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 (2)
Determine the standard Gibbs free energies of formation for each reactant and product.
Apply the formula: Δ G ∘ = ∑ n Δ G f ∘ ( p ro d u c t s ) − ∑ n Δ G f ∘ ( re a c t an t s ) .
Substitute the given values into the formula and calculate the standard reaction free energy.
Round the final answer to zero decimal places: − 76 kJ/mol .
Explanation
Problem Analysis and Data The problem asks us to calculate the standard reaction free energy ( Δ G ∘ ) for the given chemical 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 energy of formation ( Δ G f ∘ ) values for each reactant and product to calculate Δ G ∘ .
Formula for Standard Reaction Free Energy The standard reaction free energy is calculated using the following formula: Δ G ∘ = ∑ n Δ G f ∘ ( p ro d u c t s ) − ∑ n Δ G f ∘ ( re a c t an t s ) where n is the stoichiometric coefficient of each species in the balanced chemical equation.
Gathering Standard Gibbs Free Energies of Formation From the ALEKS Data tab (or common thermodynamic tables), we have the following standard Gibbs free energies of formation (in kJ/mol):
Δ G f ∘ ( T i C l 4 ( g )) = − 737.2
Δ G f ∘ ( H 2 O ( g )) = − 228.6
Δ G f ∘ ( T i O 2 ( s )) = − 889.4
Δ G f ∘ ( H Cl ( g )) = − 95.3
Calculating the Standard Reaction Free Energy Now, we apply the formula: 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 ) + 4 ⋅ ( − 95.3 )] − [ 1 ⋅ ( − 737.2 ) + 2 ⋅ ( − 228.6 )] 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
Final Answer Rounding the result to zero decimal places, we get: Δ G ∘ = − 76 kJ/mol
Examples
Understanding the Gibbs free energy is crucial in various real-world applications. For instance, in designing new chemical processes, engineers use Gibbs free energy to determine whether a reaction will occur spontaneously under specific conditions. In environmental science, it helps predict the feasibility of pollutant degradation reactions. Moreover, in materials science, it aids in understanding phase transformations and the stability of different material structures. By calculating the Gibbs free energy, scientists and engineers can optimize processes, develop new technologies, and ensure the sustainability of chemical reactions.
To calculate the standard reaction free energy ( Δ G ∘ ) for the given reaction, we gathered the standard Gibbs free energies of formation for each reactant and product and applied the formula. The calculated value is Δ G ∘ = − 76 kJ/mol . This value indicates the reaction is thermodynamically favorable under standard conditions.
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