Hydrate Isomers: Using Conductivity and Chloride Precipitation
Three unlabelled bottles from a school stockroom each contain a hydrated chromium(III) chloride with the same empirical formula, CrCl3·6H2O, but different arrangements of water and chloride ligands. The teacher labels them A, B and C. A student prepares 0.010 mol dm^-3 aqueous solutions and measures molar conductivity. The values are A: 430 S cm² mol^-1, B: 260 S cm² mol^-1, C: 130 S cm² mol^-1. Separate 10.0 cm³ portions of each 0.010 mol dm^-3 solution are treated with excess AgNO3(aq), and the dried AgCl precipitates are weighed: A gives 0.0430 g, B gives 0.0287 g, C gives 0.0143 g. The teacher says the precipitates show how many chloride ions are outside the coordination sphere; the conductivity order supports the same conclusion. The student also notices that A is violet, B is pale green, and C is dark green. The class must assign a likely structure to each compound and decide whether any of them can exist as geometrical isomers. Assume each complex ion is octahedral and that AgCl precipitation is complete.
1. Use the AgCl masses to determine how many chloride ions are outside the coordination sphere in A, B and C. Assign a likely formula to each compound and explain the conductivity order.
Read the worked answer
Each 10.0 cm³ portion contains 0.010 mol dm^-3 × 0.0100 dm³ = 1.00 × 10^-4 mol of complex.
Moles of AgCl: A = 0.0430 / 143.3 = 3.00 × 10^-4 mol, i.e. 3 Cl^- per complex. B = 0.0287 / 143.3 = 2.00 × 10^-4 mol, i.e. 2 Cl^- per complex. C = 0.0143 / 143.3 = 1.00 × 10^-4 mol, i.e. 1 Cl^- per complex.
Likely structures: A = [Cr(H2O)6]Cl3; B = [CrCl(H2O)5]Cl2·H2O; C = [CrCl2(H2O)4]Cl·2H2O.
A gives three ions per formula unit in solution (1 complex cation + 3 Cl^-), B gives three ions but with a 2+ cation and two Cl^-, and C gives two ions (1+ cation + one Cl^-). A has the highest conductivity, then B, then C, consistent with the decreasing number and charge of free ions.
2. Which of A, B or C can show geometrical isomerism? Explain using the arrangement of ligands around the octahedral centre.
Read the worked answer
C, [CrCl2(H2O)4]^+, can show geometrical isomerism because it is an octahedral complex of type MA4B2. The two Cl^- ligands can be adjacent (cis) or opposite (trans), giving cis and trans isomers with different physical properties.
B is [CrCl(H2O)5]^2+, an MA5B complex; with only one Cl^- there is no alternative relative position, so it has no geometrical isomer. A is [Cr(H2O)6]^3+, an MA6 complex, and also has no geometrical isomer. The different colours arise because replacing H2O by Cl^- changes the ligand-field splitting and therefore the d-d absorption.
3. A student claims that the conductivity data alone prove the structures. Evaluate this claim and state what other evidence from the setup supports the assignments.
Read the worked answer
Conductivity alone gives the electrolyte type, but it does not directly count which chloride ions are free or coordinated. Other factors such as ion size, mobility and ion pairing can affect molar conductivity, so the exact values should be treated as a trend rather than a proof.
The AgCl precipitation is stronger evidence: it quantitatively measures the chloride ions that are free in solution and can be precipitated by Ag+. The sequence 3, 2 and 1 free Cl^- per complex supports the three formulae. The colour sequence is consistent with changing ligand field as H2O is replaced by Cl^-, but colour alone would not identify the structures. Together, the precipitation data, conductivity trend and octahedral ligand-count logic give a consistent assignment.