A continuous distillation column is used to produce a $65\%$ ABV rum as distillate product from an $8\%$ ABV wash. Reflux is established through a dephlegmator$/$partial condenser. Energy is saved by using the wash as the cooling fluid in the partial condenser.

The wash is supplied at $100$ kmol$/$h at an initial temperature of $20\backslash$deg C$,$ and leaves the partial condenser at $80\backslash$deg C$.$ The pre$-$heated wash is then heated further up to its bubble point using steam, before being fed into the column. The bottom product contains $0\mathrm{.}2$ mol$\%$ ethanol $(0\mathrm{.}65\%$ ABV$).$

Demonstrate that the reflux ratio is approximately $1\mathrm{.}61\mathrm{.}7$

Calculate the number of theoretical plates required in the rectifying section only for this continuous column set$-$up$.$ Provide an explanation for whether you would have expected this answer

Solve step by step giving appropriate explanation

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