Consider the following reaction scheme:
Which among the following statements is correct?
Show Hint
Stronger field ligands (like $\text{NH}_3$) cause larger d-orbital splitting ($\Delta_o$).
Larger splitting requires higher energy (blue/violet light, shorter wavelength) for electronic excitation, meaning the weaker-field complex P absorbs at a higher wavelength.
P shows geometrical isomerism and absorbs light of higher wavelength than that of Q.
Both P and Q show geometrical isomerism and P absorbs light of higher wavelength than that of Q.
Q shows geometrical isomerism and absorbs light of higher wavelength than that of P.
P shows geometrical isomerism and absorbs light of lower wavelength than that of Q.
Show Solution
The Correct Option isA
Solution and Explanation
Step 1 : Understanding the Question:
The question asks us to identify the coordination formulas of compounds P and Q based on a reaction scheme and then compare their geometrical isomerism and light absorption properties. Step 2 : Key Formulas and Approach:
We will use Werner's coordination theory to write the formulas of the complex isomers.
We will use Crystal Field Theory (CFT) to evaluate their crystal field splitting energy ($\Delta_o$).
The relationship between energy ($\Delta_o$) and wavelength of light absorbed ($\lambda$) is given by:
\[ \Delta_o = \frac{hc}{\lambda} \implies \lambda \propto \frac{1}{\Delta_o} \] Step 3 : Detailed Explanation:
Determining Formula of P:
The hydrate isomer of $\text{CrCl}_3 \cdot 6\text{H}_2\text{O}$ (P) reacts with excess $\text{AgNO}_3$ to precipitate 1 mole of $\text{AgCl}$ per mole of P.
This means there is exactly one counter chloride ion outside the coordination sphere.
Thus, the formula of P is $[\text{Cr}(\text{H}_2\text{O})_4\text{Cl}_2]\text{Cl} \cdot 2\text{H}_2\text{O}$.
Since P is of the type $[\text{MA}_4\text{B}_2]\text{Y}$, it can exist as both {cis} and {trans} isomers, thus exhibiting geometrical isomerism.
Determining Formula of Q:
Treating P with excess concentrated $\text{NH}_3$ solution replaces both coordinated water and chloride ligands with ammine ($\text{NH}_3$) ligands.
The resulting product Q precipitates 3 moles of $\text{AgCl}$ per mole of Q, meaning all three chloride ions are now outside the coordination sphere.
Thus, the formula of Q is $[\text{Cr}(\text{NH}_3)_6]\text{Cl}_3$.
Since Q is of the type $[\text{MA}_6]\text{Y}_3$, it does not show geometrical isomerism.
Comparing Absorption Wavelength:
According to the spectrochemical series, $\text{NH}_3$ is a stronger field ligand than both $\text{H}_2\text{O}$ and $\text{Cl}^-$.
Therefore, the crystal field splitting energy ($\Delta_o$) of the hexammine complex Q is larger than that of P:
\[ \Delta_o(\text{Q})>\Delta_o(\text{P}) \]
Since $\lambda$ is inversely proportional to $\Delta_o$, the wavelength of light absorbed by P is higher than that absorbed by Q:
\[ \lambda_{\text{absorb}}(\text{P})>\lambda_{\text{absorb}}(\text{Q}) \]
Step 4 : Final Answer:
Therefore, P shows geometrical isomerism and absorbs light of higher wavelength than Q.
This corresponds to Option (A).
