Problem 45 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

A compound of iron and chlorine is soluble in water. An excess of silver nitrate was added to precipitate all chloride ions as silver chloride. If a \(127 \mathrm{mg}\) sample of the compound gave \(287 \mathrm{mg} \mathrm{AgCl}\), what is the formula of the compound? \((\mathrm{Fe}=56\), \(\mathrm{Ag}=108\) ) (a) \(\mathrm{FeCl}_{2}\) (b) \(\mathrm{FeCl}_{3}\) (c) \(\mathrm{FeCl}\) (d) \(\mathrm{FeCl}_{6}\)

Step-by-Step Solution

Answer

The formula of the compound is FeCl3.

Step 1: Calculate moles of AgCl

Use the molar mass of AgCl (Ag = 107.8682, Cl = 35.453; AgCl = 143.3212 g/mol) to calculate moles of precipitated AgCl. This can be done using the formula: moles = mass (in grams) / molar mass (in grams/mol). For the given 287 mg (0.287 g) of AgCl, the moles of AgCl are calculated as: moles of AgCl = 0.287 g / 143.3212 g/mol.

Step 2: Calculate moles of Cl in the compound

Because AgCl is formed in a 1:1 ratio with Cl, the moles of Cl in the original compound will be equal to the moles of AgCl. Thus, moles of Cl = moles of AgCl.

Step 3: Calculate the mass of Cl in the compound

Use the moles of Cl and the molar mass of Cl (35.453 g/mol) to find the mass of Cl in the original compound: mass of Cl = moles of Cl * molar mass of Cl.

Step 4: Find the mass of Fe in the compound

Subtract the mass of Cl from the total mass of the compound to find the mass of Fe: mass of Fe = total mass of the compound - mass of Cl.

Step 5: Calculate moles of Fe in the compound

Using the molar mass of Fe (55.845 g/mol), calculate the moles of Fe present in the original compound: moles of Fe = mass of Fe / molar mass of Fe.

Step 6: Determine the mole ratio of Fe to Cl

Dividing the moles of Cl by the moles of Fe gives us the simplest mole ratio of Cl to Fe. This ratio determines the subscript numbers in the empirical formula of the iron chloride compound.

Step 7: Identify the correct formula

Use the mole ratio determined in the previous step to establish which of the given formulas corresponds with the empirical formula. The ratio will give us the subscript number for Cl in the chemical formula FeClx.

Key Concepts

Mole Concept

The mole concept is a fundamental principle in chemistry that serves as a bridge between the microscopic world of atoms and molecules and the macroscopic world we can measure and observe. One mole represents Avogadro's number, which is approximately 6.022 x 10^23 entities, be they atoms, ions, or molecules, and provides chemists with a means of quantifying substances based on the number of particles rather than their mass.

In the given exercise, the mole concept is utilized to convert the mass of silver chloride (AgCl) precipitate into the number of moles. Since the atomic and molar masses of Ag and Cl are provided, the student can calculate the molar mass of AgCl and use it with the mass of the precipitate to find the number of moles of AgCl. This reveals the number of moles of chloride ions in the original iron chloride compound, since each mole of AgCl contains one mole of chloride ions.

To understand this better, let's break it down using simple arithmetic. If you need to know how many packets of cookies you can get from a box containing 12 cookies per packet, you would divide the total number of cookies by 12. Similarly, chemists divide the total mass of a compound by its molar mass to determine how many 'packets' of that compound they have, with one packet being one mole.

Empirical Formula Determination

Determining an empirical formula means finding the simplest whole-number ratio of atoms in a compound. This ratio gives us the basic proportion of elements present, but not necessarily the exact arrangement or the number of atoms in a molecule, that's the job of the molecular formula.

In the exercise involving iron and chlorine, the student calculates the moles of chlorine from a known mass of silver chloride precipitate. This is the reverse of baking, where instead of using proportions of ingredients to make a cake, the student is working backwards from the cake (the compound), separating it into its basic ingredients (elements) in their simplest ratio.

The process is akin to deducing the original recipe used for a batch of pancakes by knowing that every pancake uses one egg and two cups of flour. If one discovered they had 10 eggs and 20 cups of flour, the simplest ratio of eggs to flour would be 1:2. This corresponds to the ratio of iron to chlorine in the compound: for every mole of Fe, there are 'x' moles of Cl, where 'x' gives the simplest whole-number ratio.

Chemical Reaction Quantification

Quantifying chemical reactions involves using stoichiometric relationships, which are based on the balanced chemical equation for the reaction. Stoichiometry allows chemists to predict the amount of reactants needed or products formed in a chemical reaction.

The step-by-step solution of the exercise illustrates this quantification by showing how to work from the amount of one product, silver chloride, to determine the composition of the original reactant, the iron chloride compound. This is like a chef who knows that a recipe produces a certain amount of dough and can thus calculate how much of each ingredient was originally used.

The amounts of reactants and products in a chemical reaction are directly related through the ratios of moles established by the balanced chemical equation. In our case, the precipitation reaction of silver nitrate with chloride ions is known to proceed in a 1:1 mole ratio, since one mole of Ag+ reacts with one mole of Cl- to produce one mole of AgCl. By understanding this, students can reverse-engineer the problem to find not just the quantity but the identity of the original compound, making stoichiometry a powerful tool for interrogation as well as construction in chemistry.