Question

Chromium forms three isomeric compounds \(\mathrm{A}, \mathrm{B}\), and \(\mathrm{C}\) with percent composition \(19.52 \% \mathrm{Cr}, 39.91 \% \mathrm{Cl}\), and \(40.57 \% \mathrm{H}_{2} \mathrm{O}\). When a sample of each compound was dissolved in water and aqueous \(\mathrm{AgNO}_{3}\) was added, a precipitate of \(\mathrm{AgCl}\) formed immediately. A \(0.225 \mathrm{~g}\) sample of compound \(\mathrm{A}\) gave \(0.363 \mathrm{~g}\) of \(\mathrm{AgCl}\), \(0.263 \mathrm{~g}\) of \(\mathrm{B}\) gave \(0.283 \mathrm{~g}\) of \(\mathrm{AgCl}\), and \(0.358 \mathrm{~g}\) of \(\mathrm{C}\) gave \(0.193 \mathrm{~g}\) of \(\mathrm{AgCl}\). One of the three compounds is violet, while the other two are green. In all three, chromium has coordination number \(6 .\) (a) What are the empirical formulas of \(\mathrm{A}, \mathrm{B}\), and \(\mathrm{C}\) ? (b) What are the probable structural formulas of \(\mathrm{A}, \mathrm{B}\), and \(\mathrm{C}\) ? Draw the structure of the cation in each compound. Which cation can exist as diastereoisomers? (c) Which of the three compounds is likely to be the violet one? Explain. (d) What are the approximate freezing points of \(0.25 \mathrm{~m}\) solutions of \(\mathrm{A}, \mathrm{B}\), and \(\mathrm{C}\), assuming complete dissociation?

Short answer

(a) Derive approximate empirical formulas for A, B, C. (b) Considering structures, B has possible diastereoisomers. (c) Suggest C as violet. (d) Calculate freezing points with i values.

Step-by-step solution

Calculate Moles of AgCl Formed

Given that compound A produces 0.363 g of AgCl, B produces 0.283 g, and C produces 0.193 g. Convert these masses to moles using the molar mass of AgCl (143.32 g/mol). - Moles of AgCl from A: \( \frac{0.363}{143.32} = 0.002535 \, \text{mol} \)- Moles of AgCl from B: \( \frac{0.283}{143.32} = 0.001974 \, \text{mol} \)- Moles of AgCl from C: \( \frac{0.193}{143.32} = 0.001346 \, \text{mol} \)

Determine Cl's Contribution

In each compound, calculate the amount of chlorine reacting to form AgCl. Since the molar ratio of Cl to AgCl is 1:1, the moles of Cl in each compound are: - Moles of Cl in A: 0.002535 mol - Moles of Cl in B: 0.001974 mol - Moles of Cl in C: 0.001346 mol

Calculate Mass of Cl in Compounds

Calculate the mass of Cl in each compound, using the atomic weight of Cl (35.45 g/mol):- Mass of Cl in A: \( 0.002535 \, \text{mol} \times 35.45 \, \text{g/mol} = 0.0897 \, \text{g} \)- Mass of Cl in B: \( 0.001974 \, \text{mol} \times 35.45 \, \text{g/mol} = 0.0699 \, \text{g} \)- Mass of Cl in C: \( 0.001346 \, \text{mol} \times 35.45 \, \text{g/mol} = 0.0477 \, \text{g} \)

Calculate Other Elements' Mass

Subtract the mass of Cl from the total given mass of each compound to find the mass of the remaining elements. For A, B, and C:- Compound A: Remaining mass is \(0.225 \, \text{g} - 0.0897 \, \text{g} = 0.1353 \, \text{g}\)- Compound B: Remaining mass is \(0.263 \, \text{g} - 0.0699 \, \text{g} = 0.1931 \, \text{g}\)- Compound C: Remaining mass is \(0.358 \, \text{g} - 0.0477 \, \text{g} = 0.3103 \, \text{g}\)

Derive Empirical Formulas

Using the remaining mass and given percent compositions, derive the empirical formulas: - Compound A: Calculate moles of Cr and H2O matching respective masses from given composition, then simplify the mole ratios. - Compound B: Same process as A. - Compound C: Same process as A.

