Step 1:The element of the 3d series with the lowest enthalpy of atomisation is copper (Cu). Copper has a completely filled \( 3d^{10} \) configuration, which makes it highly stable. The stability of the \( 3d^{10} \) configuration reduces the energy required to break the metallic bonds during atomisation, hence lowering the enthalpy of atomisation. In contrast, elements like zinc (Zn) and manganese (Mn) have less stable electron configurations and require more energy to break the bonds during atomisation.
Step 2: Thus, copper (Cu) has the lowest enthalpy of atomisation due to the stability provided by its filled \( 3d^{10} \) configuration. \bigskip
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).
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).
Choose the option that correctly matches the items in Group 1 with those in Group 2.
A school is organizing a debate competition with participants as speakers and judges. $ S = \{S_1, S_2, S_3, S_4\} $ where $ S = \{S_1, S_2, S_3, S_4\} $ represents the set of speakers. The judges are represented by the set: $ J = \{J_1, J_2, J_3\} $ where $ J = \{J_1, J_2, J_3\} $ represents the set of judges. Each speaker can be assigned only one judge. Let $ R $ be a relation from set $ S $ to $ J $ defined as: $ R = \{(x, y) : \text{speaker } x \text{ is judged by judge } y, x \in S, y \in J\} $.