Calculate the enthalpy change for the reaction P4 O6(s)+2 O2(g) -⋯P4 O10(s) given the following

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Calculate the enthalpy change for the reaction P4 O6(s)+2...

Calculate the enthalpy change for the reaction $$ \mathrm{P}_{4} \mathrm{O}_{6}(s)+2 \mathrm{O}_{2}(g) \stackrel{-\cdots}{\mathrm{P}}_{4} \mathrm{O}_{10}(s) $$ given the following enthalpies of reaction: $$ \begin{array}{ll} \mathrm{P}_{4}(\mathrm{~s})+3 \mathrm{O}_{2}(g)-\mathrm{r} \rightarrow \mathrm{P}_{4} \mathrm{O}_{6}(s) & \Delta H=-1640.1 \mathrm{~kJ} \\ \mathrm{P}_{4}(s)+5 \mathrm{O}_{2}(g)-\cdots \mathrm{P}_{4} \mathrm{O}_{1} 0(s) & \Delta H=-2940.1 \mathrm{~kJ} \end{array} $$

Calculate the enthalpy change for the reaction
$$
\mathrm{P}_{4} \mathrm{O}_{6}(s)+2 \mathrm{O}_{2}(g) \stackrel{-\cdots}{\mathrm{P}}_{4} \mathrm{O}_{10}(s)
$$
given the following enthalpies of reaction:
$$
\begin{array}{ll}
\mathrm{P}_{4}(\mathrm{~s})+3 \mathrm{O}_{2}(g)-\mathrm{r} \rightarrow \mathrm{P}_{4} \mathrm{O}_{6}(s) & \Delta H=-1640.1 \mathrm{~kJ} \\
\mathrm{P}_{4}(s)+5 \mathrm{O}_{2}(g)-\cdots \mathrm{P}_{4} \mathrm{O}_{1} 0(s) & \Delta H=-2940.1 \mathrm{~kJ}
\end{array}
$$

Key Concepts

Hess's Law

Hess's Law is a principle in thermochemistry which states that if a reaction can be expressed as the sum of two or more other reactions, the overall enthalpy change for the reaction is the sum of the enthalpy changes of the individual steps. This is possible because enthalpy is a state function, meaning it depends only on the initial and final states of a reaction and not on the pathway taken between them.

Enthalpy as a State Function

Enthalpy is a thermodynamic quantity that represents the heat content of a system at constant pressure. Because it is a state function, the change in enthalpy for a process depends only on the initial and final states of the system, not on how the process occurs. This characteristic facilitates the calculation of reaction enthalpies by allowing complex reactions to be broken into simpler steps and then recombined.

Reaction Manipulation

Reaction manipulation involves reversing, scaling, or adding chemical equations in order to derive the overall reaction of interest. When equations are manipulated, their corresponding enthalpy changes must also be adjusted accordingly, for example, reversing a reaction changes the sign of its enthalpy change, and multiplying a reaction by a factor multiplies the enthalpy change by the same factor. This method is essential for applying Hess’s Law in the calculation of overall enthalpy changes.

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