Problem 81 - Chemistry: The Central Science

Question

An important process in the metallurgy of titanium is the reaction between titanium dioxide and chlorine in the presence of carbon, which acts as a reducing agent, leading to the formation of gaseous \(\mathrm{TiCl}_{4}\). (a) Write a balanced chemical equation for this reaction, and use it with the values listed in Appendix \(C\) to calculate the standard enthalpy change of this reaction. Is this reaction exothermic or endothermic? (b) Write a reaction for the direct reaction between titanium dioxide and chlorine to form \(\mathrm{TiCl}_{4}\) and oxygen. Is this reaction exothermic or endothermic?

Step-by-Step Solution

Answer

The balanced chemical equation for the reaction between titanium dioxide, chlorine, and carbon is: \(\mathrm{TiO}_{2}(s) + 2\mathrm{Cl}_{2}(g) + 2\mathrm{C}(s) \rightarrow \mathrm{TiCl}_{4}(g) + 2\mathrm{CO}(g)\). Calculate the standard enthalpy change \(\Delta H_{rxn}^{\circ}\) using the given values in Appendix C. If the value is negative, the reaction is exothermic; if positive, the reaction is endothermic. The balanced chemical equation for the direct reaction between titanium dioxide and chlorine to form \(\mathrm{TiCl}_{4}\) and oxygen is: \(\mathrm{TiO}_{2}(s) + 2\mathrm{Cl}_{2}(g) \rightarrow \mathrm{TiCl}_{4}(g) + O_{2}(g)\). Calculate the standard enthalpy change for this reaction, too. If the value is negative, the direct reaction is exothermic; if positive, the direct reaction is endothermic.

Step 1: Writing the balanced chemical equation

To form \(\mathrm{TiCl}_{4}\) from titanium dioxide and chlorine with carbon as the reducing agent, the balanced chemical equation can be written as follows: \[\mathrm{TiO}_{2}(s) + 2\mathrm{Cl}_{2}(g) + 2\mathrm{C}(s) \rightarrow \mathrm{TiCl}_{4}(g) + 2\mathrm{CO}(g)\]

Step 2: Calculating the standard enthalpy change

Assuming you have the standard enthalpy of formation values from Appendix C: - \(\mathrm{TiO}_{2}(s): \Delta H_{f1}^{\circ}\) - \(\mathrm{Cl}_{2}(g): \Delta H_{f2}^{\circ}\) - \(\mathrm{C}(s): \Delta H_{f3}^{\circ}\) - \(\mathrm{TiCl}_{4}(g): \Delta H_{f4}^{\circ}\) - \(\mathrm{CO}(g): \Delta H_{f5}^{\circ}\) Now we will calculate the total standard enthalpy change of the reaction using the formula: \[\Delta H_{rxn}^{\circ} = [\Delta H_{f4}^{\circ} + 2\Delta H_{f5}^{\circ}] - [\Delta H_{f1}^{\circ} + 2\Delta H_{f2}^{\circ} + 2\Delta H_{f3}^{\circ}]\] Plug in the values from Appendix C to get the final answer.

Step 3: Determining if the reaction is exothermic or endothermic

If \(\Delta H_{rxn}^{\circ} < 0\), the reaction is exothermic. If \(\Delta H_{rxn}^{\circ} > 0\), the reaction is endothermic. Compare the calculated value from Step 2 to determine the nature of the reaction.

Step 4: Writing a reaction for the direct reaction between titanium dioxide and chlorine

The balanced chemical equation for the direct reaction between titanium dioxide and chlorine to form \(\mathrm{TiCl}_{4}\) and oxygen is as follows: \[\mathrm{TiO}_{2}(s) + 2\mathrm{Cl}_2(g) \rightarrow \mathrm{TiCl}_{4}(g) + O_{2}(g)\]

Step 5: Determining if the direct reaction is exothermic or endothermic

To determine whether the direct reaction is exothermic or endothermic, we need to calculate the total standard enthalpy change of this reaction as well. Assuming you have the standard enthalpy of formation values from Appendix C: - \(\mathrm{TiO}_{2}(s): \Delta H_{f1}^{\circ}\) - \(\mathrm{Cl}_{2}(g): \Delta H_{f2}^{\circ}\) - \(\mathrm{TiCl}_{4}(g): \Delta H_{f4}^{\circ}\) - \(\mathrm{O}_{2}(g): \Delta H_{f6}^{\circ}\) Calculate the total standard enthalpy change of the direct reaction using the formula: \[\Delta H_{rxn}^{\circ} = [\Delta H_{f4}^{\circ} + \Delta H_{f6}^{\circ}] - [\Delta H_{f1}^{\circ} + 2\Delta H_{f2}^{\circ}]\] Plug in the values from Appendix C to get the final answer. Then, compare the calculated value to determine the nature of the direct reaction (exothermic or endothermic).

Key Concepts

Balancing Chemical Equations

Balancing chemical equations is a fundamental skill in chemistry that ensures the law of conservation of mass is respected in a chemical reaction. To balance a chemical equation, you must have the same number of each type of atom on both sides of the reaction. This is crucial because it reflects the stoichiometry, which is the ratio in which reactants combine and products form.

Considering the titanium metallurgy problem, we start by writing out the reactants and products, then adjust coefficients to balance the atoms. For instance, the production of \(\mathrm{TiCl}_{4}\) from \(\mathrm{TiO}_{2}\) involves a careful balance; two molecules of chlorine and two atoms of carbon are needed to balance the reaction, resulting in one molecule of \(\mathrm{TiCl}_{4}\) and two molecules of carbon monoxide. The key to successfully balancing this equation, like others, is to count and adjust iteratively until the equation is balanced.

Standard Enthalpy Change

Standard enthalpy change, denoted as \(\Delta H^\circ\), is a measure of the heat energy released or absorbed during a reaction under standard conditions, typically 1 bar of pressure. For a reaction, \(\Delta H^\circ\) is calculated using the standard enthalpy of formation (\(\Delta H_f^\circ\)) values for the reactants and products. It helps us understand whether energy is required for a reaction to occur, or if energy is released.

In our exercise, you need to look up the standard enthalpy of formation for each species involved in the reaction from Appendix C. The standard enthalpy change for the reaction is then found by subtracting the sum of the standard enthalpies of formation of the reactants from the sum of the standard enthalpies of formation of the products. If the resulting \(\Delta H_{rxn}^\circ\) is negative, the reaction releases heat and is exothermic; if positive, the reaction absorbs heat and is endothermic.

Exothermic and Endothermic Reactions

Reactions that release heat into their surroundings are termed exothermic, often characterized by a negative standard enthalpy change, as they lose energy. Conversely, endothermic reactions absorb heat from their surroundings, indicated by a positive standard enthalpy change, as they gain energy.

Understanding whether a reaction is exothermic or endothermic is important for both practical applications and theoretical understanding in chemistry. For instance, in the metallurgy of titanium, assessing the heat exchange can inform necessary safety measures during processing or the energy efficiency of the method. Therefore, by calculating the standard enthalpy change of the given reactions and determining if the value is less than or greater than zero, students can classify each reaction as exothermic or endothermic accordingly.