Consider the reaction between methane and oxygen producing...

Consider the reaction between methane and oxygen producing carbon dioxide and water. Suppose that the reaction is carried out in a furnace used to heat a house. If $q=-890 \mathrm{~kJ}$ and $w=+5 \mathrm{~kJ},$ what is $\Delta E ? \Delta H$ at $25^{\circ} \mathrm{C} ?$

Key Concepts

Internal Energy (?E) and the First Law of Thermodynamics

This concept states that the total change in a system's internal energy (?E) is the sum of the heat exchanged (q) and the work done (w) on or by the system. It is represented by ?E = q + w. In chemical reactions, this allows us to account for both thermal energy changes and energy transferred due to expansion or compression work.

Enthalpy (?H) in Constant Pressure Processes

Enthalpy is a thermodynamic state function that is especially useful when dealing with processes at constant pressure. Under these conditions, the change in enthalpy (?H) is equal to the heat exchanged with the surroundings (q_p). This links directly to practical scenarios like furnaces where reactions occur at atmospheric pressure.

Work and Sign Conventions in Thermodynamics

Work in thermodynamics is energy transferred by forces acting over distances, and its sign convention is critical: work done on the system is positive, while work done by the system is negative. Correctly applying these sign conventions ensures that the energy balance represented by the first law is accurately maintained.

Relationship Between ?E and ?H

The connection between internal energy (?E) and enthalpy (?H) is given by the relation ?H = ?E + ?(PV). For reactions at constant pressure, any contribution from pressure–volume work (often simplified to ?n_gas·RT for ideal gases) needs to be considered. If there is no change in the number of gas moles, this additional term vanishes, and ?H is nearly equal to ?E. Otherwise, the difference accounts for the work associated with gas expansion or compression.

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