I_ \(_{2}\) is produced by the reaction of 0.4235 mol of \(\mathrm{CuCl}_{2}\) according to the following equation: \(2 \mathrm{CuCl}_{2}+4 \mathrm{KI} \longrightarrow 2 \mathrm{CuI}+4 \mathrm{KCl}+\mathrm{I}_{2}\) (a) How many molecules of I \(_{2}\) are produced? (b) What mass of I \(_{2}\) is produced?

Understanding the mole-to-mole ratio in chemical reactions is like learning the perfect recipe for your favorite cake. Just as you need the right amounts of flour to sugar, in chemical equations, the mole-to-mole ratio tells us how much of one substance reacts with another. This ratio comes straight from the balanced chemical equation and is essential for calculating how much product is formed from given reactants.

For example, in the reaction between copper(II) chloride (CuCl₂) and potassium iodide (KI) to produce iodine (I₂), the equation tells us that 2 moles of CuCl₂ react with 4 moles of KI to produce 1 mole of I₂. The mole-to-mole ratio between CuCl₂ and I₂ would be 2:1, meaning it takes twice as much CuCl₂ to produce a single mole of I₂. This ratio is pivotal when converting from moles of one substance to moles of another.

Have you ever wondered how chemists count extremely tiny particles like atoms and molecules? They use a special number called Avogadro's number, which is roughly 6.022 x 10²³. It's named after Amedeo Avogadro, and it represents the number of atoms, ions, or molecules in one mole of substance. Imagine Avogadro's number as a dozen but on a much grander scale.

When working with chemical equations, once you have the moles of a substance, you can use Avogadro's number to convert those moles into actual molecules. For instance, if you have 0.21175 moles of I₂, you multiply this by Avogadro's number to find the number of I₂ molecules. This allows chemists to understand the amount of a substance on a scale that makes sense beyond microscopic measurements.

The molar mass is similar to the atomic weight of an element, but it's used for moles instead of single atoms. It's the weight of one mole of a substance, typically expressed in grams per mole (g/mol). Calculating the molar mass involves the sum of the atomic masses of all atoms in a molecule and is essential for converting between moles of a substance and its mass in grams.

In our chemical reaction, to find the mass of iodine produced, you'd first determine the molar mass of I₂. Since iodine has an atomic mass of approximately 126.9 g/mol, the molar mass of an I₂ molecule would be 2 * 126.9 g/mol, giving us 253.8 g/mol. This molar mass helps us figure out that 0.21175 moles of I₂ would have a mass of 53.76 grams. This step is crucial for cooking up the right amount of product in a chemical reaction, just as how you need to know the weight of flour needed to bake a cake correctly.