Titanium metal is obtained from the mineral rutile, TiO2. The process requires multiple steps, as shown in the following reactions:TiO2(S) + 2 Cl2(G) + 2 C(s) → TiCl4(s) + 2 CO(g)TiCl4(s) + 2 Mg(s) → Ti(s) + 2 MgCl2(s)How many kilograms of rutile are needed to produce 95 kg of Ti?

Verified step by step guidance

1. Identify the molar masses of the compounds involved: TiO2, Ti, Cl2, C, TiCl4, Mg, and MgCl2.
2. Calculate the moles of Ti produced using its molar mass and the given mass of Ti (95 kg).
3. Use the stoichiometry of the second reaction to determine the moles of TiCl4 needed to produce the calculated moles of Ti.
4. Use the stoichiometry of the first reaction to determine the moles of TiO2 needed to produce the calculated moles of TiCl4.
5. Convert the moles of TiO2 to kilograms using its molar mass to find the mass of rutile needed.

Key Concepts

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced equations. It allows us to determine the relationships between the quantities of substances involved in a reaction, which is essential for converting between grams of reactants and products. Understanding stoichiometry is crucial for solving problems that involve mass relationships in chemical processes.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is used to convert between the mass of a substance and the number of moles, which is necessary for stoichiometric calculations. Knowing the molar masses of TiO2 and Ti is vital for determining how much rutile is needed to produce a specific mass of titanium.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products through breaking and forming chemical bonds. In this case, the reactions show how titanium is extracted from rutile through chlorination and reduction. Understanding the steps and the stoichiometry of these reactions is essential for calculating the amount of rutile required to yield a desired amount of titanium.