Question

A 0.715 g sample of titanium was heated with chlorine gas to give \(2.836 \mathrm{~g}\) of titanium chloride. What is the empirical formula of titanium chloride?

Short answer

The empirical formula of titanium chloride is \(\mathrm{TiCl}_4\).

Step-by-step solution

Determine the Mass of Chlorine

Calculate the mass of chlorine in the titanium chloride by subtracting the mass of titanium from the total mass of titanium chloride: \[ \text{Mass of chlorine} = 2.836\, \mathrm{g} - 0.715\, \mathrm{g} = 2.121\, \mathrm{g} \]

Calculate Moles of Titanium

Determine the moles of titanium by dividing its mass by its atomic mass \(47.87 \, \mathrm{g/mol}\): \[ \text{Moles of Ti} = \frac{0.715 \, \mathrm{g}}{47.87 \, \mathrm{g/mol}} = 0.01494 \, \text{mol} \]

Calculate Moles of Chlorine

Determine the moles of chlorine by dividing its mass by its atomic mass \(35.45 \, \mathrm{g/mol}\): \[ \text{Moles of Cl} = \frac{2.121 \, \mathrm{g}}{35.45 \, \mathrm{g/mol}} = 0.05985 \, \text{mol} \]

Determine Empirical Formula Ratio

Divide the moles of each element by the smaller number of moles to find the simplest ratio. Use \(0.01494 \, \text{mol}\) as the smallest value:- Titanium: \[ \frac{0.01494}{0.01494} = 1 \]- Chlorine: \[ \frac{0.05985}{0.01494} \approx 4 \]

Write the Empirical Formula

Use the ratio from Step 4 to write the empirical formula of titanium chloride. Since the ratios are approximately \(1:4\), the empirical formula is \(\mathrm{TiCl}_4\).

Key concepts

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It allows us to understand and predict the amounts of substances consumed and produced in a reaction.
To apply stoichiometry, one must first convert masses into moles, which are the "counting unit" in chemistry. This involves dividing a substance's mass by its molar mass.
Understanding stoichiometry is essential for determining the proportions of elements in compounds, such as deriving the empirical formula of a compound. In the exercise, stoichiometry is used to calculate the moles of titanium and chlorine to find the simplest whole-number ratio, essential for determining the empirical formula of titanium chloride.

• Use stoichiometry to convert masses to moles.
• Calculate mole ratios for empirical formulas.
• Predict the outcome of chemical reactions quantitatively.

Chemical Reactions

Chemical reactions involve the transformation of substances through breaking and forming of bonds, resulting in new chemical compounds. Every reaction has its specific equation balancing the reactants and products, ensuring mass conservation.
In our exercise, titanium reacts with chlorine gas to form titanium chloride. The empirical formula (\(\text{{}}{\text{{}}{{TiCl}}_4\)\}) derived from the exercise signifies the simplest type of titanium chloride formed from the reaction. Understanding the nature of a chemical reaction is crucial for writing balanced chemical equations, determining reactant or product amounts, and identifying reaction types.

• Ensure stoichiometric balance of reactants and products.
• Recognize the conversion of reactants to a totally different product.
• Identify compound formation and empirical formulas.

Mole Concept

The mole concept is a fundamental principle in chemistry that provides a method for quantifying the amount of substance. A mole is defined as the amount of any chemical substance containing the same number of atoms, molecules, or other particles as there are atoms in 12 grams of carbon-12 (\(6.022 {\text{}} \times 10^{23}\), Avogadro's number).
In determining the empirical formula of a compound, the mole concept connects the mass of a substance to the number of moles, which further aids in identifying the ratio of elements present.
In the exercise, once we have calculated moles for both titanium and chlorine, it becomes possible to establish the mole ratio, crucial for finding the simplest formula of a compound like titanium chloride.

• 1 mole represents \(6.022 \times 10^{23}\) particles.
• Convert mass to moles using the molar mass.
• Utilize mole ratios to deduce empirical formulas.