Sodium metal reacts with water to form aqueous sodium hydroxide and hydrogen gas. (a) Write a balanced chemical equation for this reaction. (b) Which reactant is limiting if \(100.0 \mathrm{~g}\) of \(\mathrm{Na}\) and \(4.00\) moles of water are used?

Understanding the balanced chemical equation is crucial in chemistry. It represents the principle of conservation of mass, ensuring that the number of atoms of each element remains constant before and after a chemical reaction. For the given reaction of sodium metal with water to form sodium hydroxide and hydrogen gas, the balanced equation is arrived at by making sure that the number of sodium, hydrogen, and oxygen atoms on the reactants side equals the number on the products side.

Here's how it works: you start with an unbalanced equation and systematically adjust the coefficients—the numbers placed before the chemical formulas—to balance each element. The coefficients indicate the relative amounts in moles of each of the substances involved in the reaction. The balancing process can be challenging, but it forms the foundation for understanding stoichiometry and chemical reactions overall.

The mole calculation is a pivotal concept in chemistry, serving as the bridge between the macroscopic world we can see and the atomic world we cannot. A mole is a counting unit similar to a dozen, except that it represents approximately 6.022 x 10²³ items, usually atoms or molecules—this number is known as Avogadro's number. In our exercise, we converted the mass of sodium metal into moles by using its molar mass, which is the mass of one mole of that substance.

The formula for this conversion is straightforward: moles = mass / molar mass. Mole calculations allow chemists to work out the precise proportions of reactants and products in a chemical reaction, which is essential for determining the limiting reactant and predicting the amount of products formed.

Stoichiometry is the section of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It's based on the balanced chemical equation and mole calculations. Once you understand how to balance an equation and calculate moles, stoichiometry becomes a powerful tool. It allows you to predict how much product will form from certain amounts of reactants and identify which reactant will limit the reaction—an aspect that was key in our exercise.

The stoichiometric coefficients in a balanced equation provide the ratios needed to determine the limiting reactant. These ratios indicate how many moles of each reactant are needed to produce the desired amount of product in a reaction—essentially, they are the recipe for the chemical reaction. In our case, we compared the mole ratio of Na to H₂O with the stoichiometric ratio to identify the limiting reactant.

A chemical reaction is a process where substances, known as reactants, transform into new substances called products. During this transformation, chemical bonds are broken and formed, which results in a change in the arrangement of atoms. The principles of a balanced chemical equation and stoichiometry are exemplified through chemical reactions, as they illustrate the rearrangements and proportions of atoms involved.

Understanding the specifics of a chemical reaction, such as the one outlined in our exercise between sodium and water, allows us to make predictions about the behavior of matter. This understanding is not only key for academic purposes but also has practical applications in industries ranging from pharmaceuticals to materials science, where controlling the outcome of chemical reactions is fundamental.