The complete combustion of methane, \(\mathrm{CH}_{4}(g)\), to form \(\mathrm{H}_{2} \mathrm{O}(l)\) and \(\mathrm{CO}_{2}(g)\) at constant pressure releases \(890 \mathrm{~kJ}\) of heat per mole of \(\mathrm{CH}_{4}\). (a) Write a balanced thermochemical equation for this reaction. (b) Draw an enthalpy diagram for the reaction.

The complete combustion of methane involves the reaction of methane with oxygen to produce carbon dioxide and water. We start by writing the unbalanced equation: \( \mathrm{CH}_{4}(g) + \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) + \mathrm{H}_{2}\mathrm{O}(l) \) In order to balance the equation, we need to make sure that the number of atoms of each element on the reactant and product sides matches. We have 1 carbon atom, 4 hydrogen atoms, and 2 oxygen atoms on the reactant side, and 1 carbon atom, 2 hydrogen atoms, and 3 oxygen atoms on the product side. To balance the equation, we will perform the following steps: 1. Balance the hydrogen atoms by placing a coefficient of 2 in front of \(\mathrm{H}_{2}\mathrm{O}(l)\): \( \mathrm{CH}_{4}(g) + \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) + 2\mathrm{H}_{2}\mathrm{O}(l) \) 2. Balance the oxygen atoms by placing a coefficient of 2 in front of \(\mathrm{O}_{2}(g)\): \( \mathrm{CH}_{4}(g) + 2\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) + 2\mathrm{H}_{2}\mathrm{O}(l) \) Now that the chemical equation is balanced, we can include the enthalpy change information: \( \mathrm{CH}_{4}(g) + 2\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) + 2\mathrm{H}_{2}\mathrm{O}(l) \hspace{10mm} \Delta H = -890 \mathrm{~kJ} \)

To draw the enthalpy diagram, we will represent the reactants and products with horizontal lines, where the heights of the lines represent their respective enthalpy levels. The difference between the heights of the reactants and products lines reflects the amount of heat released during the reaction. 1. Label the y-axis as "Enthalpy, H". 2. Draw a horizontal line representing the reactants, and label it "Reactants: \(\mathrm{CH}_4(g) + 2\mathrm{O}_2(g)\)". 3. Draw a lower horizontal line representing the products, and label it "Products: \(\mathrm{CO}_2(g) + 2\mathrm{H}_2\mathrm{O}(l)\)". 4. Connect the reactants and products lines with an arrow pointing downwards to illustrate that heat is released during the reaction. 5. Label the arrow with the heat released: "\(\Delta H = -890 \mathrm{~kJ}\)". The enthalpy diagram should look like: [![Enthalpy Diagram][1]][1] [1]: https://i.stack.imgur.com/k5SRk.png