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)$[/tex]
What is [tex]$\Delta H_{ rxn }[/tex] for the overall reaction?
Answer (2)
Add the two given chemical equations to obtain the target equation.
Add the corresponding enthalpy changes: Δ H r x n = Δ H 1 + Δ H 2 = − 802 k J + ( − 88 k J ) .
Calculate the numerical value of Δ H r x n = − 890 k J .
The enthalpy change for the overall reaction is − 890 kJ.
Explanation
Problem Analysis We are given two chemical equations and their corresponding enthalpy changes, Δ H 1 and Δ H 2 . Our goal is to find the enthalpy change, Δ H r x n , for the overall reaction. We can achieve this by adding the two given equations together, which means we also add their enthalpy changes.
Combining Equations and Enthalpy Changes The first equation is: C H 4 ( g ) + 2 O 2 ( g ) → C O 2 ( g ) + 2 H 2 O ( g ) Δ H 1 = − 802 kJ The second equation is: 2 H 2 O ( g ) → 2 H 2 O ( l ) Δ H 2 = − 88 kJ Adding these two equations gives us the target equation: C H 4 ( g ) + 2 O 2 ( g ) → C O 2 ( g ) + 2 H 2 O ( l ) To find the overall enthalpy change, we add the individual enthalpy changes: Δ H r x n = Δ H 1 + Δ H 2
Calculating the Overall Enthalpy Change Now, we substitute the given values of Δ H 1 and Δ H 2 into the equation: Δ H r x n = − 802 kJ + ( − 88 kJ ) Calculating the sum: Δ H r x n = − 802 kJ − 88 kJ = − 890 kJ
Final Answer Therefore, the enthalpy change for the overall reaction is -890 kJ.
Examples
Enthalpy changes are crucial in many real-world applications, such as designing efficient combustion engines or understanding the energy balance in chemical reactors. For example, when designing a new type of fuel, engineers need to know the enthalpy change of the combustion reaction to predict how much energy will be released. This information helps them optimize the fuel composition and engine design for maximum efficiency and minimal environmental impact. Similarly, in industrial chemistry, understanding enthalpy changes allows chemists to control reaction conditions to maximize product yield and minimize energy consumption, leading to more sustainable and cost-effective processes.
The overall reaction's enthalpy change [ Δ H r x n ] can be calculated by summing the enthalpy changes of the two given chemical equations. This results in a total of [ − 890 kJ ] for the reaction [{ C H 4 ( g ) + 2 O 2 ( g ) → C O 2 ( g ) + 2 H 2 O ( l ) }].
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