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Chapter 23: Problem 81

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?

Short Answer

Expert verified
The first reaction, involving titanium dioxide (TiO鈧�), chlorine (Cl鈧�), and carbon (C) forming titanium tetrachloride (TiCl鈧�) and carbon dioxide (CO鈧�), is exothermic, with a standard enthalpy change of -213 kJ/mol. The balanced chemical equation is: \(TiO_2 (s) + 2 Cl_2 (g) + C (s) \rightarrow TiCl_4 (g) + CO_2 (g)\) The second reaction, involving the direct reaction between titanium dioxide (TiO鈧�) and chlorine (Cl鈧�) to form titanium tetrachloride (TiCl鈧�) and oxygen (O鈧�), is endothermic, with a standard enthalpy change of 181 kJ/mol. The balanced chemical equation is: \(TiO_2 (s) + 2 Cl_2 (g) \rightarrow TiCl_4 (g) + O_2 (g)\)

Step by step solution

01

Write a balanced chemical equation

The given reaction is between titanium dioxide (TiO_2), chlorine (Cl_2), and carbon (C) producing titanium tetrachloride (TiCl_4). The balanced chemical equation is: TiO_2 (s) + 2 Cl_2 (g) + C (s) -> TiCl_4 (g) + CO_2 (g)
02

Calculate the standard enthalpy change

We need to find the standard enthalpy change for this reaction using the given values from Appendix C. The following enthalpies of formation are for each of the compounds: TiO_2(s): -944 kJ/mol Cl_2(g): 0 kJ/mol (since it is in its standard state) C(s): 0 kJ/mol (since it is in its standard state) TiCl_4(g): -763 kJ/mol CO_2(g): -394 kJ/mol Now, we can calculate the standard enthalpy change (鈭咹) for the entire reaction using the equation: 鈭咹 = 危 (products' enthalpies) - 危 (reactants' enthalpies) 鈭咹 = [(1)(-763) + (1)(-394)] - [(1)(-944) + (2)(0) + (1)(0)] 鈭咹 = (-763 - 394) - (-944) 鈭咹 = -1157 + 944 = -213 kJ/mol
03

Determine if the reaction is exothermic or endothermic

Since the standard enthalpy change (鈭咹) is negative, we can conclude that the reaction is exothermic (heat is released). (b) Write a reaction for the direct reaction between titanium dioxide and chlorine to form TiCl_4 and oxygen, and determine if this reaction is exothermic or endothermic.
04

Write a balanced chemical equation

The given reaction is between titanium dioxide (TiO_2) and chlorine (Cl_2) producing titanium tetrachloride (TiCl_4) and oxygen (O_2). The balanced chemical equation is: TiO_2 (s) + 2 Cl_2 (g) -> TiCl_4 (g) + O_2 (g)
05

Calculate the standard enthalpy change

Using the values from Appendix C, the enthalpy of formation for O_2 is 0 kJ/mol (since it is in its standard state). Now, we can calculate the standard enthalpy change (鈭咹) for the entire reaction: 鈭咹 = 危 (products' enthalpies) - 危 (reactants' enthalpies) 鈭咹 = [(1)(-763) + (1)(0)] - [(1)(-944) + (2)(0)] 鈭咹 = (-763) - (-944) 鈭咹 = -763 + 944 = 181 kJ/mol
06

Determine if the reaction is exothermic or endothermic

Since the standard enthalpy change (鈭咹) is positive, we can conclude that the reaction is endothermic (heat is absorbed).

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