9.93 - Chemistry: Molecular Nature Of Matter And Change

Question

Heats of reaction calculated from bond energies and from heats of formation are often, but not always, close to each other.

a) Industrial ethanol (${\mathbf{CH}}_3{\mathbf{CH}}_2\mathbf{OH}$ ) is produce by a catalytic reaction of ethylene (${\mathbf{H}}_2\mathbf{C}\mathbf{=}{\mathbf{CH}}_2$ ) with water at high pressure and temperatures. Calculate ${{\mathbf{\Delta H}}^o}_{\mathrm{rx}}$  for this gas-phase hydration of ethylene to ethanol, using bond energies and then using heats of formation.

b) ethylene glycol is produced by the catalytic oxidation of ethylene to ethylene oxide, which then reacts with water to form ethylene glycol:

 

The ${{\mathbf{\Delta H}}^o}_{\mathrm{rx}}$  for this hydrolysis step, based on heat of formation, is -97kJ/mol. Calculate ${{\mathbf{\Delta H}}^o}_{\mathrm{rx}}$  for the hydrolysis using bond energies.

c) why are two values relatively close for the hydration in part (a) but not close for the hydrolysis in part(b).

Step-by-Step Solution

Answer

  a) ${{\mathbf{\Delta H}}^o}_{\mathrm{rx}}$for gas-phase hydration of ethylene to ethanol, using bond energies is –

    37kJ and  ${{\mathbf{\Delta H}}^o}_{\mathrm{rx}}$   for gas-phase hydration of ethylene to ethanol, using heats of 

    formation is -42kJ.

b) ${{\mathbf{\Delta H}}^o}_{\mathrm{rx}}$  for the hydrolysis of ethylene oxide using bond energies is 347kJ.

c) The calculated value of ${{\mathbf{\Delta H}}^o}_{\mathrm{rx}}$   (-42kJ) is not the enthalpy of the formation of ethyl alcohol because the reaction does not involve the formation of ethyl alcohol from its constituent elements but using bond energies the value of heat of reaction is -37kJ which is nearly equal to the heat of formation. It is given that the enthalpy of formation of ethylene glycol is -92kJ/mol, and the calculated value of heat of formation from bond energies is 347kJ.

Definition

Bond energy is a measure of the bond strength of a chemical bond and is the amount of energy needed to break the atoms involved in a molecular bond into free atoms.

 

The amount of heat absorbed or evolved when one mole of a compound is formed from its constituent elements is called heat of formation.

ΔH o rx for ethyl alcohol

bond energies

C-H        413kJ/mol

C-O        358kJ/mol

O-H        467kJ/mol

C=C       614kJ/mol

C-C        347kJ/mol

 

Industrial ethanol is produced by a catalytic reaction of ethylene with water at high pressure and temperatures.

 ${\mathbf{CH}}_2\mathbf{=}{\mathbf{CH}}_2\mathbf{+}{\mathbf{H}}_2\mathbf{O}\to {\mathbf{C}}_2{\mathbf{H}}_5\mathbf{OH}$

  

Calculation of heat of reaction using bond energies:

$\begin{array}{c}\\ {{\mathbf{\Delta H}}^o}_{\mathrm{rx}}\mathbf{=}\mathbf{[}\mathbf{4}\mathbf{\times }\mathbf{B}{\mathbf{E}}_{C-H}\mathbf{+}\mathbf{1}\mathbf{\times }{\mathbf{BE}}_{C=C}\mathbf{+}\mathbf{2}\mathbf{\times }{\mathbf{BE}}_{O-H}\mathbf{]}\mathbf{+}\mathbf{[}\mathbf{5}\mathbf{\times }\mathbf{B}{\mathbf{E}}_{C-H}\mathbf{+}\mathbf{1}\mathbf{\times }{\mathbf{BE}}_{C-C}\mathbf{+}\mathbf{1}\mathbf{\times }{\mathbf{BE}}_{C-O}\mathbf{+}\mathbf{1}\mathbf{\times }{\mathbf{BE}}_{O-H}\mathbf{]}\\ \text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}}\mathbf{=}\mathbf{[}\mathbf{4}\mathbf{mol}\mathbf{\times }\mathbf{413}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{+}\mathbf{1}\mathbf{mol}\mathbf{\times }\mathbf{614}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{+}\mathbf{2}\mathbf{mol}\mathbf{\times }\mathbf{467}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{]}\mathbf{+}\\ \mathbf{[}\mathbf{5}\mathbf{mol}\mathbf{\times }\mathbf{(}\mathbf{-}\mathbf{413}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{)}\mathbf{+}\mathbf{1}\mathbf{mol}\mathbf{\times }\mathbf{(}\mathbf{-}\mathbf{347}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{)}\mathbf{+}\\ \mathbf{1}\mathbf{mol}\mathbf{\times }\mathbf{(}\mathbf{-}\mathbf{358}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{)}\mathbf{+}\mathbf{1}\mathbf{mol}\mathbf{\times }\mathbf{(}\mathbf{-}\mathbf{467}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{)}\mathbf{]}\\ \mathbf{=}\mathbf{3200}\mathbf{+}\mathbf{(}\mathbf{-}\mathbf{3237}\mathbf{)}\\ \mathbf{=}\mathbf{-}\mathbf{37}\mathbf{kJ}\end{array}$  

