For the conversion of [Pt(L)Cl\(_3\)]\(^-\) to \(\textit{trans}\)-[Pt(L)Cl\(_2\)(H\(_2\)O)], the\( \textit{trans}\)-effect is LEAST when the ligand L is
Step 1: Recall the trans-effect. In square-planar Pt(II) complexes, ligands differ in their ability to accelerate substitution of the ligand positioned \(\textit{trans}\) to them (kinetic\(\textit{trans}\)-effect). Strong \(\pi\)-acceptors and soft donors show a large \(\textit{trans}\)-effect; hard, weak \(\sigma\)-donors show a small one.
Step 2: Rank the given ligands qualitatively. \[ \text{(weak)}\quad \text{H}_2\text{O} \;<\; \text{NH}_3 \;<\; \text{DMSO (via S)} \;<\; \text{C}_2\text{H}_4 \quad \text{(strong)} \]
\(\mathbf{H_2O}\): very weak \(\sigma\)-donor (hard base) \(\Rightarrow\) least \( \textit{trans}\)-effect.
\(\mathbf{NH_3}\): slightly stronger \(\sigma\)-donor than water \(\Rightarrow\) larger effect than H\(_2\)O.
\(\mathbf{DMSO}\) (S-bound): softer donor, moderate \(\textit{trans}\)-effect.
\(\mathbf{C_2H_4}\): \(\pi\)-acceptor olefin, strong \(\textit{trans}\)-effect.
Step 3: Conclusion. Since H\(_2\)O has the smallest \(\textit{trans}\)-effect in this set, the conversion will be slowest when \(L = \text{H}_2\text{O}\). Hence, option (A) is correct.
A regular dodecagon (12-sided regular polygon) is inscribed in a circle of radius \( r \) cm as shown in the figure. The side of the dodecagon is \( d \) cm. All the triangles (numbered 1 to 12 in the figure) are used to form squares of side \( r \) cm, and each numbered triangle is used only once to form a square. The number of squares that can be formed and the number of triangles required to form each square, respectively, are:
In the given figure, the numbers associated with the rectangle, triangle, and ellipse are 1, 2, and 3, respectively. Which one among the given options is the most appropriate combination of \( P \), \( Q \), and \( R \)?
The Lineweaver-Burk plot for an enzyme obeying the Michaelis-Menten mechanism is given below.
The slope of the line is \(0.36 \times 10^2\) s, and the y-intercept is \(1.20\) mol\(^{-1}\) L s. The value of the Michaelis constant (\(K_M\)) is ________ \( \times 10^{-3} \) mol L\(^{-1}\) (in integer). [Note: \(v\) is the initial rate, and \([S]_0\) is the substrate concentration]
Consider a Carnot engine with a hot source kept at 500 K. From the hot source, 100 J of energy (heat) is withdrawn at 500 K. The cold sink is kept at 300 K. The efficiency of the Carnot engine is ___________ (rounded off to one decimal place).
For the cell reaction, \[ Hg_2Cl_2 (s) + H_2 (1 \, {atm}) \rightarrow 2Hg (l) + 2H^+ (a=1) + 2Cl^- (a=1) \] The standard cell potential is \( \mathcal{E}^0 = 0.2676 \) V, and \( \left(\frac{\partial \mathcal{E}^0}{\partial T}\right)_P = -3.19 \times 10^{-4} \) V K\(^{-1}\). The standard enthalpy change of the reaction (\( \Delta_r H^0 \)) at 298 K is \( -x \) kJ mol\(^{-1}\). The value of \( x \) is ___________ (rounded off to two decimal places). [Given: Faraday constant \( F = 96500 \) C mol\(^{-1}\)]