Question

In a binary distillation column, if the feed contains \(40\) mole \(\%\) vapour, the slope of a \(q\)-line is

• A. \(0.6\)
• B. \(-1.5\)
• C. \(-0.6\)
• D. \(1.5\)

Hint:

For a feed containing vapour fraction \(0.40\), liquid fraction \(q=0.60\). The \(q\)-line slope is \(\frac{q}{q-1}\).

Answer 1

The Correct Option is B

In McCabe-Thiele method, the slope of the feed line or \(q\)-line is: \[ \frac{q}{q-1} \] Here \(q\) is the fraction of feed that is liquid. The feed contains \(40\) mole \(\%\) vapour. Therefore, vapour fraction is: \[ 0.40 \] So liquid fraction is: \[ q=1-0.40 \] \[ q=0.60 \] Now slope of \(q\)-line: \[ m=\frac{q}{q-1} \] \[ m=\frac{0.60}{0.60-1} \] \[ m=\frac{0.60}{-0.40} \] \[ m=-1.5 \] Therefore, the slope of the \(q\)-line is: \[ -1.5 \]