The left and right compartments of a thermally isolated container of length $L$ are separated by a thermally conducting, movable piston of area $A$. The left and right compartments are filled with $\frac{3}{2}$ and 1 moles of an ideal gas, respectively. In the left compartment the piston is attached by a spring with spring constant $k$ and natural length $\frac{2L}{5}$. In thermodynamic equilibrium, the piston is at a distance $\frac{L}{2}$ from the left and right edges of the container as shown in the figure. Under the above conditions, if the pressure in the right compartment is $P = \frac{kL}{A} \alpha$, then the value of $\alpha$ is ____
Let $ S $ denote the locus of the point of intersection of the pair of lines $$ 4x - 3y = 12\alpha,\quad 4\alpha x + 3\alpha y = 12, $$ where $ \alpha $ varies over the set of non-zero real numbers. Let $ T $ be the tangent to $ S $ passing through the points $ (p, 0) $ and $ (0, q) $, $ q > 0 $, and parallel to the line $ 4x - \frac{3}{\sqrt{2}} y = 0 $.
Then the value of $ pq $ is
Stereoisomers occur when the ligands have the same bonds, but the bonds are in different orientations relative to one another. Structural isomerism occurs when the bonds are different. Isomers are distinct compounds that can have different physical properties such as color, crystal structure, and melting point.
In octahedral complexes—with four of one ligand and two of another—and square planar complexes—with two of one ligand and two of another—there are two different arrangements of the same atoms with the same bonds. These different arrangements are called cis and trans. In cis molecules, the two ligands are on the same side of the complex. In trans molecules, the similar ligands are on the opposite sides of the molecules, meaning the bond angle is 180 degrees.
Optical isomerism occurs when a molecule is not superimposable with its mirror image.
When three identical ligands occupy one face of an octahedron, the isomer is said to be facial or fac. If these three ligands and the metal ion are in one plane, the isomer is said to be meridional or mer.