Problem 42 - Chemistry The Molecular Nature of Matter

Question

How many moles of iodine molecules correspond to \(1.80 \times 10^{24}\) molecules of \(\mathrm{I}_{2} ?\)

Step-by-Step Solution

Answer

There are approximately 2.99 moles of iodine molecules \(I_2\).

Step 1: Use Avogadro's Number

Determine the number of molecules in one mole using Avogadro's number, which is approximately \(6.022 \times 10^{23}\) molecules/mol.

Step 2: Calculate the number of moles

Divide the given number of molecules by Avogadro's number to find the number of moles. \[ \text{Number of moles} = \frac{1.80 \times 10^{24} \text{ molecules of } I_2}{6.022 \times 10^{23} \text{ molecules/mol}} \]

Step 3: Perform the calculation

Execute the division to arrive at the number of moles of \(I_2\). \[ \text{Number of moles} = \frac{1.80 \times 10^{24}}{6.022 \times 10^{23}} \approx 2.99 \text{ moles} \]

Key Concepts

Mole Concept

The mole concept is a fundamental idea in chemistry that relates the microscopic world of atoms and molecules to the macroscopic world that we can measure. It serves as a bridge between the number of particles and the amount of substance that can be observed and handled in the laboratory.

One mole of any substance contains exactly Avogadro's number of particles, which is approximately \(6.022 \times 10^{23}\) particles. This number is named after the scientist Amedeo Avogadro, and it's the same for all substances, whether it's atoms of helium or molecules of water. The mole concept is crucial for quantifying substances and performing chemical calculations because it allows chemists to count particles by weighing them.

For example, if we have 2 moles of iodine molecules \(I_2\), we actually have \(2 \times 6.022 \times 10^{23}\) molecules of iodine. Understanding the mole concept is essential for solving problems involving mass-mass, mass-volume, or volume-volume relationships in chemistry.

Stoichiometry

Stoichiometry is the area of chemistry that pertains to the quantitative relationships between the reactants and products in a chemical reaction. It is based on the conservation of mass and the mole concept. The coefficients in a balanced chemical equation indicate the ratio of moles of each substance involved in the reaction.

Using stoichiometry, chemists can predict how much product will form from a certain amount of reactants, or how much of one reactant is needed to react completely with another. This forms the basis of many calculations in chemistry, such as determining the yield of a reaction or the amount of a reagent required for a given process.

Improving the exercise means emphasizing the importance of balancing the chemical equation before performing stoichiometric calculations to ensure accuracy. Understanding the ratios established by the balanced equation is crucial when using stoichiometry to solve problems.

Chemical Calculation

Chemical calculations involve using mathematical techniques to understand and predict the outcomes of chemical reactions. It encompasses concepts like the mole, molarity, molecular weight, and gas laws. These calculations are essential in determining quantities like the amount of reactants needed or the volume of gas produced in a reaction.

Chemical calculations often start with a balanced chemical equation and utilize conversion factors derived from the coefficients of that equation. For example, when we know the number of moles of \(I_2\), we can calculate the mass by multiplying by the molar mass of iodine, which is the mass of one mole of \(I_2\) molecules.

To achieve clarity in the exercise, it is critical to point out the necessity of unit conversion and dimensional analysis. These fundamental skills ensure that the calculated values accurately represent the desired quantities in the correct units, setting a solid foundation for success in chemistry.