91Ó°ÊÓ

${{\mathbf{Δ\pm á}}^o}_{\mathrm{rx}}$ can be calculated by the addition of bond energies of a bond broken and bond formed.

Firstly, we write the chemical reaction of the formation of dimethyl ether from methane and oxygen.

$\mathbf{2}{\mathbf{CH}}_4\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}{\mathbf{O}}_2\mathbf{\left(}\mathbf{g}\mathbf{\right)}→{\mathbf{CH}}_3{\mathbf{OCH}}_3\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}{\mathbf{H}}_2\mathbf{O}\mathbf{\left(}\mathbf{g}\mathbf{\right)}$

Bond energies

$\mathbf{C}\mathbf{-}\mathbf{H}\text{ â¶Ä„â¶Ä„}\mathbf{413}\mathbf{kJ}\mathbf{/}\mathbf{mol}$

$\mathbf{O}\mathbf{-}\mathbf{H}\text{ â¶Ä‰â¶Ä„}\mathbf{467}\mathbf{kJ}\mathbf{/}\mathbf{mol}$

$\mathbf{C}\mathbf{-}\mathbf{O}\text{ â¶Ä‰â¶Ä‰â¶Ä‰}\mathbf{358}\mathbf{kJ}\mathbf{/}\mathbf{mol}$

$\mathbf{O}\mathbf{=}\mathbf{O}\text{ â¶Ä„}\mathbf{498}\mathbf{kJ}\mathbf{/}\mathbf{mol}$

$\begin{array}{l}{{\mathbf{Δ\pm á}}^o}_{\mathrm{rx}}\mathbf{=}{{\mathbf{Δ\pm á}}^o}_{\mathbf{bonds}\text{ }\mathbf{broken}}\mathbf{+}{{\mathbf{Δ\pm á}}^o}_{\mathbf{bonds}\text{ }\mathbf{formed}}\\ \mathbf{=}\mathbf{[}\mathbf{8}\mathbf{×}\mathbf{B}{\mathbf{E}}_{C-H}\mathbf{+}\mathbf{1}\mathbf{×}{\mathbf{BE}}_{O=O}\mathbf{]}\mathbf{+}\mathbf{[}\mathbf{6}\mathbf{×}\mathbf{B}{\mathbf{E}}_{C-H}\mathbf{+}\mathbf{2}\mathbf{×}{\mathbf{BE}}_{C-H}\mathbf{+}\mathbf{2}\mathbf{×}{\mathbf{BE}}_{C-O}\mathbf{+}\mathbf{2}\mathbf{×}{\mathbf{BE}}_{O-H}\mathbf{]}\end{array}$

$\begin{array}{l}=[8\mathrm{mol}×413\mathrm{kJ}/\mathrm{mol}+1\mathrm{mol}×498\mathrm{kJ}/\mathrm{mol}]+[6\mathrm{mol}×-413\mathrm{kJ}/\mathrm{mol}+2×-358\mathrm{kJ}/\mathrm{mol}+\\ 2\mathrm{mol}×467\mathrm{kJ}/\mathrm{mol}]\end{array}$

$\mathbf{=}\mathbf{-}\mathbf{326}\mathbf{kJ}$

Formation of ethanol from methane and oxygen.

$\mathbf{2}{\mathbf{CH}}_4\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}{\mathbf{O}}_2\mathbf{\left(}\mathbf{g}\mathbf{\right)}→{\mathbf{CH}}_3{\mathbf{CH}}_2\mathbf{OH}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}{\mathbf{H}}_2\mathbf{O}\mathbf{\left(}\mathbf{g}\mathbf{\right)}$

