A chemist prepared an aqueous solution by mixing \(2.50 \mathrm{~g}\) of ammonium phosphate trihydrate, \(\left(\mathrm{NH}_{4}\right)_{3} \mathrm{PO}_{4} \cdot 3 \mathrm{H}_{2} \mathrm{O}\) and \(1.50 \mathrm{~g}\) of potassium phosphate, \(\mathrm{K}_{3} \mathrm{PO}_{4}\), with \(500 \mathrm{~g}\) of water. (a) Determine the number of moles of formula units of each compound that was measured. (b) How many moles of \(\mathrm{PO}_{4}{ }^{3-}\) are present in solution? (c) Calculate the mass of phosphate ions present in the solution. (d) What is the total mass of the water present in the solution?

Stoichiometry is a branch of chemistry that deals with the quantitative relationships of the substances in chemical reactions. It allows chemists to predict the amounts of substances consumed and produced in a given reaction.

To understand stoichiometry, you must first grasp the concept of the mole, which is a standard scientific unit for measuring large quantities of very small entities such as atoms, molecules, or other specified particles. One mole is equivalent to Avogadro's number, which is approximately 6.022×10²³ particles.

In the given exercise, stoichiometry is used to determine the number of moles of each compound by dividing the mass of the compound by its molar mass. This calculation is crucial for finding how much of each reactant is needed or how much of a product can be formed. Chemists also use stoichiometry to calculate the mass of substances produced in a chemical reaction, given the mass of the reactants.

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all atoms in a molecule as listed on the periodic table, taking into account their stoichiometric coefficients in the compound's chemical formula.

For instance, to find the molar mass of ammonium phosphate trihydrate \( (NH_4)_3PO_4 \cdot 3H_2O \), sum the atomic masses of nitrogen (N), hydrogen (H), phosphorus (P), and oxygen (O), remembering to count the atoms in the water of crystallization. Once the total molar mass is obtained, it can be used to convert between grams and moles, a critical step in many stoichiometric calculations.

Solution concentration describes how much solute is present in a given quantity of solvent and is commonly measured in terms of molarity (M), expressed as moles of solute per liter of solution.

In the exercise, the solution concentration is not directly calculated, but understanding the concept is important for further calculations and dilutions. The number of moles of solute present in the solution can be used to find molarity if the total volume of the solution is known. Concentration can also influence the reactivity and properties of a solution, underscoring its importance in chemical reactions and analysis.

A chemical formula provides important information about the composition of a compound. It indicates the types and numbers of atoms in a molecule, giving insight into the compound's proportions and stoichiometry. For a molecule like \( (NH_4)_3PO_4 \cdot 3H_2O \), the chemical formula shows that each unit contains three ammonium ions \( (NH_4)^+ \) and one phosphate ion \( (PO_4)^{3-} \) along with three water molecules (\text{3H}_2\text{O}\text{.)}

The chemical formula is pivotal in calculations of molar mass and in understanding the contributions of each ion to the properties of the compound, such as the number of phosphate ions contributing to the final concentration in a solution, as seen in the provided exercise.