The ring of tert-butylchlorocyclohexane is locked with the tert-butyl group equatorial. With $(\mathrm{CH}{}_3){}_3\mathrm{COK}$ in $(\mathrm{CH}{}_3){}_3\mathrm{COH}$ at 298 K, the second-order E2 rate constants are $3.0\times 10^{-3}$ for the cis-1-tert-butyl-4-chlorocyclohexane and $4.0\times 10^{-6}\mathrm{L}\mathrm{mo}{\mathrm{l}}^{-1}{\mathrm{s}}^{-1}$ for the trans isomer. With $R=8.314\mathrm{J}\mathrm{mo}{\mathrm{l}}^{-1}{\mathrm{K}}^{-1}$, which statement is correct?

1. AThe cis isomer reacts faster because its chlorine is equatorial; $\Delta \Delta G^{‡}\approx 1.64\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$
2. BThe cis isomer reacts faster because its chlorine is axial in the locked chair; $\Delta \Delta G^{‡}\approx 16.4\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$
3. CThe cis isomer reacts faster because its chlorine is axial; $\Delta \Delta G^{‡}\approx 7.1\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$
4. DThe trans isomer reacts faster because its chlorine is axial; $\Delta \Delta G^{‡}\approx 16.4\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$