A sample of iron weighing \(15.0 \mathrm{~g}\) was heated with potassium chlorate \(\left(\mathrm{KClO}_{3}\right)\) in an evacuated container. The oxygen generated from the decomposition of \(\mathrm{KClO}_{3}\) converted some of the Fe to \(\mathrm{Fe}_{2} \mathrm{O}_{3}\). If the combined mass of Fe and \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) was \(17.9 \mathrm{~g}\), calculate the mass of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) formed and the mass of \(\mathrm{KClO}_{3}\) decomposed.

Understanding stoichiometric calculations is crucial when delving into the intricacies of chemical reactions. These calculations involve using the law of conservation of mass and the coefficients of a balanced equation to determine the relative quantities of reactants and products.

Consider the example where iron reacts with potassium chlorate to form iron(III) oxide. First, you need to know the masses of reactants to start the calculations. For instance, knowing that 15.0 g of iron reacted, we utilize the reaction's stoichiometry to find out how much product is formed. By subtracting the initial mass of iron from the total mass of iron and the product, we get the mass of iron(III) oxide.

These calculations become simple when you grasp the concept of the mole ratio from the balanced chemical equation, which tells us how many moles of one chemical are needed or produced in relation to another chemical in the reaction.

The molar mass of a substance is the weight of 6.022 x 10^23 particles (one mole) of the substance, usually expressed in grams per mole (g/mol). This property is fundamental when converting between the mass of a substance and the number of moles.

In the example involving iron and potassium chlorate, we needed molar mass to convert the mass of iron(III) oxide to moles. The calculation involved dividing the mass of the iron(III) oxide by its molar mass, approximately 159.7 g/mol. By using molar mass, we bring a tangible quantity (grams) to a mole concept, bridging the gap between the macroscopic world and the molecular level.

A chemical reaction describes the process by which one or more substances (reactants) are transformed into one or more different substances (products). The reaction must be balanced, meaning that the number of atoms for each element present in the reactants must be equal to that in the products, adhering to the conservation of mass.

For the reaction between iron and potassium chlorate generating iron(III) oxide, understanding the balanced chemical equation is essential to perform stoichiometric calculations. By knowing the coefficients that balance the reaction, we can determine how much reactant is needed to make a certain amount of product or vice versa. It's the road map that guides us in predicting the outcome of the chemical process.

In chemical reactions, the limiting reactant is the substance that is entirely consumed when the reaction goes to completion. This reactant dictates the maximum amount of product that can be formed.

In our example, if we had also known the mass of potassium chlorate used, we could have determined which reactant was limiting by calculating the theoretical amounts of products each reactant could produce. The one capable of producing the lesser amount of product would be the limiting reactant. Once the limiting reactant is consumed, the reaction stops, and no further products are formed, even if the other reactant remains in excess.