Consider the reaction: $$ \mathrm{K}_{2} \mathrm{~S}(a q)+\mathrm{Co}\left(\mathrm{NO}_{3}\right)_{2}(a q) \longrightarrow 2 \mathrm{KNO}_{3}(a q)+\mathrm{CoS}(\mathrm{s}) $$ What volume of \(0.225 \mathrm{M} \mathrm{K}_{2} \mathrm{~S}\) solution is required to completely react with \(175 \mathrm{~mL}\) of \(0.115 \mathrm{M} \mathrm{Co}\left(\mathrm{NO}_{3}\right)_{2}\) ?

Stoichiometry is the section of chemistry that pertains to the calculation of the quantities of reactants and products in chemical reactions. It is a mathematical approach to quantifying elements and compounds involved in chemical reactions.

Understanding stoichiometry begins with a balanced chemical equation that provides the molar ratios among the reactants and products. These molar ratios serve as conversion factors and are essential in stoichiometry calculations. To solve a stoichiometry problem, one typically follows these steps:

• Balance the chemical equation for the reaction.
• Convert all given information into moles (using molarity, if solutions are involved).
• Use the molar ratios from the balanced equation to calculate the number of moles of any unknown substance.
• Convert moles back to required units, which may include volume or mass.

In our exercise, the molar ratio between \(\mathrm{K}_2\mathrm{S}\) and \(\mathrm{Co}\left(\mathrm{NO}_3\right)_2\) is 1:1, and through stoichiometry, we could calculate the needed volume of \(\mathrm{K}_2\mathrm{S}\) solution to react with a given volume of \(\mathrm{Co}\left(\mathrm{NO}_3\right)_2\) solution.

Molarity is a way of expressing concentration in chemistry and is defined as the number of moles of solute per liter of solution. The unit for molarity is moles per liter (M). This concentration measure plays a pivotal role in stoichiometric calculations, particularly when dealing with solutions.

To convert from volume to moles using molarity, the formula is:
\[\text{Moles} = \text{Molarity} \times \text{Volume}\]
where volume must be in liters. Molarity allows scientists to relate the volume of a solution to the amount of substance present. In challenges where you're required to find out how much of a solution is necessary to react completely with a certain amount of another substance, like in our textbook exercise, molarity is the key. The solution provides a clear example of using molarity to find the volume of one substance that reacts with a specific volume of another, ensuring both reactants are used completely.

A balanced chemical equation is one where the number of atoms for each element is the same on the reactant side as on the product side. Achieving this balance is fundamental in stoichiometry since the equations serve as a blueprint for the stoichiometric calculations.

The law of conservation of mass states that matter cannot be created or destroyed. This principle underlines the need for equations to be balanced. When dealing with chemical reactions, it's this balance that allows us to apply mole ratios and thereby conduct stoichiometry calculations accurately.

• The coefficients in a balanced equation represent the molar ratio of the reactants and products.
• Each side of the equation should have the same total number of atoms of each element.

In our problem, the balanced equation provided the molar ratio needed to find out exactly how much \(\mathrm{K}_2\mathrm{S}\) solution is required to completely react with the \(\mathrm{Co}\left(\mathrm{NO}_3\right)_2\) solution, enforcing the stoichiometric principle that matter is neither created nor destroyed in chemical reactions.