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)
a. Write mole ratios to show the relationship between the reactants and products for each reaction.

Verified step by step guidance

1. Step 1: Understand the concept of mole ratios. Mole ratios are derived from the coefficients of a balanced chemical equation and represent the proportional relationship between reactants and products in a chemical reaction.
2. Step 2: For the first reaction, TiO₂(s) + 2 Cl₂(g) + 2 C(s) → TiCl₄(s) + 2 CO(g), identify the coefficients of each substance. These coefficients are: 1 for TiO₂, 2 for Cl₂, 2 for C, 1 for TiCl₄, and 2 for CO.
3. Step 3: Write the mole ratios for the first reaction. For example, the mole ratio between TiO₂ and Cl₂ is 1:2, between TiO₂ and C is 1:2, between TiO₂ and TiCl₄ is 1:1, and between TiO₂ and CO is 1:2. Similarly, you can write mole ratios for other pairs of reactants and products.
4. Step 4: For the second reaction, TiCl₄(s) + 2 Mg(s) → Ti(s) + 2 MgCl₂(s), identify the coefficients of each substance. These coefficients are: 1 for TiCl₄, 2 for Mg, 1 for Ti, and 2 for MgCl₂.
5. Step 5: Write the mole ratios for the second reaction. For example, the mole ratio between TiCl₄ and Mg is 1:2, between TiCl₄ and Ti is 1:1, and between TiCl₄ and MgCl₂ is 1:2. Similarly, you can write mole ratios for other pairs of reactants and products.

Key Concepts

Mole Ratios

Mole ratios are derived from the coefficients of a balanced chemical equation and represent the proportional relationship between the amounts of reactants and products involved in a reaction. They are essential for stoichiometric calculations, allowing chemists to predict how much of each substance is needed or produced in a reaction. For example, in the reaction of TiO2 with Cl2 and C, the mole ratio indicates that one mole of TiO2 reacts with two moles of Cl2 and two moles of C to produce one mole of TiCl4 and two moles of CO.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the substances involved in chemical reactions. It allows for the calculation of reactants and products in a reaction based on the balanced equation. Understanding stoichiometry is crucial for determining how much titanium can be produced from a given amount of rutile, as it provides the necessary framework for converting between moles of reactants and products.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products through the breaking and forming of chemical bonds. Each reaction can be represented by a balanced equation that shows the identity and quantity of each substance involved. In the provided reactions, the conversion of TiO2 to TiCl4 and then to titanium illustrates the multi-step nature of chemical processes, highlighting the importance of understanding each step to accurately write mole ratios and predict outcomes.