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Understanding molar mass is crucial for solving problems in chemical stoichiometry. The molar mass of a substance refers to the mass of one mole of its molecules or formula units. It is expressed in units of grams per mole (g/mol). To find the molar mass, we sum up the atomic masses of all the elements in a molecule.
For example, let's consider rutile, \(\text{TiO}_2\). The molar mass is calculated by adding the atomic mass of titanium (Ti), which is 47.87 g/mol, to twice the atomic mass of oxygen (O), which is 16.00 g/mol each. Therefore, the molar mass of \(\text{TiO}_2\) is:

• \( 47.87 + 2 \times 16.00 = 79.87 \, \text{g/mol} \)

These calculations are essential because they allow us to convert between mass and moles, facilitating further stoichiometric calculations.

Stoichiometric calculations aim to determine the quantitative relationships between reactants and products in a chemical reaction. This involves using the balanced chemical equation to find the proportion, or ratio, in which the substances react. The ratios are derived from the coefficients in the chemical equation.
For the task at hand, two reactions are involved:

• The conversion of \(\text{TiO}_2\) to \(\text{TiCl}_4\) and \(\text{TiCl}_4\) to Ti.

Each of these reactions shows a one-to-one correspondence between reactants and products. This means that 1 mole of \(\text{TiO}_2\) yields 1 mole of \(\text{TiCl}_4\), which then yields 1 mole of Ti. Such relationships allow us to calculate how much titanium can be produced from a given amount of \(\text{TiO}_2\).
To perform this calculation, first convert the mass of \(\text{TiO}_2\) to moles using its molar mass, then apply the stoichiometric coefficients from the balanced equations.

Chemical reactions describe how substances transform into new products. The balanced chemical equations provide a symbolic representation of these transformations. Each reactant and product in a reaction has a specific formula and a corresponding coefficient to fulfill the law of conservation of mass.
In our example, the processes involve:

• The first reaction transforms \(\text{TiO}_2\) into \(\text{TiCl}_4\) using chlorine and carbon.
• The second reaction converts \(\text{TiCl}_4\) into titanium using magnesium.

The coefficients, like the ones from the balanced equations of these two reactions, are crucial. They guide us in performing accurate stoichiometric calculations by showing us how moles of reactants convert into moles of products.
Understanding the nature of these transformations helps predict the feasible outcomes of the reactions, facilitating precise measurement and material usage in practical applications.