The solvolysis of tert-butyl chloride (t-BuCl) in aqueous ethanol can yield two…

CHEMISTRY · Multi-part · AP · Chemistry · Thermodynamics and Electrochemistry · Thermodynamics and Electrochemistry

Problem

The solvolysis of tert-butyl chloride (t-BuCl) in aqueous ethanol can yield two alkene isomers, A and B, according to the simplified scheme t-BuCl

\to

A activation energy

E_a(A)

t-BuCl

\to

B activation energy

E_a(B)

Thermodynamic data (per mole of alkene) at

298\,\text{K}

are tabulated below.

	$\Delta H^\circ$ ( $\text{kJ mol}^{-1}$ )	$\Delta S^\circ$ ( $\text{J mol}^{-1}\,\text{K}^{-1}$ )
A	$-92$	$-155$
B	$-98$	$-170$

Additional kinetic information:

E_a(A)=45\,\text{kJ mol}^{-1}

and

E_a(B)=30\,\text{kJ mol}^{-1}

. Assume identical pre-exponential factors for both pathways and ideal behavior of all species. (a) Calculate

\Delta G^\circ

for formation of each alkene at

298\,\text{K}

. (b) Identify which alkene is thermodynamically more stable at

298\,\text{K}

and quantify the free-energy difference between the products. (c) Using the Arrhenius equation and the given activation energies, determine the ratio

k_B / k_A

of the rate constants at

298\,\text{K}

(assume equal pre-exponential factors). (d) The reaction is run at

298\,\text{K}

for

10\,\text{min}

and then quenched. Which alkene is expected to predominate in the crude product mixture? Justify your answer with reference to both your free-energy and rate calculations.

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