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 ∘ ( 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 Δ G ∘ .
Round the result to zero decimal places: − 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 species to calculate Δ G ∘ . The formula is:
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 for each species in the balanced chemical equation.
Gathering Data First, we need to find the standard Gibbs free energy of formation ( Δ G f ∘ ) for each reactant and product. From the ALEKS Data tab (or a similar source), we have the following values (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 Standard Reaction Free Energy Now, we can calculate the standard reaction free energy using 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 ))]
Substituting the values, we get:
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
Rounding the Answer Finally, we round the answer to zero decimal places:
Δ G ∘ ≈ − 76 kJ
Final Answer Therefore, the standard reaction free energy for the given chemical reaction is approximately -76 kJ.
Examples
Understanding the standard reaction free energy is crucial in various real-world applications. For instance, in industrial chemistry, it helps determine whether a reaction will occur spontaneously under standard conditions, which is vital for designing efficient chemical processes. In environmental science, it can be used to predict the feasibility of reactions that remove pollutants from the environment. Moreover, in materials science, it aids in understanding the stability and formation of new materials, such as titanium dioxide ( T i O 2 ), which is widely used in sunscreen, paints, and catalysts. By calculating Δ G ∘ , scientists and engineers can make informed decisions about the feasibility and efficiency of chemical reactions in diverse fields.
