Problem: Meals-ready-to-eat (MREs) are military meals that can be heated on a flameless heater. The heat is produced by the following reaction: Mg(s) + 2 H2O(l) → Mg(OH)2(s) + H2(g).Calculate the number of grams of Mg needed for this reaction to release enough energy to increase the temperature of 76 mL of water from 26˚C to 76˚C.

FREE Expert Solution

$\boxed{\mathbf{\Delta H}{\mathbf{°}}_{\mathbf{rxn}}\mathbf{=}\mathbf{\Delta H}{\mathbf{°}}_{\mathbf{f}\mathbf{,}\mathbf{ }\mathbf{prod}}\mathbf{-}\mathbf{\Delta H}{\mathbf{°}}_{\mathbf{f}\mathbf{,}\mathbf{ }\mathbf{react}}}$

$$\begin{gathered} \mathbf{\Delta H}{\mathbf{°}}_{\mathbf{rxn}}\mathbf{=}\left[\mathbf{(}\mathbf{1}\mathbf{ }\cancel{\mathbf{mol}\mathbf{ }\mathbf{Mg}{\mathbf{\left(}\mathbf{OH}\mathbf{\right)}}_{\mathbf{2}}}\mathbf{)}\left(\frac{\mathbf{-}\mathbf{924}\mathbf{.}\mathbf{5}\mathbf{ }\mathbf{kJ}}{\mathbf{1}\mathbf{ }\cancel{\mathbf{mol}\mathbf{ }\mathbf{Mg}{\mathbf{\left(}\mathbf{OH}\mathbf{\right)}}_{\mathbf{2}}}}\right)\mathbf{+}\mathbf{0}\right] \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{-}\left[\mathbf{0}\mathbf{+}\mathbf{(}\mathbf{2}\mathbf{ }\cancel{\mathbf{mol}\mathbf{ }{\mathbf{H}}_{\mathbf{2}}\mathbf{O}}\mathbf{)}\left(\frac{\mathbf{-}\mathbf{241}\mathbf{.}\mathbf{8}\mathbf{ }\mathbf{kJ}}{\mathbf{1}\mathbf{ }\cancel{\mathbf{mol}\mathbf{ }{\mathbf{H}}_{\mathbf{2}}\mathbf{O}}}\right)\right] \end{gathered}$$

$\mathbf{∆}{\mathbf{H}}_{\mathbf{rxn}}\mathbf{=}\mathbf{-}\mathbf{682}\mathbf{.}\mathbf{7}\mathbf{ }\frac{\cancel{\mathbf{kJ}}}{\mathbf{mol}}\mathbf{\times }\frac{{\mathbf{10}}^{\mathbf{3}}\mathbf{ }\mathbf{J}}{\mathbf{1}\mathbf{ }\cancel{\mathbf{kJ}}}$

ΔH˚_rxn = –6.827 × 10⁵ J/mol

$$\begin{gathered} \boxed{\mathbf{q}\mathbf{=}\mathbf{mc}\mathbf{∆}\mathbf{T}} \\ \mathbf{q}\mathbf{=}\mathbf{mc}(T_f-T_i) \end{gathered}$$