Chapter 18, Problem 18.72P

Reaction of p-cresol with two equivalents of $2$-methylprop- $1$-ene affords BHT, a preservative with molecular formula ${\text{C}}_{\text{15}}{\text{H}}_{\text{24}}\text{O}$. BHT gives the following ${}^{\text{1}}\text{H}$ NMR spectral data: $1.4$ (singlet, $\text{18}\text{H}$), $2.27$ (singlet, $\text{3}\text{H}$), $5.0$ (singlet, $\text{1}\text{H}$), and $7.0$ (singlet, $\text{2}\text{H}$) ppm. What is the structure of BHT? Draw a stepwise mechanism illustrating how it is formed.