How many millilitres of \(0.1 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) must be added to \(50 \mathrm{~mL}\) of \(0.1 \mathrm{M} \mathrm{NaOH}\) to give a solution that has a concentration of \(0.05 \mathrm{M}\) in \(\mathrm{H}_{2} \mathrm{SO}_{4}\) ? (a) \(400 \mathrm{~mL}\) (b) \(200 \mathrm{~mL}\) (c) \(100 \mathrm{~mL}\) (d) None of these

Chemical stoichiometry involves the calculation of the quantities of reactants and products in chemical reactions. It's based on the law of conservation of mass and the stoichiometric coefficients derived from balanced chemical equations. When solving acid-base titration problems, stoichiometry allows us to determine the exact amounts of acid and base that will react to reach neutralization.

For instance, in the given problem, sulphuric acid (\r\(H_2SO_4\)) and sodium hydroxide (\r\(NaOH\)) react in a stoichiometric ratio, which is determined by the balanced chemical equation for the neutralization reaction. This ratio is crucial because it tells us how many moles of acid are needed to neutralize a given number of moles of base.

In our example, the neutralization reaction between \r\(H_2SO_4\) and \r\(NaOH\) occurs in a 1:2 molar ratio because sulphuric acid is diprotic, meaning each molecule can donate two protons. With this knowledge, we can calculate the moles of acid needed to neutralize the moles of base initially present in the solution.

Molarity is a measure of the concentration of a solution, expressed as the number of moles of solute per liter of solution. It plays a fundamental role in quantifying the strength of an acid or base in solution; it's symbolized by the unit M (moles per liter). To calculate molarity, we use the formula: \r\[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \].

In acid-base titration problems, molarity can be used to determine the volume of one solution required to react completely with a given volume of another solution at known concentrations. By rearranging the molarity formula to solve for volume or moles, as necessary, we can find out how much acid must be added to a known volume of base to reach the desired concentration.

This calculation was demonstrated in the solution to our titration problem. The molarity of the sodium hydroxide solution and the target molarity of the sulphuric acid solution were key data points used to determine the volume of sulphuric acid needed for neutralization.

A neutralization reaction is a chemical reaction in which an acid and a base react to form water and a salt. This reaction typically involves the transfer of protons from the acid to the base and is pivotal in titration exercises. Understanding neutralization can help students predict the outcome of mixing specific volumes and molarities of acid and base solutions.

In the context of our example, neutralization occurs when the sulphuric acid (\r\(H_2SO_4\)) reacts with sodium hydroxide (\r\(NaOH\)) to form water (\r\(H_2O\)) and sodium sulphate (\r\(Na_2SO_4\)). The balanced equation guides us in determining the stoichiometric amounts needed for complete neutralization.

Moreover, as the neutralization reaches its endpoint, it allows us to link the stoichiometry of the reactants to the molarity calculation, eventually finding the volume of acid required to achieve a new molarity post-reaction. A clear understanding of the neutralization reaction, combined with the molarity of the solutions, enabled the calculation of the precise volume of \r\(H_2SO_4\) necessary to arrive at the specified final concentration.