Question

The balanced equation for the dissolving of sodium phosphate in water is $$ \mathrm{Na}_{3} \mathrm{PO}_{4}(s) \stackrel{\mathrm{H}_{\mathrm{O}} \mathrm{O}}{\longrightarrow} 3 \mathrm{Na}^{+}(a q)+\mathrm{PO}_{4}{ }^{3}{ }^{-}(a q) $$ (a) How many \(\mathrm{Na}^{+}\)and \(\mathrm{PO}_{4}{ }^{3}\) ions form for each \(\mathrm{Na}_{3} \mathrm{PO}_{4}\) formula unit that dissolves? (b) How many moles of \(\mathrm{Na}^{+}\)and \(\mathrm{PO}_{4}{ }^{3}\) form for each mole of \(\mathrm{Na}_{3} \mathrm{PO}_{4}\) that dissolves?

Short answer

For each formula unit of \( \mathrm{Na}_{3} \mathrm{PO}_{4} \) that dissolves, 3 sodium ions and 1 phosphate ion form. And for every mole of \( \mathrm{Na}_{3} \mathrm{PO}_{4} \) that dissolves, 3 moles of sodium ions and 1 mole of phosphate ion form.

Step-by-step solution

Understand the Chemical Equation

The chemical equation given is represented as follows: \( \mathrm{Na}_{3} \mathrm{PO}_{4}(s) \rightarrow 3 \mathrm{Na}^{+}(a q)+\mathrm{PO}_{4}{ }^{3}{ }^{-}(a q) \). This means that each unit of sodium phosphate that dissolves yields 3 sodium ions and 1 phosphate ion.

Answer to Question (a)

To answer the first part of the exercise, we examine the chemical equation. We know that \( \mathrm{Na}_{3} \mathrm{PO}_{4} \rightarrow 3 \mathrm{Na}^{+} +\mathrm{PO}_{4}{ }^{3}{ }^{-} \). From this, one can note that each formula unit of \( \mathrm{Na}_{3} \mathrm{PO}_{4} \) that dissolves forms 3 sodium ions and 1 phosphate ion.

Understand Moles and Stoichiometry

In chemistry, the concept of moles is a way to measure a specific amount of particles. According to the method of stoichiometry, the coefficients in a chemical reaction denote the ratio in which the reactants react and the products are formed.

Answer to Question (b)

To answer the second part of the exercise, we refer back to our chemical equation and understanding of stoichiometry. As we know from the coefficients in the equation, when one mole of \( \mathrm{Na}_{3} \mathrm{PO}_{4} \) dissolves, it forms 3 moles of \( \mathrm{Na}^{+} \) ions and 1 mole of \( \mathrm{PO}_{4}{ }^{3}{ }^{-} \) ions.

Key concepts

Dissolving Sodium Phosphate

Understanding the process of dissolving sodium phosphate (Na_3PO_4) in water is essential for grasping key chemical concepts. Let's explore what happens when this ionic compound interacts with water. Ionic compounds are substances composed of positive and negative ions held together by electrostatic forces. In water, the molecules of Na_3PO_4 break down into their individual ions.

This breakdown can be represented by a chemical equation:
Na_3PO_4(s) → 3 Na^+(aq) + PO_4^{3-}(aq). Here, '(s)' denotes the solid state of sodium phosphate before dissolving, and '(aq)' indicates that the ions are in an aqueous, or water-based, solution after dissolving. As sodium phosphate dissolves, each formula unit separates into three sodium ions (Na^+) and one phosphate ion (PO_4^{3-}).

Understand that dissolving is a physical change, as it involves a substance going from one phase to another without altering the actual composition of the substance. The sodium phosphate still consists of sodium and phosphate ions; they are just dispersed in water. This process is greatly influenced by water’s polarity, which allows it to surround and separate the ions, facilitating their solubility in the solution.

Chemical Equation Representation

A proper chemical equation representation is crucial for visualizing and understanding the transformations that occur during a chemical reaction. The balanced chemical equation for the dissolving of sodium phosphate in water can be written as:
Na_3PO_4(s) → 3 Na^+(aq) + PO_4^{3-}(aq).

This equation operates as a recipe, telling us that for each unit, or formula unit, of solid sodium phosphate (Na_3PO_4), water helps to produce exactly three sodium ions (Na^+) and one phosphate ion (PO_4^{3-}) in solution. This 'recipe' adheres strictly to the law of conservation of mass, meaning the amount of mass remains constant throughout the reaction; it's neither created nor destroyed, simply rearranged.

The coefficients in front of each substance within the equation indicate the number of moles that participate in the reaction. In this case, '3' in front of Na^+ means that three moles of sodium ions are produced for every one mole of sodium phosphate that dissolves. These coefficients are the cornerstone of stoichiometry, guiding us to quantitatively analyze the reaction.

Mole Concept in Chemistry

The mole concept is a fundamental principle used to measure quantities in chemistry. A mole is defined as the amount of a substance that contains as many entities (atoms, ions, molecules, or other particles) as there are atoms in 12 grams of pure carbon-12. This number, Avogadro's number, is approximately 6.022 × 10^{23} entities per mole.

In the context of our exercise, this concept helps to determine the number of ions formed when a substance dissolves. When combining the mole concept with stoichiometry, you discover that one mole of Na_3PO_4 will yield three moles of sodium ions (Na^+) and one mole of phosphate ions (PO_4^{3-}) when dissolved in water, as per the coefficients in the chemical equation.

This also implies that the number of particles of the ions is directly related to Avogadro's number. Therefore, one mole of Na_3PO_4 dissolving results in roughly 3 × 6.022 × 10^{23} sodium ions and 6.022 × 10^{23} phosphate ions. By understanding moles and their relation to chemical equations, students can accomplish an accurate quantitative analysis of chemical reactions, including the amounts of reactants consumed and products formed. This conceptual framework is key to mastering stoichiometry, a central topic in chemical education.