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Ch.21 - Transition Elements and Coordination Chemistry
Chapter 21, Problem 139

Chromium forms three isomeric compounds A, B, and C with percent composition 19.52% Cr, 39.91% Cl, and 40.57% H2O. When a sample of each compound was dissolved in water and aqueous AgNO3 was added, a precipitate of AgCl formed immediately. A 0.225-g sample of compound A gave 0.363 g of AgCl, 0.263 g of B gave 0.283 g of AgCl, and 0.358 g of C gave 0.193 g of AgCl. One of the three compounds is violet, while the other two are green. In all three, chromium has a coordination number of 6. (a) What are the empirical formulas of A, B, and C? (b) What are the probable structural formulas of A, B, and C? Draw the structure of the cation in each compound. Which cation can exist as diastereoisomers? (c) What are the approximate freezing points of 0.25 m solutions of A, B, and C, assuming complete dissociation?

Verified step by step guidance
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Step 1: Determine the moles of AgCl formed from each compound. Use the molar mass of AgCl (143.32 g/mol) to convert the mass of AgCl to moles for each compound: \( \text{moles of AgCl} = \frac{\text{mass of AgCl}}{143.32 \text{ g/mol}} \).
Step 2: Calculate the moles of Cl in each compound. Since each mole of AgCl corresponds to one mole of Cl, the moles of Cl in the compound are equal to the moles of AgCl formed.
Step 3: Use the percent composition to find the moles of Cr and H2O in each compound. Assume 100 g of each compound to simplify calculations. For Cr, use \( \text{moles of Cr} = \frac{19.52}{51.996} \), and for H2O, use \( \text{moles of H2O} = \frac{40.57}{18.015} \).
Step 4: Determine the empirical formula for each compound by finding the simplest whole number ratio of moles of Cr, Cl, and H2O. Divide the moles of each element by the smallest number of moles calculated in the previous steps.
Step 5: Analyze the structural formulas and coordination chemistry. Chromium's coordination number of 6 suggests octahedral complexes. Consider the possibility of isomerism, such as cis-trans or facial-meridional isomers, and identify which compound can exist as diastereoisomers based on the arrangement of ligands around the chromium center.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Empirical Formula

The empirical formula represents the simplest whole-number ratio of the elements in a compound. It is determined from the percent composition of each element, allowing chemists to deduce the basic composition of a compound without knowing its molecular structure. For example, if a compound contains 50% carbon and 50% oxygen by mass, its empirical formula would be CO.
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Coordination Chemistry

Coordination chemistry involves the study of coordination compounds, which consist of a central metal atom bonded to surrounding molecules or ions called ligands. The coordination number indicates how many ligands are attached to the metal, influencing the compound's geometry and properties. In this case, chromium has a coordination number of 6, suggesting an octahedral geometry, which is common for transition metal complexes.
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Freezing Point Depression

Freezing point depression is a colligative property that describes how the addition of solute to a solvent lowers the freezing point of the solution. The extent of freezing point depression depends on the number of solute particles in solution, not their identity. For ionic compounds like AgCl, which dissociate in solution, the total number of particles affects the freezing point, making it essential to calculate the molality of the solutions to determine their freezing points.
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