Titanium metal is obtained from the mineral rutile, TiO2. How many kilograms of rutile are needed to produce 100.0 kg of Ti?

검증된 단계별 안내

Identify the chemical reaction involved in obtaining titanium from rutile: \( \text{TiO}_2 \rightarrow \text{Ti} \).

Determine the molar masses of \( \text{TiO}_2 \) and \( \text{Ti} \) using the periodic table: \( \text{TiO}_2 \) has a molar mass of approximately 79.87 g/mol (Ti: 47.87 g/mol, O: 16.00 g/mol each).

Calculate the moles of titanium needed: \( \text{moles of Ti} = \frac{100.0 \text{ kg of Ti}}{47.87 \text{ g/mol}} \).

Use the stoichiometry of the reaction to find the moles of \( \text{TiO}_2 \) required: Since the reaction is \( 1:1 \), the moles of \( \text{TiO}_2 \) needed are equal to the moles of \( \text{Ti} \).

Convert the moles of \( \text{TiO}_2 \) to kilograms: \( \text{mass of TiO}_2 = \text{moles of TiO}_2 \times 79.87 \text{ g/mol} \) and convert grams to kilograms.

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주요 개념

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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 how much of a substance is needed or produced based on the balanced chemical equation. In this case, understanding the stoichiometric ratios between titanium (Ti) and rutile (TiO2) is essential for determining the amount of rutile required to produce a specific mass of titanium.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is crucial for converting between the mass of a substance and the number of moles, which is necessary for stoichiometric calculations. For this question, knowing the molar masses of titanium (Ti) and rutile (TiO2) will enable the calculation of how many kilograms of rutile are needed to yield 100.0 kg of titanium.

Chemical Composition

Chemical composition refers to the types and amounts of elements that make up a compound. In the case of rutile (TiO2), it consists of titanium and oxygen in a specific ratio. Understanding the composition of rutile is important for determining how much titanium can be extracted from a given mass of rutile, which directly impacts the stoichiometric calculations needed to answer the question.