Problem 81 - Chemistry and Chemical Reactivity

Question

Some metal halides react with water to produce the metal oxide and the appropriate hydrogen halide (see photo). For example, $$ \mathrm{TiCl}_{4}(\ell)+2 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow \mathrm{TiO}_{2}(\mathrm{s})+4 \mathrm{HCl}(\mathrm{g}) $$ (IMAGE CANNOT COPY) (a) Name the four compounds involved in this reaction. (b) If you begin with \(14.0 \mathrm{mL}\) of \(\mathrm{TiCl}_{4}(d=1.73 \mathrm{g} / \mathrm{mL})\) what mass of water, in grams, is required for complete reaction? (c) What mass of each product is expected?

Step-by-Step Solution

Answer

(a) Titanium(IV) chloride, water, titanium dioxide, hydrogen chloride. (b) 4.60 g of water needed. (c) 10.20 g of \(\mathrm{TiO}_2\) and 18.63 g of \(\mathrm{HCl}\) produced.

Step 1: Naming the Compounds

Identify and name the compounds in the reaction \( \mathrm{TiCl}_{4}(\ell) + 2 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow \mathrm{TiO}_{2}(\mathrm{s}) + 4 \mathrm{HCl}(\mathrm{g}) \). The four compounds are: \( \mathrm{TiCl}_{4} \) is Titanium(IV) chloride, \( \mathrm{H}_{2} \mathrm{O} \) is water, \( \mathrm{TiO}_{2} \) is titanium dioxide, and \( \mathrm{HCl} \) is hydrogen chloride.

Step 2: Calculate Moles of \(\mathrm{TiCl}_{4}\)

Start by finding the mass of \( \mathrm{TiCl}_{4} \) using its volume and density. \( \text{Mass} = 14.0 \text{ mL} \times 1.73 \text{ g/mL} = 24.22 \text{ g} \). Then, calculate the moles of \( \mathrm{TiCl}_{4} \) using its molar mass \( (189.71 \text{ g/mol}) \). Moles of \( \mathrm{TiCl}_{4} = \frac{24.22}{189.71} \approx 0.1277 \text{ moles} \).

Step 3: Determine Mass of Water Required

According to the balanced equation, 2 moles of water are required per mole of \( \mathrm{TiCl}_{4} \). Therefore, the water moles needed are \( 2 \times 0.1277 = 0.2554 \text{ moles} \). Use the molar mass of water \( (18.02 \text{ g/mol}) \) to find the mass: \( \text{Mass of water} = 0.2554 \times 18.02 \approx 4.60 \text{ g} \).

Step 4: Calculate Mass of Titanium Dioxide Produced

From the reaction, 1 mole of \( \mathrm{TiCl}_{4} \) produces 1 mole of \( \mathrm{TiO}_{2} \). Thus, the moles of \( \mathrm{TiO}_{2} \) are the same as \( \mathrm{TiCl}_{4} \): \( 0.1277 \text{ moles} \). The molar mass of \( \mathrm{TiO}_{2} \) is \( 79.87 \text{ g/mol} \), so the mass is \( 0.1277 \times 79.87 \approx 10.20 \text{ g} \).

Step 5: Calculate Mass of Hydrogen Chloride Produced

The reaction indicates that 1 mole of \( \mathrm{TiCl}_{4} \) produces 4 moles of \( \mathrm{HCl} \). Therefore, \( 0.1277 \times 4 = 0.5108 \text{ moles of } \mathrm{HCl} \). The molar mass of \( \mathrm{HCl} \) is \( 36.46 \text{ g/mol} \), so the mass is \( 0.5108 \times 36.46 \approx 18.63 \text{ g} \).

Key Concepts

Chemical Reactions

Chemical reactions are processes where reactants transform into products. They are characterized by the rearrangement of atoms. In the reaction provided, we see titanium(IV) chloride \( \text{TiCl}_4 \) reacting with water \( \text{H}_2\text{O} \) to form titanium dioxide \( \text{TiO}_2 \) and hydrogen chloride \( \text{HCl} \).
This is a typical example of a substitution reaction where one element or group in a molecule is replaced by another. The equation describing this process is already balanced, indicating that reactants and products contain equal numbers of each type of atom.
To fully understand this reaction, it's essential to recognize the type of chemical transformation occurring. It simplifies predicting similar reactions with different compounds.

Stoichiometry

Stoichiometry is a branch of chemistry focusing on the quantitative relationships in chemical reactions. It helps predict the amount of products formed from given reactants.
In the example with titanium(IV) chloride, stoichiometry allows us to determine how much water is needed to react with a given amount of \( \text{TiCl}_4 \), as well as the mass of products \( \text{TiO}_2 \) and \( \text{HCl} \) formed.

• First, convert given quantities (like volume or mass) to moles using density and molar mass.
• Use stoichiometric coefficients from the balanced chemical equation to relate moles of different substances.
• Finally, convert moles back to mass if needed, using molar masses.

These steps ensure precise calculations of substances involved in chemical reactions.

Titanium Dioxide

Titanium dioxide \( \text{TiO}_2 \) is a white solid used widely in paints, sunscreens, and food coloring due to its excellent opacity and brightness properties. It's also a crucial product in this chemical reaction.
Titanium dioxide forms as a result of titanium(IV) chloride reacting with water. Its solid nature implies that it can be collected as a precipitate in the reaction medium.
The role of \( \text{TiO}_2 \) here also illustrates its chemical stability, a reason it's regularly used in various applications. Understanding the production and utility of \( \text{TiO}_2 \) helps grasp its significance in both industrial and chemical contexts.

Hydrogen Chloride

Hydrogen chloride \( \text{HCl} \) is a gas at room temperature. However, when dissolved in water, it is known as hydrochloric acid, widely used in industrial and laboratory settings.
During the given chemical reaction, hydrogen chloride is a gaseous product formed alongside titanium dioxide. The molecular formation of \( \text{HCl} \) indicates a synthesis reaction occurring simultaneously during the substitution reformation with water.
The significance of \( \text{HCl} \) in reactions like this extends to its application in manufacturing, metal pickling, and even pH regulation in solutions. Understanding the production of \( \text{HCl} \) contributes to a deeper insight into the diverse applications of this important chemical compound.