Question

There are three salts that contain complex ions of chromium and have the molecular formula \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\). Treating \(0.27 \mathrm{~g}\) of the first salt with a strong dehydrating agent resulted in a mass loss of \(0.036 \mathrm{~g}\). Treating \(270 \mathrm{mg}\) of the second salt with the same dehydrating agent resulted in a mass loss of \(18 \mathrm{mg}\). The third salt did not lose any mass when treated with the same dehydrating agent. Addition of excess aqueous silver nitrate to \(100.0\) -mL portions of \(0.100 M\) solutions of each salt resulted in the formation of different masses of silver chloride; one solution yielded \(1430 \mathrm{mg} \mathrm{AgCl}\); another, \(2870 \mathrm{mg} \mathrm{AgCl}\); the third, \(4300 \mathrm{mg} \mathrm{AgCl}\). Two of the salts are green and one is violet. Suggest probable structural formulas for these salts, defending your answer on the basis of the preceding observations. State which salt is most likely to be violet. Would a study of the magnetic properties of the salts be helpful in determining the structural formulas? Explain.

Short answer

In summary, we propose the following structural formulas based on the given observations: 1. First salt: \(\text{Cr}(\text{H}_2\text{O})_4\text{Cl}_2\text{Cl}\cdot2\text{H}_2\text{O}\) 2. Second salt: \(\text{Cr}(\text{H}_2\text{O})_2\text{Cl}_4\cdot4\text{H}_2\text{O}\) 3. Third salt: \(\text{Cr}(\text{H}_2\text{O})_3\text{Cl}_3\cdot3\text{H}_2\text{O}\) The third salt is most likely to be violet due to its octahedral geometry, which exhibits colors due to d-d transitions of its electrons. Studying the magnetic properties of the salts can be helpful in determining their structural formulas, as differences in the number of unpaired electrons in the d orbitals of chromium can provide further evidence for the proposed structures.

Step-by-step solution

Analyze the mass loss after dehydration

First, let's analyze the mass loss after treating each salt with a strong dehydrating agent. We observe that: - \(0.27\,\text{g}\) of the first salt loses \(0.036\,\text{g}\). - \(270\,\text{mg}\) of the second salt loses \(18\,\text{mg}\). - The third salt does not lose any mass. The loss in mass corresponds to the water molecules contained in their coordination sphere, which are lost upon treatment with a dehydrating agent. We infer that the more significant the mass loss, the more water molecules are present in the complex ion.

Relate the mass loss to water molecules in the complex

Now let's determine the amount of water molecules in each complex ion based on the mass loss after dehydration: For the first salt, the mass loss of \(\text{H}_2\text{O}\) is \(0.036\,\text{g}\). Since the molar mass of water is \(18\,\text{g/mol}\), we calculate the moles of water lost as follows: \[\frac{0.036\,\text{g}}{18\,\text{g/mol}} = 0.002\,\text{mol}\] For the second salt, the mass loss is \(18\,\text{mg}\) or \(0.018\,\text{g}\). The moles of water lost are: \[\frac{0.018\,\text{g}}{18\,\text{g/mol}} = 0.001\,\text{mol}\] The moles of chromium complex in each case is: \[\frac{0.27\,\text{g}}{266.45\,\text{g/mol}} = 0.001\,\text{mol}\] \[\frac{270\,\text{mg}}{266.45\,\text{g/mol}} = 0.001\,\text{mol}\] Comparing the moles of water to the moles of chromium complex, we find that in: - The first salt, there are \(2\,\text{H}_2\text{O}\) molecules. - The second salt, there is \(1\,\text{H}_2\text{O}\) molecule. - The third salt, there are no \(\text{H}_2\text{O}\) molecules in the complex ion.

Examine the formation of silver chloride

We are given that the addition of aqueous silver nitrate to \(100.0\,\text{mL}\) portions of \(0.100\,\text{M}\) solutions of the salts yielded different amounts of silver chloride. This implies that the number of chloride ions in the complex ions is different for each salt. Based on the mass of precipitated silver chloride, we can calculate the moles of chloride ions in each case. The molar mass of silver chloride is \(143.32\,\text{g/mol}\). The calculated moles of chloride ions are: 1. \(\frac{1.43\,\text{g}}{143.32\,\text{g/mol}} = 0.01\,\text{mol}\) 2. \(\frac{2.87\,\text{g}}{143.32\,\text{g/mol}} = 0.02\,\text{mol}\) 3. \(\frac{4.3\,\text{g}}{143.32\,\text{g/mol}} = 0.03\,\text{mol}\) Comparing the moles of chloride ions to the moles of chromium complex (\(0.01\,\text{mol}\)), we find that: 1. The first salt has \(1\,\text{Cl}^{-}\) ion. 2. The second salt has \(2\,\text{Cl}^{-}\) ions. 3. The third salt has \(3\,\text{Cl}^{-}\) ions.

