Given the following thermochemical equation:
[tex]2 H_2(g)+O_2(g) \rightarrow 2 H_2 O(I) \quad \Delta H^{\circ}=-571.6 kJ[/tex]
Determine the enthalpy change for the reaction below:
[tex]4 H_2 O(l) \rightarrow 4 H_2(g)+2 O_2(g) \quad \Delta H^{\circ}=?[/tex]
A. -2286 kJ
B. -1143 kJ
C. -571.6 kJ
D. 1143 kJ
E. 2286 kJ
Answer (2)
Reverse the given reaction, which changes the sign of Δ H ∘ to +571.6 kJ.
Multiply the reversed reaction by 2 to match the target reaction.
Multiply the enthalpy change by 2: 2 × 571.6 k J = 1143.2 k J .
The enthalpy change for the target reaction is approximately 1143 k J .
Explanation
Analyze the Problem We are given the thermochemical equation: 2 H 2 ( g ) + O 2 ( g ) → 2 H 2 O ( I ) \t Δ H ∘ = − 571.6 k J We need to find the enthalpy change for the reaction: 4 H 2 O ( l ) → 4 H 2 ( g ) + 2 O 2 ( g ) \t Δ H ∘ = ? This problem involves manipulating the given thermochemical equation to match the target reaction and then calculating the corresponding enthalpy change.
Reverse the Reaction First, we need to reverse the given reaction. When a reaction is reversed, the sign of Δ H ∘ also changes. 2 H 2 O ( I ) → 2 H 2 ( g ) + O 2 ( g ) \t Δ H ∘ = + 571.6 k J
Multiply the Reaction Next, we need to multiply the reversed reaction by 2 so that it matches the target reaction: 2 × ( 2 H 2 O ( I ) → 2 H 2 ( g ) + O 2 ( g )) ⇒ 4 H 2 O ( l ) → 4 H 2 ( g ) + 2 O 2 ( g ) When we multiply a reaction by a factor, we also multiply the enthalpy change by the same factor. Δ H ∘ = 2 × 571.6 k J = 1143.2 k J
Final Answer Therefore, the enthalpy change for the reaction 4 H 2 O ( l ) → 4 H 2 ( g ) + 2 O 2 ( g ) is 1143.2 kJ. Among the given options, 1143 kJ is the closest value.
Examples
Thermochemical equations and enthalpy changes are used in various fields, such as chemical engineering and material science. For example, when designing a chemical plant, engineers need to know the enthalpy changes of various reactions to calculate the energy requirements of the plant. Similarly, when developing new materials, scientists need to know the enthalpy changes of various reactions to predict the stability of the materials. Understanding enthalpy changes helps in optimizing processes and ensuring safety in industrial applications.
The enthalpy change for the reaction 4 H_2 O(l) to 4 H_2(g) + 2 O_2(g) is 1143 kJ. This is calculated by reversing the original equation and multiplying it by 2. Therefore, the answer is option D.
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