\(\mathrm{Mn}^{2+}(\) aq \()\) can be determined by titration with \(\mathrm{MnO}_{4}^{-}(\) aq \()\) $$ 3 \mathrm{Mn}^{2+}+2 \mathrm{MnO}_{4}^{-} \longrightarrow 6 \mathrm{MnO}_{2}+2 \mathrm{H}_{2} \mathrm{O} $$ A \(25.00 \mathrm{~mL}\) sample of \(\mathrm{Mn}^{2+}\) (aq) requires \(34.77 \mathrm{~mL}\) of \(0.05876 M\) \(\mathrm{KMnO}_{4}\) (aq) for its titration. What is the molarity of the \(\mathrm{Mn}^{2+}\) (aq)?

Molarity, often represented by the symbol 'M', is a measure of concentration for a chemical solution. It is defined as the number of moles of solute (the substance being dissolved) per liter of solution. Understanding molarity is crucial in chemistry, as it allows chemists to quantify the concentration of substances in a solution and is particularly important in titration problems.

To calculate molarity, one can use the simple formula: \[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]

In the given exercise, the molarity of a \(\mathrm{KMnO}_4\) solution is used to determine how much of the \(\mathrm{Mn}^{2+}\) solute is present in a sample. To find the number of moles of \(\mathrm{KMnO}_4\), we multiply its molarity by the volume of the solution that was used in the titration (converted to liters). Then, using the balanced stoichiometry from the chemical equation, we can calculate the moles, and ultimately the molarity, of the \(\mathrm{Mn}^{2+}\) in the original sample.

Stoichiometry is the section of chemistry that deals with the relative quantities of reactants and products in chemical reactions. It is based on the conservation of mass and the concept of moles, allowing chemists to predict the amounts of substances consumed and created in a reaction.

When using stoichiometry to solve a problem, the following steps are often involved:

• Write a balanced chemical equation.
• Convert all given information into moles (if they aren’t already).
• Use the mole ratio from the balanced equation to calculate the number of moles of the desired substance.
• Convert moles back to the desired units, such as grams or liters, if necessary.

In the context of the given titration problem, stoichiometry allows us to use the mole ratio from the balanced equation to find the relationship between moles of the titrant (\(\mathrm{KMnO}_{4}\)) and the analyte (\(\mathrm{Mn}^{2+}\)). This is pivotal to then calculating the molarity of the analyte solution.

Redox reactions are chemical reactions involving the transfer of electrons from one reactant to another, leading to changes in the oxidation states of the involved species. These reactions are characterized by the gain of electrons (reduction) by one substance and the loss of electrons (oxidation) by another. Redox can be identified by changes in the oxidation numbers of atoms in a chemical reaction.

To analyze a redox reaction:

• Assign oxidation states to all atoms before and after the reaction.
• Identify which atoms are oxidized (increase in oxidation state) and which are reduced (decrease in oxidation state).
• Ensure that the number of electrons lost equals the number of electrons gained, which may involve balancing the chemical equation with respect to both mass and charge.

In our exercise, the titration of \(\mathrm{Mn}^{2+}\) with \(\mathrm{KMnO}_{4}\) is a redox reaction where \(\mathrm{Mn}^{2+}\) is oxidized to \(\mathrm{MnO}_{2}\) and \(\mathrm{MnO}_{4}^{-}\) is reduced, as indicated by the balanced chemical equation provided. This concept is integral to understanding the mole-to-mole relationships established in the balanced equation, which are in turn used to calculate molarities in the titration problem.