Q9.92CP - Chemistry: Molecular Nature Of Matter And Change

Question

Dimethyl ether (${\mathbf{CH}}_3{\mathbf{OCH}}_3$ ) and ethanol (${\mathbf{CH}}_3{\mathbf{CH}}_2\mathbf{OH}$ ) are constitutional isomers.

a) Calculate ${{\mathbf{\Delta H}}^o}_{\mathrm{rx}}$  for the formation of each compound as a gas from methane and oxygen; water vapor forms. 

b) state which reaction is more exothermic.

c) calculate ${{\mathbf{\Delta H}}^o}_{\mathrm{rx}}$  for the conversion of ethanol to dimethyl ether

Step-by-Step Solution

Answer

a) ${{\mathbf{\Delta H}}^o}_{\mathrm{rx}}$  in the formation of dimethyl ether is $\mathbf{-}\mathbf{326}\mathbf{ }\mathit{k}\mathit{J}$  and for the formation of ethanol is $\mathbf{-}\mathbf{369}\mathbf{kJ}$

     

b) formation of ethanol from ethane and oxygen is more exothermic.

c)   ${{\mathbf{\Delta H}}^o}_{\mathrm{rx}}$  for the conversion of ethanol from methanol is  $\mathbf{-}\mathbf{315}\mathbf{kJ}$. 

Calculation of ΔH o rx

${{\mathbf{\Delta H}}^o}_{\mathrm{rx}}$  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.

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

  

 

Bond energies 

 $\mathbf{C}\mathbf{-}\mathbf{H}\mathbf{413}\mathbf{kJ}\mathbf{/}\mathbf{mol}$

  $\mathbf{O}\mathbf{-}\mathbf{H}\mathbf{467}\mathbf{kJ}\mathbf{/}\mathbf{mol}$

  $\mathbf{C}\mathbf{-}\mathbf{O}\mathbf{358}\mathbf{kJ}\mathbf{/}\mathbf{mol}$

 $\mathbf{O}\mathbf{=}\mathbf{O}\mathbf{498}\mathbf{kJ}\mathbf{/}\mathbf{mol}$

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

 

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

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

 

 

 

 

Formation of ethanol from methane and oxygen.

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

 $\begin{array}{l}{{\mathbf{\Delta H}}^o}_{\mathrm{rx}}\mathbf{=}{{\mathbf{\Delta H}}^o}_{\mathbf{bonds}\mathbf{broken}}\mathbf{+}{{\mathbf{\Delta H}}^o}_{\mathbf{bonds}\text{\hspace{0.33em}}\mathbf{formation}}\\ \mathbf{=}\mathbf{[}\mathbf{8}\mathbf{\times }\mathbf{B}{\mathbf{E}}_{C-H}\mathbf{+}\mathbf{1}\mathbf{\times }{\mathbf{BE}}_{O=O}\mathbf{]}\mathbf{+}\mathbf{[}\mathbf{5}\mathbf{\times }\mathbf{B}{\mathbf{E}}_{C-H}\mathbf{+}\mathbf{1}\mathbf{\times }{\mathbf{BE}}_{C-C}\mathbf{+}\mathbf{1}\mathbf{\times }{\mathbf{BE}}_{C-O}\mathbf{+}\mathbf{3}\mathbf{\times }{\mathbf{BE}}_{O-H}\mathbf{]}\\ \mathbf{=}\mathbf{[}\mathbf{8}\mathbf{mol}\mathbf{\times }\mathbf{413}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{+}\mathbf{1}\mathbf{mol}\mathbf{\times }\mathbf{498}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{]}\mathbf{+}\mathbf{[}\mathbf{5}\mathbf{mol}\mathbf{\times }\mathbf{-}\mathbf{413}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{+}\\ \text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}}\mathbf{1}\mathbf{mol}\mathbf{\times }\mathbf{-}\mathbf{347}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{+}\mathbf{1}\mathbf{mol}\mathbf{\times }\mathbf{-}\mathbf{358}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{+}\mathbf{3}\mathbf{mol}\mathbf{\times }\mathbf{-}\mathbf{467}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{]}\\ \mathbf{=}\mathbf{-}\mathbf{369}\mathbf{kJ}\end{array}$

 

exothermic

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 that involves the formation of ethanol from methane and oxygen is more exothermic.

Conversion of ethanol to dimethyl ether

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

 

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

Ethanol                dimethyl ether

$\begin{array}{l}{{\mathbf{\Delta H}}^o}_{\mathrm{rx}}\mathbf{=}{{\mathbf{\Delta H}}^o}_{\mathbf{bonds}\mathbf{broken}}\mathbf{+}{{\mathbf{\Delta H}}^o}_{\mathbf{bonds}\mathbf{formation}}\\ \mathbf{=}\mathbf{[}\mathbf{5}\mathbf{\times }\mathbf{B}{\mathbf{E}}_{C-H}\mathbf{+}\mathbf{1}\mathbf{\times }{\mathbf{BE}}_{C-C}\mathbf{+}\mathbf{1}\mathbf{\times }{\mathbf{BE}}_{O-H}\mathbf{]}\mathbf{+}\mathbf{[}\mathbf{6}\mathbf{\times }\mathbf{B}{\mathbf{E}}_{C-H}\mathbf{+}\mathbf{2}\mathbf{\times }{\mathbf{BE}}_{C-O}\mathbf{]}\\ \text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}}\mathbf{=}\mathbf{[}\mathbf{5}\mathbf{mol}\mathbf{\times }\mathbf{413}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{+}\mathbf{1}\mathbf{mol}\mathbf{\times }\mathbf{347}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{+}\mathbf{1}\mathbf{mol}\mathbf{\times }\mathbf{467}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{]}\mathbf{+}\\ \mathbf{[}\mathbf{6}\mathbf{mol}\mathbf{\times }\mathbf{(}\mathbf{-}\mathbf{413}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{)}\mathbf{+}\mathbf{2}\mathbf{\times }\mathbf{(}\mathbf{-}\mathbf{358}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{)}\\ \mathbf{=}\mathbf{[}\mathbf{2879}\mathbf{-}\mathbf{3194}\mathbf{]}\mathbf{kJ}\\ \mathbf{=}\mathbf{-}\mathbf{315}\mathbf{kJ}\end{array}$