Chapter 1.6, Problem 50P

Consider the combustion of one mole of methane gas: $C{H}_4\left(gas\right) +2O_2\left(gas\right)\to C{O}_2\left(gas\right)+2H_{2}O\left(gas\right).$

The system is at standard temperature (298 K) and pressure (10⁵ Pa) both before and after the reaction.

1. First imagine the process of converting a mole of methane into its elemental consituents (graphite and hydrogen gas). Use the data at the back of this book to find ΔH for this process.
2. Now imagine forming a mole of $C{O}_2$ and two moles of water vapor from their elemental constituents. Determine $\Delta H$ for this process.
3. What is $\Delta H$ for the actual reaction in which methane and oxygen form carbon dioxide and water vapor directly? Explain.
4. How much heat is given off during this reaction, assuming that no “other” forms of work are done?
5. What is the change in the system’s energy during this reaction? How would your answer differ if the $H_{2}O$ ended up as liquid water instead of vapor?
6. The sun has a mass $2\times {10}^{30}kg$ and gives off energy at a rate $3.9\times {10}^{26}$ watts. If the source of the sun’s energy were ordinary combustion of a chemical fuel such as methane, about how long could it last?