Using the thermodynamic information in the ALEKS Data tab, calculate the standard reaction free energy of the following chemical reaction:
[tex]TiCl_4(g)+2 H_2 O(g) \rightarrow TiO_2(s)+4 HCl(g)[/tex]
Round your answer to zero decimal places.
Answer (1)
Determine the standard Gibbs free energy of formation for each reactant and product.
Apply the formula: Δ G ∘ = ∑ n Δ G f ∘ ( products ) − ∑ n Δ G f ∘ ( reactants ) .
Substitute the given values into the formula and calculate the standard reaction free energy.
Round the final result to zero decimal places: − 76 kJ/mol .
Explanation
Problem Analysis We are asked to calculate the standard reaction free energy ( Δ G ∘ ) for the reaction: T i C l 4 ( g ) + 2 H 2 O ( g ) → T i O 2 ( s ) + 4 H Cl ( g ) We will use the standard Gibbs free energies of formation ( Δ G f ∘ ) for each reactant and product from the ALEKS Data tab to calculate Δ G ∘ .
Gathering Data The standard Gibbs free energy of formation values are:
Δ G f ∘ ( T i O 2 ( s )) = − 889.4 kJ/mol
Δ G f ∘ ( H Cl ( g )) = − 95.3 kJ/mol
Δ G f ∘ ( T i C l 4 ( g )) = − 737.2 kJ/mol
Δ G f ∘ ( H 2 O ( g )) = − 228.6 kJ/mol
Formula for Calculation The standard reaction free energy is calculated as follows: Δ G ∘ = ∑ n Δ G f ∘ ( products ) − ∑ n Δ G f ∘ ( reactants ) where n is the stoichiometric coefficient for each species in the balanced chemical equation.
Calculating the Value Substituting the values into the equation: Δ G ∘ = [ 1 ⋅ Δ G f ∘ ( T i O 2 ( s )) + 4 ⋅ Δ G f ∘ ( H Cl ( g ))] − [ 1 ⋅ Δ G f ∘ ( T i C l 4 ( g )) + 2 ⋅ Δ G f ∘ ( H 2 O ( g ))] Δ G ∘ = [ 1 ⋅ ( − 889.4 kJ/mol ) + 4 ⋅ ( − 95.3 kJ/mol )] − [ 1 ⋅ ( − 737.2 kJ/mol ) + 2 ⋅ ( − 228.6 kJ/mol )] Δ G ∘ = [ − 889.4 − 381.2 ] − [ − 737.2 − 457.2 ] Δ G ∘ = − 1270.6 − ( − 1194.4 ) Δ G ∘ = − 1270.6 + 1194.4 Δ G ∘ = − 76.2 kJ/mol
Rounding the Result Rounding the result to zero decimal places, we get: Δ G ∘ ≈ − 76 kJ/mol
Final Answer The standard reaction free energy for the given chemical reaction is approximately -76 kJ/mol.
Examples
Understanding the standard reaction free energy is crucial in various real-world applications. For instance, in chemical engineering, it helps determine the feasibility of a reaction under standard conditions, which is essential for designing industrial processes. In environmental science, it can be used to predict the spontaneity of reactions that affect pollution levels. For example, knowing the Δ G ∘ of a reaction like the formation of acid rain can help scientists develop strategies to mitigate its impact. The calculation of Δ G ∘ involves using the equation Δ G ∘ = ∑ n Δ G f ∘ ( products ) − ∑ n Δ G f ∘ ( reactants ) , where n represents the stoichiometric coefficients and Δ G f ∘ represents the standard Gibbs free energy of formation.
