Question

A mixture of \(254 \mathrm{~g}\) of iodine and \(142 \mathrm{~g}\) of chlorine is made to react completely to give a mixture of \(\mathrm{ICl}\) and \(\mathrm{ICl}_{3} .\) How many moles of each product are formed? \((\mathrm{I}=127, \mathrm{Cl}=35.5)\) (a) \(0.1 \mathrm{~mol}\) of \(\mathrm{ICl}\) and \(0.1 \mathrm{~mol}\) of \(\mathrm{ICl}_{3}\) (b) \(1.0 \mathrm{~mol}\) of \(\mathrm{ICl}\) and \(1.0 \mathrm{~mol}\) of \(\mathrm{ICl}_{3}\) (c) \(0.5 \mathrm{~mol}\) of \(\mathrm{ICl}\) and \(0.1 \mathrm{~mol}\) of \(\mathrm{ICl}_{3}\) (d) \(0.5 \mathrm{~mol}\) of \(\mathrm{ICl}\) and \(1.0 \mathrm{~mol}\) of \(\mathrm{ICl}_{3}\)

Short answer

Answer: In our analysis, we found out that 2 moles of ICl and 1 mole of ICl3 are formed from the given amounts of reactants. However, none of the provided options match our solution, which indicates that there may be an error or missing information in the problem.

Step-by-step solution

Convert grams of reactants to moles

To convert the mass of iodine and chlorine to moles, we need to use their respective molar masses. Divide the mass of each element by its molar mass to find the moles: Moles of Iodine (I): \[\frac{254\,\text{g}}{127\,\text{g/mol}} = 2\,\text{mol}\] Moles of Chlorine (Cl): \[\frac{142\,\text{g}}{35.5\,\text{g/mol}} = 4\,\text{mol}\]

Determine the limiting reactant and moles of product formed

In this case, we are given a reaction where iodine and chlorine can form two products, ICl and ICl3. The possible reactions are: \[ \text{I} + \text{Cl} \rightarrow \text{ICl} \] \[ \text{I} + 3\,\text{Cl} \rightarrow \text{ICl}_3 \] Since iodine has a 1:1 stoichiometry with ICl and a 1:3 stoichiometry with ICl3, its moles are the limiting reactant. Now, we can use the stoichiometry of the balanced reactions to determine the moles of products formed. If we use all iodine to form ICl: \[2\,\text{mol}\, \text{I} \times \frac{1\,\text{mol}\, \text{ICl}}{1\,\text{mol}\, \text{I}} = 2\,\text{mol}\, \text{ICl}\] But we only have 4 moles of Cl available, so we can only form 2 moles of ICl using 2 moles of Cl, while the other 2 moles of Cl form 1 mole of ICl3 with the remaining 1 mole of I.

Compare with the given options

The number of moles of ICl and ICl3 formed in our analysis is 2 moles and 1 mole, respectively. Comparing it with the given options, none of the options match with our analysis. So, the problem may have an error or missing information as none of the provided options match our solution.

Key concepts

Stoichiometry

Stoichiometry is the mathematical relationship between reactants and products in a chemical reaction. It involves using the balanced chemical equation to work out the ratio in which substances react or form.

The stoichiometric coefficients in a balanced equation tell us how many moles of each substance are involved. For example, in the reaction \[\text{aA} + \text{bB} \rightarrow \text{cC} + \text{dD}\] the coefficients 'a', 'b', 'c', and 'd' represent the number of moles of each compound A, B, C, and D that react or form.

In our textbook exercise involving iodine and chlorine, we use stoichiometry to predict that 1 mole of iodine will react with 1 mole of chlorine to form 1 mole of ICl and similarly, 1 mole of iodine will react with 3 moles of chlorine to form 1 mole of ICl₃.

Limiting Reactant

The limiting reactant is the reactant that gets used up first in a chemical reaction and thus determines how much product can be formed.

To identify the limiting reactant, we compare the ratio of moles of reactants we have to the ratio needed according to the balanced chemical equation. The reactant in the lesser amount, based on the required stoichiometric ratio, is the limiting reactant.

In the given chemical reactions for the formation of ICl and ICl₃, iodine is the limiting reactant because it will run out before the chlorine does. We derived this by comparing the available moles of iodine and chlorine and their usage ratios in each possible product.

Mole Concept

The mole concept is a fundamental principle in chemistry for quantifying substances. One mole is equivalent to Avogadro's number (approximately 6.022 x 10²³) of atoms, molecules, or ions.

We use molar mass, which is the mass of one mole of a substance, to convert between mass and moles. In our exercise, we used the molar mass of iodine (127 g/mol) and chlorine (35.5 g/mol) to convert the given masses to moles before proceeding with the stoichiometry of the reaction:

• Moles of Iodine = Mass of Iodine / Molar Mass of Iodine
• Moles of Chlorine = Mass of Chlorine / Molar Mass of Chlorine

This conversion is critical to solving stoichiometry problems because reactions proceed in mole ratios, not mass ratios.

Chemical Reaction

A chemical reaction is a process where substances, known as reactants, convert to different substances, known as products. For chemical reactions to occur, the reactants must collide with sufficient energy to overcome the activation energy barrier.

In the context of our textbook problem, iodine reacts with chlorine to form the compounds ICl and ICl₃. This is a synthesis reaction, where simpler substances combine to form more complex compounds.

The formation of products depends on the available reactants, which must be present in specific molar ratios as dictated by the balanced chemical equation. Understanding the nature of the reacting substances and the type of reaction helps in predicting products and their amounts.