Consider the chemical equations shown here.
[tex]
\begin{array}{l}
NO(g)+O_3(g) \rightarrow NO_2(g)+O_2(g) \Delta H_1=-198.9 kJ \\
\frac{3}{2} O_2(g) \rightarrow O_3(g) \Delta H_2=142.3 kJ \\
O(g) \rightarrow \frac{1}{2} O_2(g) \Delta H_3=-247.5 kJ
\end{array}
[/tex]
What is [tex]$\Delta H_{\text {rxn }}$[/tex] for the reaction shown below?
[tex]$NO(g)+O(g) \rightarrow NO_2(g)$[/tex]
Answer (2)
Apply Hess's Law to find the enthalpy change for the target reaction.
Reverse the second equation and keep the first and third equations as is.
Add the enthalpy changes of the manipulated equations: Δ H r x n = Δ H 1 − Δ H 2 + Δ H 3 .
Calculate the enthalpy change: Δ H r x n = − 198.9 k J − 142.3 k J − 247.5 k J = − 588.7 k J .
Explanation
Problem Analysis and Strategy We are given three chemical equations with their corresponding enthalpy changes, and we want to find the enthalpy change for the reaction NO ( g ) + O ( g ) r i g h t a rro wN O 2 ( g ) . We will use Hess's Law, which states that the enthalpy change for a reaction is the same whether it occurs in one step or in multiple steps. Therefore, we can manipulate the given equations to obtain the target reaction and then add their enthalpy changes to find the enthalpy change for the target reaction.
Listing Given Equations The given equations are:
NO ( g ) + O 3 ( g ) r i g h t a rro wN O 2 ( g ) + O 2 ( g ) \trianle H 1 = − 198.9 k J
2 3 O 2 ( g ) r i g h t a rro w O 3 ( g ) \trianle H 2 = 142.3 k J
O ( g ) r i g h t a rro w 2 1 O 2 ( g ) \trianle H 3 = − 247.5 k J
Our target reaction is:
NO ( g ) + O ( g ) r i g h t a rro wN O 2 ( g )
Manipulating Equations We need to manipulate the given equations to match the target reaction. We can keep equation (1) as is, reverse equation (2), and keep equation (3) as is. This gives us:
NO ( g ) + O 3 ( g ) r i g h t a rro wN O 2 ( g ) + O 2 ( g ) \trianle H 1 = − 198.9 k J
O 3 ( g ) r i g h t a rro w 2 3 O 2 ( g ) − \trianle H 2 = − 142.3 k J
O ( g ) r i g h t a rro w 2 1 O 2 ( g ) \trianle H 3 = − 247.5 k J
Adding these equations together, we get:
NO ( g ) + O 3 ( g ) + O 3 ( g ) + O ( g ) r i g h t a rro wN O 2 ( g ) + O 2 ( g ) + 2 3 O 2 ( g ) + 2 1 O 2 ( g )
Combining the Equations However, this is not quite the target reaction. Notice that if we cancel O 3 from the left side of equation 1 with O 3 from the right side of the reversed equation 2, we get 2 3 O 2 on the right side. Also, notice that 2 1 O 2 + O 2 = 2 3 O 2 . So, the equation becomes:
NO ( g ) + O ( g ) r i g h t a rro wN O 2 ( g )
Calculating Enthalpy Change Now, we add the enthalpy changes for the manipulated equations:
\trianle H r x n = \trianle H 1 − \trianle H 2 + \trianle H 3 = − 198.9 k J − 142.3 k J + ( − 247.5 k J ) = − 588.7 k J
Final Answer Therefore, the enthalpy change for the reaction NO ( g ) + O ( g ) r i g h t a rro wN O 2 ( g ) is − 588.7 k J .
Examples
Hess's Law is useful in determining the enthalpy change of a reaction that cannot be measured directly. For example, if you want to find the enthalpy change for the formation of a compound from its elements, but the reaction is too slow or produces unwanted side products, you can use Hess's Law to calculate the enthalpy change from a series of reactions that can be measured. This is commonly used in industrial processes to optimize reaction conditions and improve efficiency.
By applying Hess's Law, we manipulated the given equations to derive the target reaction NO ( g ) + O ( g ) → N O 2 ( g ) . The calculated enthalpy change for this reaction is − 588.7 k J .
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