Using the standard enthalpies of formation, what is the standard enthalpy of reaction?
[tex]CO(g)+H_2 O(g) \longrightarrow CO_2(g)+H_2(g)[/tex]
[tex]\Delta H_{ rxn }^{\circ}=[/tex] kJ
Answer (1)
Determine the standard enthalpies of formation for each reactant and product.
Apply Hess's Law: Δ H r x n ∘ = ∑ Δ H f ∘ ( products ) − ∑ Δ H f ∘ ( reactants ) .
Substitute the standard enthalpies of formation into Hess's Law.
Calculate the standard enthalpy of reaction: Δ H r x n ∘ = − 41.2 kJ/mol .
The standard enthalpy of reaction is − 41.2
Explanation
Understanding the Problem and Applying Hess's Law Let's calculate the standard enthalpy of reaction using the given reaction and standard enthalpies of formation. The reaction is: CO ( g ) + H 2 O ( g ) ⟶ C O 2 ( g ) + H 2 ( g ) We will use Hess's Law, which states that the standard enthalpy of reaction is the sum of the standard enthalpies of formation of the products minus the sum of the standard enthalpies of formation of the reactants.
Finding Standard Enthalpies of Formation We need to find the standard enthalpies of formation for each compound. From standard thermodynamic tables, we have:
Δ H f ∘ ( CO ( g )) = − 110.5 kJ/mol
Δ H f ∘ ( H 2 O ( g )) = − 241.8 kJ/mol
Δ H f ∘ ( C O 2 ( g )) = − 393.5 kJ/mol
Δ H f ∘ ( H 2 ( g )) = 0.0 kJ/mol
Applying Hess's Law Equation Now, we apply Hess's Law: Δ H r x n ∘ = ∑ Δ H f ∘ ( products ) − ∑ Δ H f ∘ ( reactants ) Δ H r x n ∘ = [ Δ H f ∘ ( C O 2 ( g )) + Δ H f ∘ ( H 2 ( g ))] − [ Δ H f ∘ ( CO ( g )) + Δ H f ∘ ( H 2 O ( g ))]
Calculating the Standard Enthalpy of Reaction Substitute the values into the equation: Δ H r x n ∘ = [( − 393.5 kJ/mol ) + ( 0.0 kJ/mol )] − [( − 110.5 kJ/mol ) + ( − 241.8 kJ/mol )] Δ H r x n ∘ = − 393.5 − ( − 110.5 − 241.8 ) Δ H r x n ∘ = − 393.5 − ( − 352.3 ) Δ H r x n ∘ = − 393.5 + 352.3 Δ H r x n ∘ = − 41.2 kJ/mol
Final Answer Therefore, the standard enthalpy of reaction is: Δ H r x n ∘ = − 41.2 kJ/mol So, the standard enthalpy of the reaction is -41.2 kJ.
Examples
Understanding enthalpy changes is crucial in many real-world applications. For example, in designing chemical reactors, knowing the enthalpy of reaction helps engineers determine the amount of heat that needs to be added or removed to maintain the reaction at a desired temperature. This is also important in combustion processes, where the heat released can be used to generate power. In environmental science, understanding enthalpy changes helps in assessing the energy balance of ecosystems and the impact of pollutants on the environment. For instance, the reaction between carbon monoxide and water is important in industrial processes and understanding its enthalpy change helps optimize these processes.
