Chapter 18, Problem 18.122QP

Coal is used as a fuel in some electric-generating plants. Coal is a complex material, but for simplicity we may consider it to be a form of carbon. The energy that can be derived from a fuel is sometimes compared with the enthalpy of the combustion reaction:

$\text{C}(s)+{\text{O}}_2(g)\stackrel{}{\to }{\text{CO}}_2(g)$

Calculate the standard enthalpy change for this reaction at 25°C. Actually, only a fraction of the heat from this reaction is available to produce electric energy. In electric generating plants, this reaction is used to generate heat for a steam engine, which turns the generator. Basically the steam engine is a type of heat engine in which steam enters the engine at high temperature (T_h), work is done, and the steam then exits at a lower temperature (T_l). The maximum fraction, f, of heat available to produce useful energy depends on the difference between these temperatures (expressed in kelvins), f = (T_h − T_l)/T_h. What is the maximum heat energy available for useful work from the combustion of 1.00 mol of C(s) to CO₂(g)? (Assume the value of ΔH° calculated at 25°C for the heat obtained in the generator.) It is possible to consider more efficient ways to obtain useful energy from a fuel. For example, methane can be burned in a fuel cell to generate electricity directly. The maximum useful energy obtained in these cases is the maximum work, which equals the free-energy change. Calculate the standard free-energy change for the combustion of 1.00 mol of C(s) to CO₂(g). Compare this value with the maximum obtained with the heat engine described here.