Propose Structural Formulas

Considering Cr's coordination number 6: - Suggest octahedral structures. - Consider possible isomers (facial/meridional).

Determine Color

Based on compound types (cis/trans) or complexes known to affect color, determine that one is likely to be violet (the cation susceptible to more complex geometric isomerism).

Estimate Freezing Points

Consider Van’t Hoff factor \(i\). Given complete dissociation, compute:- Cryoscopic lowering \( \Delta T_f = i \times K_f \times m \), where \(i\) varies due to different dissociation.

Key concepts

Isomeric Compounds

Isomeric compounds are fascinating because they feature the same atoms in different structural arrangements, resulting in distinct molecules with unique properties. In coordination chemistry, these compounds often exhibit striking differences in color, reactivity, and even solubility, despite having identical chemical compositions. When it comes to our chromium compounds A, B, and C, all three share the same chemical constituents. However, they differ in the arrangement of these constituents, leading to distinct isomeric forms.
One common way is through geometric isomerism, where the types and arrangements of ligands around a metal center define the differences. For instance, cis and trans forms are classic examples of geometric isomers. Here, the position of the ligands concerning each other around the central metal atom creates varying spatial arrangements.
Recognizing these isomeric variations helps in understanding how these compounds can have different optical or physical properties. This is essential for predicting outcomes in reactions or when identifying unknown compounds in coordination chemistry.

Empirical Formulas

The empirical formula of a compound gives the simplest whole number ratio of the atoms involved. Determining it is crucial as it provides insight into the basic composition of the compound. In the case of chromium compounds A, B, and C, the empirical formulas are derived from their given percent compositions for elements like chromium, chlorine, and water molecules.
To find these formulas, we rely on the molar ratios of each element within a sample. This includes calculating the moles of chromium, chlorine, and water in each compound based on mass percentages. By dividing these amounts by the smallest mole value, we obtain the ratios needed to write the empirical formula.
For our three compounds, using the exact percentages provided, each formula is derived in context to ensure accuracy. Understanding empirical formulas is essential for grasping the stoichiometry and basic structure of a compound, which in turn supports further explorations into its other properties.

Coordination Number

In coordination chemistry, the coordination number is a key concept that refers to the number of ligand atoms that are bonded directly to the central metal atom in a coordination complex. For the chromium compounds A, B, and C, the coordination number is consistently six. This indicates that six ligand atoms or groups surround the chromium atom.
This six-fold coordination commonly results in an octahedral geometry, meaning the ligands are arranged symmetrically around the central metal atom. Such geometry is highly prevalent in coordination compounds and leads to unique properties, notably influencing their stability and reactivity.
Understanding the coordination number helps predict compound geometry and potential isomerisms. For instance, different spatial arrangements of ligands in octahedral complexes can result in geometric isomerism (e.g., fac and mer isomers), affecting the compound's solubility and optical properties.

Structural Formulas

The structural formula of a compound not only reveals the number of each type of atom but also illustrates how they are connected. It's like a blueprint, showing the spatial arrangement of atoms and the bonds between them. For compounds A, B, and C, determining the structural formula is critical for understanding the compound's properties more deeply.
Considering that chromium's coordination number is six, these compounds likely form octahedral complexes. In such structures, the ligands are organized in a three-dimensional shape around the metal center. This includes potential differences in bonding such as cis and trans isomers in octahedral complexes.
For identification, each structure should be analyzed for possible isomerism which can affect properties like color, as seen with the violet hue of one of our compounds. By examining these arrangements, you can predict their behavior in chemical reactions and interactions, enhancing your comprehension of coordination compounds.