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 X (b) How many moles of oxide were formed, and how many moles of semimetal were in the initial 0.200 g sample?

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Identify the balanced chemical equation for the reaction between the semimetal oxide \( M_2O_3 \) and \( \text{MnO}_4^- \).

Calculate the moles of \( \text{MnO}_4^- \) used in the titration using the formula: \( \text{moles} = \text{volume (L)} \times \text{molarity (mol/L)} \).

Use the stoichiometry of the balanced equation to determine the moles of \( M_2O_3 \) that reacted with the \( \text{MnO}_4^- \).

Since the oxide \( M_2O_3 \) is formed from the semimetal \( M \), use the stoichiometry of the formation reaction to find the moles of \( M \) in the initial sample.

Verify the calculations by checking the stoichiometric ratios and ensuring the mass balance is consistent with the initial sample mass.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It allows us to calculate the amounts of substances consumed and produced in a reaction based on balanced chemical equations. Understanding stoichiometry is essential for determining the moles of semimetal and oxide formed in this scenario.

Molarity and Titration

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. In titration, a solution of known concentration (titrant) is used to determine the concentration of an unknown solution. The volume of KMnO4 used in the titration provides the necessary data to calculate the moles of oxide present, which is crucial for solving the problem.

Molecular Weight and Moles

The molecular weight of a substance is the mass of one mole of that substance, expressed in grams per mole. To find the number of moles of a substance, you can divide the mass of the sample by its molecular weight. In this question, calculating the moles of the semimetal and the oxide requires knowledge of their respective molecular weights, which are derived from their chemical formulas.