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 moles of TiO2 are needed to form one mole of titanium?

Verified step by step guidance

1. Identify the overall goal: We need to determine how many moles of TiO2 are required to produce one mole of Ti.
2. Examine the first reaction: TiO2(S) + 2 Cl2(G) + 2 C(s) → TiCl4(s) + 2 CO(g). This reaction shows that one mole of TiO2 produces one mole of TiCl4.
3. Examine the second reaction: TiCl4(s) + 2 Mg(s) → Ti(s) + 2 MgCl2(s). This reaction shows that one mole of TiCl4 produces one mole of Ti.
4. Combine the reactions: Since one mole of TiO2 produces one mole of TiCl4, and one mole of TiCl4 produces one mole of Ti, it follows that one mole of TiO2 is needed to produce one mole of Ti.
5. Conclude that the stoichiometry of the reactions indicates that one mole of TiO2 is required to form one mole of titanium.

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 us to calculate the amounts of substances involved based on balanced chemical equations. Understanding stoichiometry is essential for determining how many moles of a reactant are needed to produce a desired amount of product.

Mole Concept

The mole concept is a fundamental principle in chemistry that defines the amount of substance. One mole is equivalent to 6.022 x 10^23 entities, such as atoms or molecules. This concept is crucial for converting between grams and moles, enabling chemists to quantify reactants and products in chemical reactions.

Balanced Chemical Equations

A balanced chemical equation represents a chemical reaction with equal numbers of each type of atom on both sides of the equation. Balancing ensures the law of conservation of mass is upheld. In the context of the given reactions, balancing is necessary to determine the mole ratios between TiO2 and titanium, which is key to solving the problem.