Consider the chemical equations shown here.
[tex]$\begin{array}{l}
CH_4(g)+2 O_2(g) \rightarrow CO_2(g)+2 H_2 O(g) \Delta H_1=-802 kJ \\
2 H_2 O(g) \rightarrow 2 H_2 O(l) \Delta H_2=-88 kJ
\end{array}$[/tex]
Which equation shows how to calculate [tex]$\Delta H_{ rxn }$[/tex] for the equation below?
[tex]$CH_4(g)+2 O_2(g) \rightarrow CO_2(g)+2 H_2 O(l)$[/tex]
Answer (2)
Apply Hess's Law to determine the enthalpy change of the target reaction by summing the enthalpy changes of the given reactions.
Add the two given chemical equations to obtain the target equation.
Sum the corresponding enthalpy changes: Δ H r x n = Δ H 1 + Δ H 2 = − 802 kJ + ( − 88 kJ ) .
Calculate the final enthalpy change: Δ H r x n = − 890 kJ .
− 890 kJ
Explanation
Problem Analysis and Hess's Law We are given two chemical equations and their corresponding enthalpy changes:
Equation 1: C H 4 ( g ) + 2 O 2 ( g ) → C O 2 ( g ) + 2 H 2 O ( g ) with Δ H 1 = − 802 kJ Equation 2: 2 H 2 O ( g ) → 2 H 2 O ( l ) with Δ H 2 = − 88 kJ
We want to find the enthalpy change for the following reaction:
Target Equation: C H 4 ( g ) + 2 O 2 ( g ) → C O 2 ( g ) + 2 H 2 O ( l )
According to Hess's Law, the enthalpy change for a reaction is the same whether it occurs in one step or multiple steps. Therefore, we can add the given equations to obtain the target equation and add their corresponding enthalpy changes to find the enthalpy change for the target reaction.
Combining the Equations Adding the two given equations:
C H 4 ( g ) + 2 O 2 ( g ) → C O 2 ( g ) + 2 H 2 O ( g ) ( Δ H 1 = − 802 kJ )
2 H 2 O ( g ) → 2 H 2 O ( l ) ( Δ H 2 = − 88 kJ )
Adding these two equations gives:
C H 4 ( g ) + 2 O 2 ( g ) + 2 H 2 O ( g ) → C O 2 ( g ) + 2 H 2 O ( g ) + 2 H 2 O ( l )
Since 2 H 2 O ( g ) appears on both sides, we can cancel it out, which results in the target equation:
C H 4 ( g ) + 2 O 2 ( g ) → C O 2 ( g ) + 2 H 2 O ( l )
Calculating the Enthalpy Change Now, we add the corresponding enthalpy changes:
Δ H r x n = Δ H 1 + Δ H 2 = − 802 kJ + ( − 88 kJ )
Δ H r x n = − 802 kJ − 88 kJ = − 890 kJ
Final Answer Therefore, the equation to calculate Δ H r x n for the target equation is:
Δ H r x n = − 802 kJ + ( − 88 kJ ) = − 890 kJ
The enthalpy change for the reaction C H 4 ( g ) + 2 O 2 ( g ) → C O 2 ( g ) + 2 H 2 O ( l ) is − 890 kJ .
Examples
Hess's Law is useful in many real-world applications, such as calculating the energy released or absorbed in complex chemical reactions. For example, in industrial processes, chemists often need to determine the enthalpy change for reactions that are difficult to measure directly. By breaking down the reaction into a series of simpler steps with known enthalpy changes, they can calculate the overall enthalpy change using Hess's Law. This helps in designing efficient and safe chemical processes, optimizing energy usage, and predicting the stability of chemical compounds. Understanding Hess's Law allows engineers to optimize combustion processes in engines, design efficient heating systems, and develop new materials with specific energy properties.
To find the enthalpy change (b4H_{rxn}) for the reaction C H 4 ( g ) + 2 O 2 ( g ) → C O 2 ( g ) + 2 H 2 O ( l ) , apply Hess's Law. Combine the given reactions and sum their enthalpy changes: b4H_{rxn} = -802 \text{ kJ} + (-88 \text{ kJ}) = -890 \text{ kJ} . Hence, the overall change is -890 kJ, indicating an exothermic reaction.
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