Question

Several transition metals are prepared by reduction of the metal halide with magnesium. Titanium is prepared by the Kroll method, in which the ore (ilmenite) is converted to the gaseous chloride, which is then reduced to Ti metal by molten \(\mathrm{Mg}\) (see the discussion on the isolation of magnesium in Section 22.4 ). Assuming yiclds of \(84 \%\) for step 1 and \(93 \%\) for step \(2,\) and an excess of the other reactants, what mass of Ti metal can be prepared from 21.5 metric tons of ilmenite?

Short answer

18.13 metric tons of Ti metal can be prepared from 21.5 metric tons of ilmenite.

Step-by-step solution

Convert ilmenite to TiCl4

Calculate the theoretical yield of TiCl4 from the given mass of ilmenite based on stoichiometric relationships. Use the ilmenite formula FeTiO3.

Calculate actual yield of TiCl4

Multiply the theoretical yield of TiCl4 by the yield percentage (84%) to get the actual yield of TiCl4.

Reduce TiCl4 to Ti with Mg

Calculate the theoretical yield of Ti from the actual yield of TiCl4 obtained in Step 2 using stoichiometric relationships.

Calculate actual yield of Ti

Multiply the theoretical yield of Ti by the yield percentage (93%) to get the actual yield of Ti metal.

Convert metric tons to kilograms

Convert the final mass of Ti metal from metric tons to kilograms for convenience, if necessary.

Key concepts

Kroll method

The Kroll method is a widely-used process to extract titanium metal. It involves transforming ilmenite ore into titanium tetrachloride (TiCl4) before reducing it to pure titanium. The initial step is to convert the ore, specifically ilmenite (FeTiO3), into TiCl4. This is achieved by reacting the ore with chlorine gas at high temperatures. Once the TiCl4 has been produced, it undergoes a reduction phase involving molten magnesium to yield titanium metal and magnesium chloride (MgCl2). This method is favored for its efficiency and the relatively high purity of the resultant titanium.

Stoichiometric calculations

Stoichiometry is crucial in determining how much product can be formed from given reactants based on balanced chemical equations. In the context of the Kroll method, stoichiometric calculations help ascertain the theoretical yield of TiCl4 from ilmenite and the subsequent yield of titanium from TiCl4. These calculations begin by using the molar ratios derived from the balanced equations. For instance, converting ilmenite to TiCl4 involves understanding the amount of each reactant needed and the expected amount of product formed under perfect conditions. Accurate stoichiometry ensures the right quantities of reactants are used and helps estimate yields, making the process both cost-effective and efficient.

Yield percentage

The yield percentage is a measure of the efficiency of a chemical reaction, comparing the actual yield to the theoretical yield. It's expressed as a percentage and calculated using the formula: \[% yield = \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100\]. In this exercise, the yield for converting ilmenite to TiCl4 is 84%, meaning only 84% of the theoretically possible TiCl4 is actually produced. Similarly, for the reduction of TiCl4 to titanium, the yield is 93%. These percentages are crucial for calculating the final amount of titanium produced. The real-world effectiveness of a reaction often falls short of theoretical predictions due to factors like side reactions, impurities, and incomplete conversions.

Ilmenite conversion

The conversion of ilmenite (FeTiO3) to titanium tetrachloride (TiCl4) is the first and essential step in the Kroll method. Ilmenite is initially treated with chlorine gas at high temperatures. This reaction replaces the oxygen in ilmenite with chlorine, producing gaseous TiCl4 and iron chloride (FeCl2). The process can be represented by the equation: \[\text{FeTiO}_3 + 3\text{Cl}_2 \rightarrow \text{TiCl}_4 + \text{FeCl}_2 + \text{O}_2\]. Accurate stoichiometric calculations ensure that the appropriate amount of chlorine is used to maximize yield while maintaining cost efficiency. This step is crucial because the conversion efficiency directly impacts the amount of titanium that can be ultimately obtained.

Metal extraction

Metal extraction encompasses various processes of obtaining metals from their naturally occurring compounds. For titanium, the Kroll method is a specialized technique. After converting ilmenite to TiCl4, the next step is its reduction using molten magnesium. This reduction reaction is given by: \[\text{TiCl}_4 + 2\text{Mg} \rightarrow \text{Ti} + 2\text{MgCl}_2\]. The reaction highlights the primary conversion of TiCl4 into pure titanium metal and magnesium chloride by-products. Effective extraction processes like these are vital for producing high-purity metals required in various applications, from aerospace to medical devices. Efficient extraction not only ensures the quality of the final product but also optimizes resource usage and minimizes waste.