The vanadium in a sample of ore is converted to \(\mathrm{VO}^{2+}\). The VO \(^{2+}\) ion is subsequently titrated with \(\mathrm{MnO}_{4}^{-}\) in acidic solution to form \(\mathrm{V}(\mathrm{OH})_{4}{ }^{+}\) and manganese(II) ion. The unbalanced titration reaction is \(\mathrm{MnO}_{4}^{-}(a q)+\mathrm{VO}^{2+}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow\) $$ \mathrm{V}(\mathrm{OH})_{4}^{+}(a q)+\mathrm{Mn}^{2+}(a q)+\mathrm{H}^{+}(a q) $$ To titrate the solution, \(26.45 \mathrm{~mL}\) of \(0.02250 \mathrm{M} \mathrm{MnO}_{4}^{-}\) was required. If the mass percent of vanadium in the ore was \(58.1 \%\), what was the mass of the ore sample? Hint: Balance the titration reaction by the oxidation states method.

When working with minerals and mining resources, it's vital to accurately determine the content and purity of the ore, like those rich in vanadium. In particular, vanadium ore analysis is essential for industries that manufacture steel, as vanadium is often used to improve the strength and toughness of the metal. A common analysis method is redox titration, which is a type of titration used to determine the concentration of an unknown sample through a redox reaction. In this type of analysis, a solution containing a known concentration and volume of titrant reacts with a substance in the sample leading to a change in oxidation state, which signifies the point at which equivalent quantities have reacted.

The exercise provided involved converting the vanadium in the ore sample to VO2+ ions. These ions were then titrated with MnO4- in an acidic solution, changing the oxidation state of the vanadium. The end result was the determination of the vanadium content in the sample based on the volume of titrant used. Accurate vanadium ore analysis via titration reveals vital economic information and ensures that subsequent usage of the ore meets the required specifications and standards for industrial processes.

In redox chemistry, understanding the oxidation states method is crucial for balancing redox reactions. This technique revolves around the concept of oxidation states which signify the hypothetical charges that an atom would have if all its bonds were ionic. In a redox reaction, the total increase and decrease in oxidation state must balance out because the number of electrons lost must equal the number of electrons gained.

By comparing oxidation states before and after the reaction, you can determine which elements have been oxidized (increase in oxidation state) and which have been reduced (decrease in oxidation state). In the given exercise, determining the change in oxidation states for manganese and vanadium helped in identifying how many electrons were transferred in the reaction. This information is critical for balancing the equation, as it ensures mass and charge are conserved. The application of the oxidation states method in balancing equations is a fundamental skill for students as it aids in understanding the underlying chemical processes and provides the basis for calculations in stoichiometry.

The core of chemical calculations is stoichiometry, a segment of chemistry that involves using relationships between reactants and/or products in a chemical reaction to determine desired quantitative data. In the context of the exercise, stoichiometry is used to calculate the amount of ore based on the redox titration results. Students should be familiar with concepts such as the mole ratio, which comes from the balanced chemical reaction and guides the calculation of how much vanadium is present.

Knowing the mole ratio allows you to understand the proportions in which reactants combine and products form. In this case, the mole ratio between MnO4- and VO2+ told us that one mole of MnO4- titrant reacts with five moles of VO2+ vanadium compound. With the stoichiometry of the balanced reaction, the volume and concentration of the MnO4- solution are used to calculate the moles of vanadium present, and subsequently, the mass of the vanadium and the ore. The step-by-step approach provided illustrates the methodical nature of stoichiometric calculations, ensuring a solid grasp of the procedure for determining quantities involved in chemical reactions.