2c$ S: $a = c$ O: $4a + b = 4c + d$ 4. Solve the system by choosing $a=1$ to obtain smallest whole-number coefficients. From $a=1$ we get $c=1$ from $a=c$. Then $b=2c=2$ from $b=2c$. Then substitute into $2a + b = 2d$ to get $2(1)+2=2d$, so $4=2d$ and $d=2$. 5. Write the balanced equation with these coefficients. $$H_2SO_4 + 2 NaOH \rightarrow Na_2SO_4 + 2 H_2O$$ 6. Final answer: The balanced chemical equation is given above.