Oxalic acid \(\left(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\right)\) is present in many plants and vegetables. If \(24.0 \mathrm{~mL}\) of \(0.0100 \mathrm{M} \mathrm{KMnO}_{4}\) solution is needed to titrate \(1.00 \mathrm{~g}\) of a sample of \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) to the equivalence point, what is the percent by mass of \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) in the sample? The net ionic equation is \(2 \mathrm{MnO}_{4}^{-}+16 \mathrm{H}^{+}+5 \mathrm{C}_{2} \mathrm{O}_{4}^{2-} \longrightarrow\) \(2 \mathrm{Mn}^{2+}+10 \mathrm{CO}_{2}+8 \mathrm{H}_{2} \mathrm{O}\)

Understanding molarity and its relationship with moles is a fundamental aspect of chemistry, especially in titration calculations. Molarity, denoted by M, is the measure of concentration of a solution in terms of the number of moles of solute per liter of solution.

To calculate the number of moles from a given molarity and volume, you can use the formula:
\( \text{moles of solute} = \text{Molarity (M)} \times \text{Volume (L)} \).
In the context of a titration, knowing the molarity of the titrant (a standard solution of known concentration) allows you to determine the moles of solute present in the sample being analyzed by using the above expression.

For instance, if a titration problem provides you with the volume of the titrant used to reach the endpoint and its molarity, you can easily calculate the number of moles of titrant that reacted. This step is crucial because it sets the groundwork for subsequent calculations and conceptual understanding of the stoichiometric relationships in the chemical reaction involved in the titration.

A net ionic equation represents a chemical reaction that eliminates the spectator ions from the complete ionic equation to focus on the actual chemical change occurring in reaction. Spectator ions are ions that do not take part in the chemical reaction and remain unchanged.

The net ionic equation is essential for understanding the chemistry behind titrations as it reveals the stoichiometry of the reaction - the ratios in which different molecules react. It breaks down the reaction into the most simplified terms, showing only those components that directly participate in the chemical process.

When looking at a net ionic equation, it's important to balance the equation by ensuring the same number of each type of atom on both sides. Moreover, the charge should also be balanced. Being able to interpret and write net ionic equations allows students to comprehend and calculate the moles of substances in a titration accurately, which is a vital step in finding the concentration of an unknown solution. For example, in the exercise provided, the net ionic equation shows the substance being titrated, oxalic acid, and its mole ratio to the titrant, which is fundamental in determining the amount of substance present in the sample.

Percent by mass (or weight percent) is a way of expressing the concentration of a component in a mixture or a solution. It is the mass of the solute divided by the total mass of the solution, multiplied by 100%.

The formula is as follows:
\( \text{Percent by mass} = \frac{\text{Mass of solute}}{\text{Mass of solution}} \times 100\% \).
In a titration problem, for instance, once the mass of the solute is determined from the moles of solute and its molecular weight, the percent by mass can be calculated if the mass of the entire sample is known.

This concept is particularly crucial in industries such as pharmaceuticals and food processing, where the composition of the substances needs to be precise. When solving chemistry problems, the percent by mass calculation offers a direct understanding of the purity or the concentration of a particular component in the sample. The final value is an easy-to-understand representation of the solution's composition, and it's used to check the consistency and quality of solutions.