Propose the structural formulas

Based on our analysis: 1. The first salt contains two \(\text{H}_2\text{O}\) molecules and one chloride ion in the complex ion. Its structural formula is: \(\,\text{Cr}(\text{H}_2\text{O})_4\text{Cl}_2\text{Cl}\cdot2\text{H}_2\text{O}\). 2. The second salt contains one \(\text{H}_2\text{O}\) molecule and two chloride ions in the complex ion. Its structural formula is: \(\,\text{Cr}(\text{H}_2\text{O})_2\text{Cl}_4\cdot4\text{H}_2\text{O}\). 3. The third salt contains no \(\text{H}_2\text{O}\) molecules and three chloride ions in the complex ion. Its structural formula is: \(\,\text{Cr}(\text{H}_2\text{O})_3\text{Cl}_3\cdot3\text{H}_2\text{O}\).

Determine the violet salt and the utility of studying magnetic properties

Among the three salts, only the third salt has \(\,\text{Cr}(\text{H}_2\text{O})_3\text{Cl}_3\) which has octahedral geometry. This geometry tends to exhibit colors due to d-d transitions of its electrons. Thus, the third salt is most likely to be violet. Studying the magnetic properties can be helpful in determining the structural formulas. The magnetic behavior is determined by the number of unpaired electrons in the d orbitals of chromium. A difference in the number of unpaired electrons can provide further evidence supporting the structural formulas proposed above.

Key concepts

Coordination Compounds

Coordination compounds are fascinating entities in chemistry where a central metal atom or ion, often a transition metal, is surrounded by molecules or ions called ligands. These ligands donate electron pairs to the metal, creating a coordination complex. Coordination compounds are integral to understanding how metals interact with other substances, playing vital roles in biochemistry, industrial chemistry, and even medicine.

The ligands can vary in number and type, giving coordination compounds a wide array of properties. They significantly influence the color, solubility, magnetic nature, and reactivity of these compounds. For example, in the compounds of chromium discussed, the color variation, including green and violet, largely depends on the arrangement of these ligands around the chromium metal. Moreover, the number of chloride ions available also affects the result of chemical reactions, such as the formation of silver chloride in our study. Understanding coordination compounds helps predict and explain such reactions effectively.

Chromium Coordination Complexes

Chromium, a transition metal, commonly forms coordination complexes due to its ability to adopt multiple oxidation states and coordinate with various ligands. In the complexes being discussed, chromium is central, surrounded by chlorine ligands and water molecules. This particular chemistry of chromium is reflected in the types and combinations of ligands, influencing the properties and reactivity of the compound.

Three different salts of chromium with the formula \(\text{CrCl}_3 \cdot 6 \text{H}_2\text{O}\) exhibit varying behaviors under dehydration and when reacting with silver nitrate. The number of water molecules and chloride ions within the coordination sphere can change, leading to different chemical and physical properties. The structural differences between these salts illustrate chromium's versatile nature in forming complexes, where the coordination environment significantly alters the properties.

Dehydration in Chemistry

Dehydration, in the context of chemistry, involves the removal of water molecules from a compound. This process can alter the composition and properties of a coordination compound dramatically. In the exercise, treating the chromium salts with a dehydrating agent removed specific numbers of water molecules.

For instance, when the first salt loses \(0.036\ \text{g}\) of water upon dehydration, it reflects the presence of water tightly bonded to the chromium center. Similarly, varying amounts of water loss in different salts suggest varied coordination spheres. This difference is crucial as it provides insights into the structural organization and reactivity of the compound. Understanding how dehydration affects complex ions enables chemists to manipulate such compounds for desired properties in industrial and laboratory settings.

Silver Chloride Formation

Silver chloride formation is a precipitation reaction where silver ions (\(\text{Ag}^+\)) react with chloride ions (\(\text{Cl}^-\)) to form insoluble silver chloride (\(\text{AgCl}\)). This reaction serves as a method to identify and quantify chloride ions present in solution.

In our exercise, varying amounts of silver chloride formation after adding silver nitrate illuminated the number of free chloride ions in different chromium complexes. The process involves forming a precipitate, which can be measured to infer the number of chloride ions not bound within the coordination sphere of the complex. This information is crucial in proposing an accurate structural formula for the salts, as it indicates how many chloride ions remain available outside the coordination sphere, affecting the overall charge and reactivity of the complex.

Chemistry of Transition Metals

Transition metals like chromium exhibit unique chemical behaviors due to their electronic structures. These metals have partially filled d orbitals, enabling them to form various oxidation states and complex geometries. This feature is evident in the coordination complexes of chromium, where different arrangements lead to diverse properties.

The distinctive electronic configurations allow transition metals to participate in a wide array of chemical reactions. In our example, chromium changes can impact color (green to violet), magnetic properties, and chemical reactivity in its salts. Transition metals' chemistry is also crucial in catalysis and forming highly stable complexes. Understanding these properties provides insight into using transition metals in chemical synthesis, environmental applications, and materials science.