Using Hess’s Law to Calculate ΔH" Methane, the main constituent of natural gas, burns in oxygen to yield carbon dioxide and water: CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(l) Use the following information to calculate ΔH° in kilojoules for the combustion of methane: CH4(g) + O2(g) → CH2O(g) + H2O(g)

Question

Using Hess’s Law to Calculate ΔHº

Methane, the main constituent of natural gas, burns in oxygen to yield carbon dioxide and water:

[latex]CH_4(g) + 2 O_2(g) → CO_2(g) + 2 H_2O[/latex] (l)

Use the following information to calculate ΔH° in kilojoules for the combustion of methane:

[latex]CH_4(g) + O_2(g) → CH_2O(g) + H_2O[/latex] (g) ΔH° = -275.6 kJ

[latex]CH_2O(g) + O_2(g) → CO_2(g) + H_2O[/latex](g) ΔH° = -526.7 kJ

[latex]H_2O(l) → H_2O[/latex](g) ΔH° = +44.0 kJ

STRATEGY

It often takes some trial and error, but the idea is to combine the individual reactions so that their sum is the desired reaction. The important points are that:

• All the reactants [[latex]CH_4(g) and \ O_2[/latex](g)] must appear on the left.

• All the products [[latex]CO_2(g) \ and \ H_2O[/latex](l)] must appear on the right.

• All intermediate products [[latex]CH_2O(g) \ and \ H_2O[/latex](g)] must occur on both the left and the right so that they cancel.

• A reaction written in the reverse of the direction given [[latex]H_2O(g) \ \rightarrow \ H_2O[/latex](l)] must have the sign of its ΔH° reversed (Section 8.7).

• If a reaction is multiplied by a coefficient [[latex]H_2O(g) \ \rightarrow H_2O[/latex](l) is multiplied by 2], then ΔH° for the reaction must be multiplied by that same coefficient.

Accepted Answer

[latex]\begin{matrix} \begin{aligned} \mathrm{CH}_4(g)+\mathrm{O}_2(g) \longrightarrow \cancel{CH_2O (g)} +\cancel{H_2O(g)} \quad \Delta H^{\circ}=-275.6 \mathrm{~kJ} \ \cancel{CH_2O(g)}+\mathrm{O}_2(g) \longrightarrow \mathrm{CO}_2(g)+\cancel{H_2O(g)} \quad \Delta H^{\circ}=-526.7 \mathrm{~kJ} \ 2\left[\cancel{H_2O(g)} \longrightarrow \mathrm{H}_2 \mathrm{O}(l) ight] \quad 2\left[\Delta H^{\circ}=-44.0 \mathrm{~kJ} ight]=-88.0 \mathrm{~kJ} \end{aligned} \ \hline \begin{aligned} \mathrm{CH}_4(g)+2 \mathrm{O}_2(g) \longrightarrow \mathrm{CO}_2(g)+2 \mathrm{H}_2 \mathrm{O}(l) \quad \Delta H^{\circ}=-890.3 \mathrm{~kJ} \end{aligned} \end{matrix} [/latex]

Question 8.6: Using Hess’s Law to Calculate ΔH" Methane, the main constitu......

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