Titanium occurs in the magnetic mineral ilmenite (FeTiO₃), which is often found mixed with sand. The ilmenite can be separated from the sand with magnets. The titanium can then be extracted from the ilmenite by the following set of reactions: FeTiO₃(s) + 3 Cl₂(g) + 3 C(s) → 3 CO(g) + FeCl₂(s) + TiCl₄(g) TiCl₄(g) + 2 Mg(s) → 2 MgCl₂(l) + Ti(s) Suppose that an ilmenite–sand mixture contains 22.8% ilmenite by mass and that the first reaction is carried out with a 90.8% yield. If the second reaction is carried out with an 85.9% yield, what mass of titanium can be obtained from 1.00 kg of the ilmenite– sand mixture?

Verified step by step guidance

1. Calculate the mass of ilmenite (FeTiO3) in the 1.00 kg mixture using the percentage by mass: \( \text{mass of ilmenite} = 1.00 \text{ kg} \times 0.228 \).
2. Determine the theoretical yield of TiCl4 from the ilmenite using stoichiometry. First, convert the mass of ilmenite to moles using its molar mass: \( \text{moles of FeTiO3} = \frac{\text{mass of FeTiO3}}{\text{molar mass of FeTiO3}} \).
3. Use the stoichiometry of the first reaction to find the moles of TiCl4 produced. According to the balanced equation, 1 mole of FeTiO3 produces 1 mole of TiCl4.
4. Adjust for the 90.8% yield of the first reaction to find the actual moles of TiCl4 produced: \( \text{actual moles of TiCl4} = \text{theoretical moles of TiCl4} \times 0.908 \).
5. Use the stoichiometry of the second reaction to find the moles of titanium produced from TiCl4. Then, adjust for the 85.9% yield of the second reaction: \( \text{actual moles of Ti} = \text{moles of TiCl4} \times 0.859 \). Finally, convert the moles of titanium to mass using its molar mass: \( \text{mass of Ti} = \text{moles of Ti} \times \text{molar mass of Ti} \).

Key Concepts

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced chemical equations. It allows chemists to determine the amount of substances consumed and produced in a reaction. Understanding stoichiometry is essential for solving problems involving yields and mass conversions, as it provides the ratios needed to relate the quantities of different substances.

Percent Yield

Percent yield is a measure of the efficiency of a chemical reaction, calculated as the ratio of the actual yield to the theoretical yield, multiplied by 100. It indicates how much product was actually obtained compared to what was expected based on stoichiometric calculations. In this question, the percent yields of the reactions are crucial for determining the final mass of titanium extracted from the ilmenite.

Mass Composition

Mass composition refers to the percentage by mass of each component in a mixture or compound. In this context, knowing the mass composition of the ilmenite-sand mixture (22.8% ilmenite) is vital for calculating the amount of ilmenite available for the reactions. This concept helps in determining how much titanium can ultimately be extracted based on the initial mass of the mixture.