Question

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

a) First imagine the process of converting a mole of methane intoits elemental constituents (graphite and hydrogen gas). Use thedata at the back of this book to find ΔH for this process.
b) Now imagine forming a mole of CO2 and two molesof water vapor from their elemental constituents. Determine ΔHfor this process.
c)What is ΔH for the actual reaction in which methane andoxygen form carbon dioxide and water vapor directly? Explain.
d) How much heat is given off during this reaction, assuming thatno "other" forms of work are done?
e) What is the change in the system's energy during this reaction?How would your answer differ if the H2O ended up asliquid water instead of vapor?
f) The sun has a mass of 2x1030 kg and gives off energyat a rate of 3.9x1026 watts. If the source of the sun'senergy were ordinary combustion of a chemical fuel such as methane,about how long could it last?
Answers are:
but please help me to understand the mathimaticalprocess--it's more important than the answers.

Answer 1

Main Answer

The actual reaction in which methane and oxygen form carbon dioxide and water vapor directly has a ΔH of -890.3 kJ/mol.

Explanation

To find the ΔH for the conversion of a mole of methane into its elemental constituents, we can use the data provided at the back of the book:

C(s, graphite) + 2e- ⇄ C(s, graphite) + 4e-

ΔH = -393.5 kJ/mol

ΔH = -571.7 kJ/mol

Combining these two reactions, we get:

ΔH = -890.3 kJ/mol

To find the ΔH for forming a mole of carbondioxide and two moles of water vapor from their elemental constituents, we can use the following reactions:

ΔH = -393.5 kJ/mol

ΔH = +40.7 kJ/mol (endothermic process)

Combining these two reactions, we get:

ΔH = -393.5 kJ/mol - (8)(40.7 kJ/mol) = -1036.1 kJ/mol (vaporization of water is an endothermic process, so it decreases the overall enthalpy change for this reaction.)

The actual reaction in which methane and oxygen form carbon dioxide and water vapor directly has a smaller enthalpy change than forming carbandioxide and water vapor from their elemental constituents because the water in the actual reaction is formed as a gas (water vapor), whereas in the second reaction it is formed as a liquid (liquid water).

This means that more energy is required to vaporize the water in the second reaction, which decreases the overall enthalpy change for that reaction.

In other words, forming carbondioxide and water vapor directly from methane and oxygen is a more exothermic process than forming them separately and then combining them.