 

Calculation of heat of reaction using the heat of formation:

The heat of combustion of ethanol and ethylene is as follows;

 $\begin{array}{l}{\mathbf{C}}_2{\mathbf{H}}_5\mathbf{OH}\mathbf{+}{\mathbf{O}}_2\to \mathbf{2}{\mathbf{CO}}_2\mathbf{+}\mathbf{3}{\mathbf{H}}_2\mathbf{O}{\mathbf{\Delta H}}^o\mathbf{=}\mathbf{-}\mathbf{1368}\mathbf{kJ}.......\mathbf{\left(}\mathbf{1}\mathbf{\right)}\\ {\mathbf{C}}_2{\mathbf{H}}_4\mathbf{+}{\mathbf{O}}_2\to \mathbf{2}{\mathbf{CO}}_2\mathbf{+}\mathbf{2}{\mathbf{H}}_2\mathbf{O}\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.17em}\hspace{0.17em}}{\mathbf{\Delta H}}^o\mathbf{=}\mathbf{-}\mathbf{1410}\mathbf{kJ}.......\mathbf{\left(}\mathbf{2}\mathbf{\right)}\\ \end{array}$

Reverse equation (1) and add to equation (2) we get an equation 

 

ΔH o rx for ethylene glycol

Calculation of heat of reaction using bond energies:

In the formation of ethylene glycol from ethylene oxide, bonds of reactants are 4 C-H, 1 C-C, 2 C-O and 2O-H and bonds of product is 4 C-H, 2O-H, 2C-O and 1 C-C. 

 

$\begin{array}{l}{\mathbf{\Delta H}}^o\mathbf{=}\mathbf{[}\mathbf{4}\mathbf{\times }\mathbf{B}{\mathbf{E}}_{C-H}\mathbf{+}\mathbf{1}\mathbf{\times }{\mathbf{BE}}_{C-C}\mathbf{+}\mathbf{2}\mathbf{\times }{\mathbf{BE}}_{C-O}\mathbf{+}\mathbf{2}\mathbf{\times }{\mathbf{BE}}_{O-H}\mathbf{]}\mathbf{+}\mathbf{[}\mathbf{4}\mathbf{\times }\mathbf{B}{\mathbf{E}}_{C-H}\mathbf{+}\mathbf{2}\mathbf{\times }{\mathbf{BE}}_{O-H}\mathbf{+}\mathbf{2}\mathbf{\times }{\mathbf{BE}}_{C-O}\mathbf{+}\mathbf{1}\mathbf{\times }{\mathbf{BE}}_{C-C}\mathbf{]}\\ \mathbf{=}\mathbf{[}\mathbf{4}\mathbf{mol}\mathbf{\times }\mathbf{413}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{+}\mathbf{2}\mathbf{mol}\mathbf{\times }\mathbf{347}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{+}\mathbf{2}\mathbf{mol}\mathbf{\times }\mathbf{358}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{+}\mathbf{2}\mathbf{\times }\mathbf{467}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{]}\mathbf{+}\\ \mathbf{[}\mathbf{4}\mathbf{mol}\mathbf{\times }\mathbf{(}\mathbf{-}\mathbf{413}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{)}\mathbf{+}\mathbf{2}\mathbf{\times }\mathbf{(}\mathbf{-}\mathbf{467}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{)}\mathbf{+}\mathbf{2}\mathbf{mol}\mathbf{\times }\mathbf{(}\mathbf{-}\mathbf{358}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{)}\\ \mathbf{+}\mathbf{1}\mathbf{mol}\mathbf{\times }\mathbf{(}\mathbf{-}\mathbf{347}\mathbf{kJ}\mathbf{/}\mathbf{mol}\mathbf{)}\mathbf{]}\\ \mathbf{=}\mathbf{3996}\mathbf{+}\mathbf{(}\mathbf{-}\mathbf{3649}\mathbf{)}\\ \mathbf{=}\mathbf{347}\mathbf{kJ}\end{array}$