- Identify reactants as sulfuric acid \(H_2SO_4\) and sodium hydroxide \(NaOH\).
- Apply the law of conservation of mass to balance the neutralization reaction.
- Determine the stoichiometry requires two moles of \(NaOH\) for every mole of \(H_2SO_4\).
- Conclude the balanced equation is \(\boxed{H_2SO_4(aq) + 2NaOH(aq) \rightarrow Na_2SO_4(aq) + 2H_2O(l)}\).
Explanation
- Analysis of the Reaction Components
The reaction involves sulfuric acid (\(H_2SO_4\)) and sodium hydroxide (\(NaOH\)). Sulfuric acid is a strong, diprotic acid, meaning each molecule can donate two protons (\(H^+\)). Sodium hydroxide is a strong base that provides one hydroxide ion (\(OH^-\)) per molecule in an aqueous solution. When these two substances react in a neutralization process, the acid and base react to form water and an ionic salt. Specifically, two hydroxide ions from two molecules of \(NaOH\) are required to neutralize the two protons from one molecule of \(H_2SO_4\).
- Balancing the Chemical Equation
To ensure the equation is balanced, we must have the same number of atoms of each element on both sides.
Reactants side:
- One molecule of sulfuric acid contains 2 hydrogen atoms, 1 sulfur atom, and 4 oxygen atoms.
- Two molecules of sodium hydroxide contain 2 sodium atoms, 2 oxygen atoms, and 2 hydrogen atoms.
Combining these, we have 2 Na, 1 S, 6 O, and 4 H atoms.
Products side:
- One molecule of sodium sulfate (\(Na_2SO_4\)) contains 2 sodium atoms, 1 sulfur atom, and 4 oxygen atoms.
- Two molecules of water (\(2H_2O\)) contain 4 hydrogen atoms and 2 oxygen atoms.
Combining these, we also have 2 Na, 1 S, 6 O, and 4 H atoms.
Since the counts of every element match, the balanced equation is:
\[H_2SO_4(aq) + 2NaOH(aq) \rightarrow Na_2SO_4(aq) + 2H_2O(l)\]
- Conclusion
Comparing our derived balanced equation with the provided options, we find that the equation \(H_2SO_4(aq) + 2NaOH(aq) \rightarrow Na_2SO_4(aq) + 2H_2O(l)\) is correct. This is the third option in the given list. The final answer is \(\boxed{H_2SO_4(aq) + 2NaOH(aq) \rightarrow Na_2SO_4(aq) + 2H_2O(l)}\).
Examples
Neutralization reactions are fundamental in chemistry for determining the concentration of unknown acid or base solutions through a process called titration. For example, if a laboratory technician has a sample of sulfuric acid of unknown strength, they can add sodium hydroxide drop by drop with a color-changing indicator until the neutralization point is reached. By knowing the precise amount of sodium hydroxide added to reach this point, they can calculate the exact concentration of the acid in the original sample, which is a standard procedure in environmental testing and quality control.