Calculate the energy change for the reaction Mg(s)+N2(g)+3 O2(g) ⟶Mg^2(NO3)2(s) from the followi

step 1 We'll take our first equation, 2S solid plus 3O2 gas producing 2SO3 gas. Enthalpy here is minus

Calculate the energy change for the reaction Mg(s)+N2(g)+3...

Calculate the energy change for the reaction $\mathrm{Mg}(s)+\mathrm{N}_{2}(g)+3 \mathrm{O}_{2}(g) \longrightarrow \mathrm{Mg}^{2}\left(\mathrm{NO}_{3}\right)_{2}(s)$ from the following: (9.6) $$ \begin{array}{ll} 8 \mathrm{Mg}(s)+\mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}(s) \longrightarrow \mathrm{Mg}_{3} \mathrm{~N}_{2}(s)+6 \mathrm{MgO}(s) \\ & \Delta H=-3281 \mathrm{~kJ} \\ \mathrm{Mg}_{3} \mathrm{~N}_{2}(s) \longrightarrow 3 \mathrm{Mg}(s)+\mathrm{N}_{2}(g) & \Delta H=+461 \mathrm{~kJ} \\ 2 \mathrm{MgO}(s) \longrightarrow 2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) & \Delta H=+1204 \mathrm{~kJ} \end{array} $$

Calculate the energy change for the reaction
$\mathrm{Mg}(s)+\mathrm{N}_{2}(g)+3 \mathrm{O}_{2}(g) \longrightarrow \mathrm{Mg}^{2}\left(\mathrm{NO}_{3}\right)_{2}(s)$ from the following: (9.6)
$$
\begin{array}{ll}
8 \mathrm{Mg}(s)+\mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}(s) \longrightarrow \mathrm{Mg}_{3} \mathrm{~N}_{2}(s)+6 \mathrm{MgO}(s) \\
& \Delta H=-3281 \mathrm{~kJ} \\
\mathrm{Mg}_{3} \mathrm{~N}_{2}(s) \longrightarrow 3 \mathrm{Mg}(s)+\mathrm{N}_{2}(g) & \Delta H=+461 \mathrm{~kJ} \\
2 \mathrm{MgO}(s) \longrightarrow 2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) & \Delta H=+1204 \mathrm{~kJ}
\end{array}
$$

Key Concepts

Hess's Law

Hess's Law states that the total enthalpy change for a chemical reaction is the same, regardless of the pathway by which the reaction occurs. This principle allows one to calculate the enthalpy change for a reaction by combining the enthalpy changes of other reactions that add up to the overall reaction, even if those reactions occur in multiple steps.

Reaction Enthalpy

Reaction enthalpy refers to the heat absorbed or released during a chemical reaction at constant pressure. It is a key thermodynamic parameter that quantifies the energy change of a system during a reaction, and it is central to predicting the energetics and feasibility of chemical processes.

Thermochemical Equations

Thermochemical equations are chemical equations that explicitly include the enthalpy change associated with the reaction. They combine both the stoichiometric details of the reaction and the energetic information, allowing for the systematic analysis and combination of reactions to solve for unknown enthalpy changes.

Manipulation of Enthalpy Values

Manipulating enthalpy values involves reversing, scaling, and combining thermochemical equations according to stoichiometric requirements. When a chemical equation is reversed, the sign of its enthalpy change is also reversed; when it is multiplied by a coefficient, the enthalpy change must be multiplied by the same factor. This careful adjustment lets one determine the overall energy change for a target reaction from multiple known reactions.

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