Oil is extracted from mustard seeds having 20 wt% oil and 80 wt% solids, using hexane as a solvent. After extraction, the hexane-free residual cake contains 1 wt% oil. Assuming negligible dissolution of cake in hexane, the percentage oil recovery in hexane is ___________ % (rounded off to the nearest integer).
Step 1: Calculate Initial and Remaining Oil Content. Initial oil content = 20% of 100 kg = 20 kg.
Oil remaining in cake = 1% of 100 kg = 1 kg.
Step 2: Calculate the Oil Extracted and Percentage Recovery. Oil extracted = Initial oil - Remaining oil = 20 kg - 1 kg = 19 kg.
Percentage recovery = \(\left(\frac{19 { kg}}{20 { kg}}\right) \times 100% = 95%\).
Methanol is produced by the reversible, gas-phase hydrogenation of carbon monoxide: \[ {CO} + 2{H}_2 \rightleftharpoons {CH}_3{OH} \] CO and H$_2$ are charged to a reactor, and the reaction proceeds to equilibrium at 453 K and 2 atm. The reaction equilibrium constant, which depends only on the temperature, is 1.68 at the reaction conditions. The mole fraction of H$_2$ in the product is 0.4. Assuming ideal gas behavior, the mole fraction of methanol in the product is ____________ (rounded off to 2 decimal places).
The residence-time distribution (RTD) function of a reactor (in min−1) is:
\[ E(t) = \begin{cases} 1 - 2t, & \text{if } t \leq 0.5\ \text{min} \\ 0, & \text{if } t > 0.5\ \text{min} \end{cases} \]
The mean residence time of the reactor is _____ min (rounded off to 2 decimal places).
Choose the option that correctly matches the items in Group 1 with those in Group 2.
An object is said to have an n-fold rotational symmetry if the object, rotated by an angle of \( \frac{2\pi}{n} \), is identical to the original.
Which one of the following objects exhibits 4-fold rotational symmetry about an axis perpendicular to the plane of the screen?
A color model is shown in the figure with color codes: Yellow (Y), Magenta (M), Cyan (Cy), Red (R), Blue (Bl), Green (G), and Black (K). Which one of the following options displays the color codes that are consistent with the color model?
The figures I, II, and III are parts of a sequence. Which one of the following options comes next in the sequence at IV?