In steam distillation, a mixture of immiscible liquids boils at a temperature lower than the boiling point of either individual component. This occurs because the total vapor pressure of the mixture is the sum of the vapor pressures of the individual components. The mixture boils when the total vapor pressure equals the atmospheric pressure. Since the organic compound is steam volatile (meaning it has a significant vapor pressure even below its boiling point) and immiscible with water, it will co-distill with water at a temperature close to, but slightly below, the boiling point of water (100$^\circ$C). The boiling point will be slightly below 100$^\circ$C due to the contribution of the organic compound's vapor pressure to the total vapor pressure.
Match List I with List II:
Choose the correct answer from the options given below:
Components \( A \) and \( B \) form an azeotrope. The saturation vapor pressures of \( A \) and \( B \) at the boiling temperature of the azeotrope are 87 kPa and 72.7 kPa, respectively. The azeotrope composition is _________ mol% \( A \) (rounded off to the nearest integer).
% Given GIVEN: \[ \ln \left( \frac{\gamma_A}{\gamma_B} \right) = 0.9 \left( x_B^2 - x_A^2 \right) \] where \( x_i \) and \( \gamma_i \) are the liquid phase mole fraction and activity coefficient of component \( i \), respectively.
A binary \(A\)-\(B\) liquid mixture containing 30 mol% \(A\) is subjected to differential (Rayleigh) distillation at atmospheric pressure in order to recover 60 mol% \(A\) in the distillate. Assuming a constant relative volatility \(\alpha_{AB} = 2.2\), the average composition of the collected distillate is __________ mol% \(A\) (rounded off to the nearest integer).
Which of the following microbes is NOT involved in the preparation of household products?
A. \(\textit{Aspergillus niger}\)
B. \(\textit{Lactobacillus}\)
C. \(\textit{Trichoderma polysporum}\)
D. \(\textit{Saccharomyces cerevisiae}\)
E. \(\textit{Propionibacterium sharmanii}\)
A sphere of radius R is cut from a larger solid sphere of radius 2R as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the Y-axis is :