On heating a 0.200 g sample of a certain semimetal M in air, the corresponding oxide M2O3 was obtained. When the oxide was dissolved in aqueous acid and titrated with KMnO4, 10.7 mL of 0.100 M MnO4- was required for complete reac-tion. The unbalanced equation is (a) Balance the equation.

Verified step by step guidance

1. Identify the oxidation states of the elements involved in the reaction. M in M2O3 is in the +3 oxidation state, and Mn in MnO4^- is in the +7 oxidation state.
2. Determine the changes in oxidation states. M is oxidized from 0 to +3, and Mn is reduced from +7 to +2.
3. Write the half-reactions for the oxidation and reduction processes. For oxidation: M -> M^{3+} + 3e^-. For reduction: MnO4^- + 8H^+ + 5e^- -> Mn^{2+} + 4H2O.
4. Balance the electrons transferred in the half-reactions. Multiply the oxidation half-reaction by 5 and the reduction half-reaction by 3 to equalize the number of electrons.
5. Combine the balanced half-reactions to form the balanced overall equation, ensuring that all atoms and charges are balanced.

Key Concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It allows chemists to predict the amounts of substances consumed and produced in a reaction based on balanced chemical equations. Understanding stoichiometry is essential for solving problems involving mass, moles, and concentrations, particularly in titration scenarios.

Balancing Chemical Equations

Balancing chemical equations is the process of ensuring that the number of atoms for each element is the same on both sides of the equation. This is crucial because it reflects the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. A balanced equation provides the correct stoichiometric ratios needed for calculations involving reactants and products.

Titration

Titration is a laboratory technique used to determine the concentration of a solute in a solution by reacting it with a solution of known concentration. In this case, KMnO4 acts as a titrant, and the volume used in the reaction helps calculate the amount of the oxide that reacted. Understanding titration is important for interpreting results and performing stoichiometric calculations based on the balanced equation.