Manganese is a key component of extremely hard steel. The...

Manganese is a key component of extremely hard steel. The element occurs naturally in many oxides. A 542.3 -g sample of a manganese oxide has an Mn/O ratio of 1.00$/ 1.42$ and con- sists of braunite $\left(\mathrm{Mn}_{2} \mathrm{O}_{3}\right)$ and manganosite $(\mathrm{MnO}) .(\mathrm{a})$ How many grams of braunite and of manganosite are in the ore? (b) What is the $\mathrm{Mn}^{3+} / \mathrm{Mn}^{2+}$ ratio in the ore?

Manganese is a key component of extremely hard steel. The element occurs naturally in many oxides. A 542.3 -g sample of a manganese oxide has an Mn/O ratio of 1.00$/ 1.42$ and con-
sists of braunite $\left(\mathrm{Mn}_{2} \mathrm{O}_{3}\right)$ and manganosite $(\mathrm{MnO}) .(\mathrm{a})$ How many grams of braunite and of manganosite are in the ore? (b) What is
the $\mathrm{Mn}^{3+} / \mathrm{Mn}^{2+}$ ratio in the ore?

Key Concepts

Oxidation States

Oxidation state refers to the apparent charge on an atom within a compound that results from the loss or gain of electrons. It is a key concept when dealing with transition metal compounds, as different oxidation states can lead to compounds with different properties. In mixed oxide systems, determining the relative amounts of different oxidation states of a metal (for example, Mn2+ versus Mn3+) is important for understanding the chemical behavior of the overall mixture.

Mole Ratios and Chemical Formulas

Mole ratios are derived from the empirical or molecular formulas of compounds and are used to relate the number of atoms of one element to another within a molecule. Understanding these ratios is crucial when dealing with mixtures of compounds, as it allows for the translation of given atomic ratios (such as the ratio of manganese to oxygen) into relationships between different species in the mixture.

Mass Balance in Mixture Problems

Mass balance is a method that relies on the conservation of mass to analyze mixtures composed of multiple substances. It involves accounting for the amount of each component in a mixture based on their individual contributions to the total mass. In problems where the overall composition and the mass ratios of elements are given, mass balance equations allow one to determine the mass of each component present.

Stoichiometry

Stoichiometry involves the quantitative relationship between reactants and products in chemical reactions. It uses balanced chemical equations and the molar masses of compounds to convert between mass, moles, and number of atoms or molecules. This concept is essential in determining how much of each compound is present in a mixture when their chemical formulae and overall composition are known.

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