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 energy of formation for each compound from the ALEKS Data tab.
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: Δ G ∘ = [ 1 ⋅ ( − 889.4 ) + 4 ⋅ ( − 95.3 )] − [ 1 ⋅ ( − 737.2 ) + 2 ⋅ ( − 228.6 )] .
Calculate the standard reaction free energy and round to zero decimal places: Δ G ∘ = − 76 kJ/mol , so the final answer is − 76 .
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 compound to calculate Δ G ∘ .
Formula Introduction The standard Gibbs free energy of reaction is calculated as follows: 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 represents the stoichiometric coefficients of the balanced chemical equation.
Gathering Data Using the values from the ALEKS Data tab: Δ G f ∘ ( T i C l 4 ( g )) = − 737.2 kJ/mol Δ G f ∘ ( H 2 O ( g )) = − 228.6 kJ/mol Δ G f ∘ ( T i O 2 ( s )) = − 889.4 kJ/mol Δ G f ∘ ( H Cl ( g )) = − 95.3 kJ/mol
Calculation Now, we substitute these 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 ) + 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 Rounding to zero decimal places, we get -76 kJ/mol.
Final Answer The standard reaction free energy for the reaction is -76 kJ/mol.
Examples
The standard free energy change of a reaction is a key concept in chemistry that helps predict the spontaneity of a chemical reaction under standard conditions. For example, in the industrial production of titanium dioxide ( T i O 2 ), calculating the standard free energy change for the reaction between titanium tetrachloride ( T i C l 4 ) and water ( H 2 O ) is crucial. If the standard free energy change is negative, the reaction is spontaneous, indicating that the process can occur without external energy input, making it economically viable. This calculation aids in optimizing reaction conditions to maximize product yield and minimize energy consumption, ensuring an efficient and cost-effective production process.
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 ) is calculated using standard Gibbs free energies of formation of each substance. The final calculated value is − 76 kJ/mol when rounded to zero decimal places. This indicates that the reaction is spontaneous under standard conditions.
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