$\begin{array}{l}{{\mathbf{Δ\pm á}}^o}_{\mathrm{rx}}\mathbf{=}{{\mathbf{Δ\pm á}}^o}_{\mathbf{bonds}\text{ }\mathbf{broken}}\mathbf{+}{{\mathbf{Δ\pm á}}^o}_{\mathbf{bonds}\text{​â¶Ä„}\mathbf{formation}}\\ \text{ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„}\mathbf{=}\mathbf{[}\mathbf{8}\mathbf{×}\mathbf{B}{\mathbf{E}}_{C-H}\mathbf{+}\mathbf{1}\mathbf{×}{\mathbf{BE}}_{O=O}\mathbf{]}\mathbf{+}\mathbf{[}\mathbf{5}\mathbf{×}\mathbf{B}{\mathbf{E}}_{C-H}\mathbf{+}\mathbf{1}\mathbf{×}{\mathbf{BE}}_{C-C}\mathbf{+}\mathbf{1}\mathbf{×}{\mathbf{BE}}_{C-O}\mathbf{+}\mathbf{3}\mathbf{×}{\mathbf{BE}}_{O-H}\mathbf{]}\\ \text{ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„}\mathbf{=}\mathbf{[}\mathbf{8}\mathbf{mol}\mathbf{×}\mathbf{413}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{+}\mathbf{1}\mathbf{mol}\mathbf{×}\mathbf{498}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{]}\mathbf{+}\mathbf{[}\mathbf{5}\mathbf{mol}\mathbf{×}\mathbf{-}\mathbf{413}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{+}\\ \text{ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ ​}\mathbf{1}\mathbf{mol}\mathbf{×}\mathbf{-}\mathbf{347}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{+}\mathbf{1}\mathbf{mol}\mathbf{×}\mathbf{-}\mathbf{358}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{+}\mathbf{3}\mathbf{mol}\mathbf{×}\mathbf{-}\mathbf{467}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{]}\\ \text{ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ }\mathbf{=}\mathbf{-}\mathbf{369}\mathbf{kJ}\end{array}$

An exothermic reaction is a reaction in which energy is released in the form of heat or light. Thus, in an exothermic reaction, energy is transferred into the surroundings rather than taking energy from the surroundings as in an endo thermic reaction.

In the formation of dimethyl ether, -326kJ amount of heat energy is released and in the formation of ethanol, -369kJ amount of heat energy is released. Since heat energy is released more in the formation of ethanol, a reaction thatinvolves the formation of ethanol from methane and oxygen is more exothermic.

Ethanol and dimethyl ether are isomers of each other with different functional groups and the same molecular formula.

${\mathbf{CH}}_3{\mathbf{CH}}_2\mathbf{OH}⇌{\mathbf{CH}}_3{\mathbf{OCH}}_3$

Ethanol dimethyl ether

$\begin{array}{l}{{\mathbf{Δ\pm á}}^o}_{\mathrm{rx}}\mathbf{=}{{\mathbf{Δ\pm á}}^o}_{\mathbf{bonds}\text{ }\mathbf{broken}}\mathbf{+}{{\mathbf{Δ\pm á}}^o}_{\mathbf{bonds}\text{ }\mathbf{formation}}\\ \text{ â¶Ä„â¶Ä„ â¶Ä‰â¶Ä„â¶Ä„â¶Ä„}\mathbf{=}\mathbf{[}\mathbf{5}\mathbf{×}\mathbf{B}{\mathbf{E}}_{C-H}\mathbf{+}\mathbf{1}\mathbf{×}{\mathbf{BE}}_{C-C}\mathbf{+}\mathbf{1}\mathbf{×}{\mathbf{BE}}_{O-H}\mathbf{]}\mathbf{+}\mathbf{[}\mathbf{6}\mathbf{×}\mathbf{B}{\mathbf{E}}_{C-H}\mathbf{+}\mathbf{2}\mathbf{×}{\mathbf{BE}}_{C-O}\mathbf{]}\\ \text{ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„​​â¶Ä„â¶Ä„}\mathbf{=}\mathbf{[}\mathbf{5}\mathbf{mol}\mathbf{×}\mathbf{413}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{+}\mathbf{1}\mathbf{mol}\mathbf{×}\mathbf{347}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{+}\mathbf{1}\mathbf{mol}\mathbf{×}\mathbf{467}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{]}\mathbf{+}\\ \text{ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„}\mathbf{[}\mathbf{6}\mathbf{mol}\mathbf{×}\mathbf{(}\mathbf{-}\mathbf{413}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{)}\mathbf{+}\mathbf{2}\mathbf{×}\mathbf{(}\mathbf{-}\mathbf{358}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{)}\\ \text{ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„}\mathbf{=}\mathbf{[}\mathbf{2879}\mathbf{-}\mathbf{3194}\mathbf{]}\mathbf{kJ}\\ \text{ â¶Ä„â¶Ä„ â¶Ä„â¶Ä„ â¶Ä„}\mathbf{=}\mathbf{-}\mathbf{315}\mathbf{kJ}\end{array}$