Problem 14 - Chemistry Matter and Change

Question

Challenge Titanium is a transition metal used in many alloys because it is extremely strong and lightweight. Titanium tetrachloride \((\mathrm{TiCl_{4 }})\) is extracted from titanium oxide \(\left(\mathrm{TiO}_{2}\right)\) using chlorine and coke (carbon). $$\mathrm{TiO}_{2}(\mathrm{s})+\mathrm{C}(\mathrm{s})+2 \mathrm{Cl}_{2}(\mathrm{g}) \rightarrow \mathrm{TiCl}_{4}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})$$ \begin{equation} \mathrm{a. Cl}_{2} \text { gas is needed to react with } 1.25 \text { mol of } \mathrm{TIO}_{2} ? \end{equation} \begin{equation} \begin{array}{l}{\text { b. What mass of } C \text { is needed to react with } 1.25 \text { mol of TiO_{2} ? }} \\ {\text { c. What is the mass of all of the products formed by reaction with } 1.25 \text { mol of TiO_{2} ? }}\end{array} \end{equation}

Step-by-Step Solution

Answer

a) 2.5 mol of \(\mathrm{Cl}_2\); b) 15.01 g of \(\mathrm{C}\); c) 292.24 g of products.

Step 1: Determine Moles of Cl2 Needed

From the balanced chemical equation \(\mathrm{TiO}_{2}(\mathrm{s})+\mathrm{C}(\mathrm{s})+2 \mathrm{Cl}_{2}(\mathrm{g}) \rightarrow \mathrm{TiCl}_{4}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})\), we see that 1 mol of \(\mathrm{TiO}_2 \) reacts with 2 mol of \(\mathrm{Cl}_2\). Therefore, for 1.25 mol of \(\mathrm{TiO}_2\), you need \(1.25 \times 2 = 2.5\) mol of \(\mathrm{Cl}_2\).

Step 2: Calculate Mass of Carbon Needed

Since 1 mol of \(\mathrm{TiO}_2\) needs 1 mol of \(\mathrm{C}\), 1.25 mol of \(\mathrm{TiO}_2\) will need 1.25 mol of \(\mathrm{C}\). The molar mass of carbon is \(12.01\) g/mol, so the mass required is \(1.25 \times 12.01 = 15.01\) grams.

Step 3: Calculate Mass of TiCl4 Formed

1 mol of \(\mathrm{TiO}_2\) produces 1 mol of \(\mathrm{TiCl}_4\). Therefore, 1.25 mol of \(\mathrm{TiO}_2\) produces 1.25 mol of \(\mathrm{TiCl}_4\). The molar mass of \(\mathrm{TiCl}_4\) is calculated as follows: \(47.87 + 4 \times 35.45 = 189.78\) g/mol. Hence, the mass of \(\mathrm{TiCl}_4\) formed is \(1.25 \times 189.78 = 237.225\) grams.

Step 4: Calculate Mass of CO2 Formed

1 mol of \(\mathrm{TiO}_2\) produces 1 mol of \(\mathrm{CO}_2\). Therefore, 1.25 mol of \(\mathrm{TiO}_2\) produces 1.25 mol of \(\mathrm{CO}_2\). The molar mass of \(\mathrm{CO}_2\) is \(12.01 + 2 \times 16.00 = 44.01\) g/mol. Hence, the mass of \(\mathrm{CO}_2\) formed is \(1.25 \times 44.01 = 55.0125\) grams.

Step 5: Calculate Total Mass of Products Formed

The total mass of the products \(\mathrm{TiCl}_4\) and \(\mathrm{CO}_2\) is \(237.225 + 55.0125 = 292.2375\) grams.

Key Concepts

Understanding Transition Metals

Transition metals are unique elements found in the center of the periodic table. They are known for their ability to form various ionic and oxidation states, which is essential in chemical reactions. Titanium, a transition metal, is incredibly valuable in industry due to its strength and low density. Transition metals often have incomplete d-orbitals, allowing them to bond in a variety of ways, creating diverse compounds.
- Transition metals usually have high melting and boiling points, making them useful in engineering and construction materials. - They can easily lose or gain electrons, making them versatile in forming compounds like titanium tetrachloride, \(\mathrm{TiCl}_{4},\) used in many industrial processes.
These properties make transition metals essential in many chemical processes including the extraction and refinement of materials like titanium.

Basics of Chemical Reactions

Chemical reactions occur when substances interact to form new products. In the given reaction, titanium dioxide \(\mathrm{TiO}_2\), carbon \(\mathrm{C}\), and chlorine gas \(\mathrm{Cl}_2\) react to form titanium tetrachloride \(\mathrm{TiCl}_4\) and carbon dioxide \(\mathrm{CO}_2\). During the process, new bonds form, and existing bonds break.
- Chemical reactions can be classified into types such as synthesis, decomposition, single replacement, and double replacement.
- In this case, it's a synthesis reaction where multiple reactants combine to form new products.
Recognizing and understanding the different types of chemical reactions is crucial for solving stoichiometry problems and predicting products in chemical equations.

Understanding Molar Mass

Molar mass is a fundamental concept in chemistry that represents the mass of one mole of a substance. It is measured in grams per mole (g/mol). Knowing the molar mass of elements and compounds is essential for converting between moles and grams.
- For example, the molar mass of carbon is \(12.01\) g/mol, which is used to calculate the grams of carbon needed in a reaction.
- Similarly, for titanium tetrachloride \(\mathrm{TiCl}_4\), the molar mass is calculated by adding the atomic masses of one titanium and four chlorine atoms, resulting in \(189.78\) g/mol.
Using molar masses, chemists can precisely measure reactants and predict the amounts of products formed in reactions.

Importance of a Balanced Chemical Equation

A balanced chemical equation is the cornerstone of stoichiometry. It ensures that the number of atoms for each element is the same on both sides of the equation, which reflects the Law of Conservation of Mass. - Every balanced equation provides the mole ratio necessary to calculate how much of each substance is used or produced.
- For instance, the equation \(\mathrm{TiO}_{2}(\mathrm{s})+\mathrm{C}(\mathrm{s})+2 \mathrm{Cl}_{2}(\mathrm{g}) \rightarrow \mathrm{TiCl}_{4}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})\) shows that \(1\) mole of \(\mathrm{TiO}_2\) needs \(2\) moles of \(\mathrm{Cl}_2\) and \(1\) mole of \(\mathrm{C}\) to produce \(1\) mole of \(\mathrm{TiCl}_4\) and \(1\) mole of \(\mathrm{CO}_2\).
Balancing chemical equations is a key skill for predicting the direction and magnitude of chemical transformations accurately.