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My book mentioned that the energy barrier for cyclohexane to reach the half-chair conformation is $50.6\ \mathrm{kJ\ mol^{-1}}$. It says that from this value, it was calculated that cyclohexane undergoes $10^5$ flips per second.

How did they calculate this? We can assume that all the conformational states possible will be of the same energy as the chair conformation (so they all encounter the same energy barrier).

I'm more interested in the principles behind the calculation – why the equation works – than just seeing the calculation done.

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Look up application of the rate of reaction equation given barrier height and energy available at room temp, $kT$ (Boltzmann's constant).

$k = A \mathrm e^{ - \frac{E_\mathrm a}{RT} }$

http://research.cm.utexas.edu/nbauld/teach/cyhexconf.jpeg

Twist-boat leads to mathematically perfect geometric chirality,
Symmetry: Culture and Science 19(4) 307-316 (2008).

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