Problem 1 - Chemistry: Atoms First

Question

Complete the changes in concentrations for each of the following reactions: (a) \(\operatorname{AgI}(s) \longrightarrow \mathrm{Ag}^{+}(a q)+\mathrm{I}^{-}(a q)\) (b) \(\mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{Ca}^{2+}(a q)+\mathrm{CO}_{3}^{2-}(a q)\) (c) \(\operatorname{Mg}(\mathrm{OH})_{2}(s) \longrightarrow \mathrm{Mg}^{2+}(a q)+2 \mathrm{OH}^{-}(a q)\) (d) \(\operatorname{Mg}_{3}\left(\mathrm{PO}_{4}\right)_{2}(s) \longrightarrow 3 \mathrm{Mg}^{2+}(a q)+2 \mathrm{PO}_{4}^{3-}(a q)\) (e) \(\operatorname{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{OH}(s) \longrightarrow 5 \mathrm{Ca}^{2+}(a q)+3 \mathrm{PO}_{4}^{3-}(a q)+\mathrm{OH}^{-}(a q)\)

Step-by-Step Solution

Answer

The changes in concentrations for each reaction are: (a) 1:1:1, (b) 1:1:1, (c) 1:1:2, (d) 1:3:2, (e) 1:5:3:1 between the solid compound and the produced ions in solution.

Step 1: Analyze the Dissolution of AgI

Start by writing the balanced equation for the dissolution of AgI. Since AgI is a solid (s), it dissolves into its ions, Ag+ and I-, which are in aqueous solution (aq). The balanced chemical equation reflects this change in state and the stoichiometry of the ions formed: \(\text{AgI}(s) \rightarrow \text{Ag}^{+}(aq) + \text{I}^{-}(aq)\). This shows a one-to-one molar ratio between AgI and each of its dissociated ions.

Step 2: Analyze the Dissolution of CaCO3

Write the balanced equation for CaCO3 dissolving. Solid CaCO3 dissociates into Ca2+ and the carbonate ion (CO3^{2-}), both in aqueous solution. The balanced chemical equation is: \(\text{CaCO}_3(s) \rightarrow \text{Ca}^{2+}(aq) + \text{CO}_{3}^{2-}(aq)\), indicating a one-to-one ratio.

Step 3: Analyze the Dissolution of Mg(OH)2

Write the balanced equation for Mg(OH)2 dissolving. Solid Mg(OH)2 splits into Mg2+ and OH- ions, with a two to one ratio as indicated by the formula. The equation is: \(\text{Mg}(\text{OH})_{2}(s) \rightarrow \text{Mg}^{2+}(aq) + 2\text{OH}^{-}(aq)\), implying that each unit of Mg(OH)2 generates two hydroxide ions.

Step 4: Analyze the Dissolution of Mg3(PO4)2

Balance the equation of Mg3(PO4)2 dissolving into its constituent ions. The equation reflects the stoichiometry of the ions: \(\text{Mg}_3(\text{PO}_4)_2(s) \rightarrow 3\text{Mg}^{2+}(aq) + 2\text{PO}_{4}^{3-}(aq)\), indicating three magnesium ions for every two phosphate ions generated from the solid.

Step 5: Analyze the Dissolution of Ca5(PO4)3OH

Write down the balanced equation for the dissolution of Ca5(PO4)3OH into calcium ions, phosphate ions, and hydroxide ions. The chemical equation is: \(\text{Ca}_5(\text{PO}_4)_3\text{OH}(s) \rightarrow 5\text{Ca}^{2+}(aq) + 3\text{PO}_{4}^{3-}(aq) + \text{OH}^{-}(aq)\), demonstrating a one-to-one-to-one molar ratio between the solid and its ions for each formula unit.

Key Concepts

Dissolution of AgI

Understanding the dissolution of AgI, or silver iodide, involves recognizing the transition from the solid state to an aqueous state where AgI separates into its component ions. This happens as follows:

• Initial Solid: AgI(s) — The undissolved silver iodide sits as a solid.
• Process: When placed in water, AgI dissociates.
• Resulting Ions: Ag^{+}(aq) + I^{-}(aq) — Free-floating in the solution, the positive silver ion and negative iodide ion are the result of dissolution.

This one-to-one breakdown means that for every mole of AgI dissolved, there is one mole of Ag+ and one mole of I- created in the solution.

Dissolution of CaCO3

Calcium carbonate (CaCO3) is a common substance found in rocks and seashells. When it dissolves in water, the process is as follows:

• Initial Solid: CaCO3(s) — Calcium carbonate is in solid form prior to interacting with the water.
• Process: Dissolution under certain conditions leads to separation of ions.
• Resulting Ions: Ca^{2+}(aq) + CO3^{2-}(aq) — The release of these ions indicates the formation of an aqueous solution.

Since CaCO3 comes apart to form one mole of Ca2+ and one mole of CO32- each, it is essential to note the formation of electrically balanced aqueous solutions.

Dissolution of Mg(OH)2

Magnesium hydroxide, Mg(OH)2, is another example of a substance that dissolves to create an aqueous solution:

• Initial Solid: Mg(OH)2(s) — The starting point is the dense solid form of magnesium hydroxide.
• Process: When soluble, it breaks down into ions in water.
• Resulting Ions: Mg^{2+}(aq) + 2OH^{-}(aq) — For each Mg(OH)2 unit that dissolves, one magnesium ion and two hydroxide ions are created, indicating a 1:2 ratio in the resultant solution.

This disproportion in the creation of hydroxide ions is a critical factor when considering the pH of the resulting solution.

Dissolution of Mg3(PO4)2

When magnesium phosphate (Mg3(PO4)2) dissolves, it follows a specific pattern:

• Initial Solid: Mg3(PO4)2(s) — The substance starts as a solid compound that is insoluble in water.
• Process: With enough energy, it can dissociate into its ions.
• Resulting Ions: 3Mg^{2+}(aq) + 2PO4^{3-}(aq) — This shows that three magnesium ions pair with two phosphate ions for each formula unit of the solid dissolved.

It is important to remember the stoichiometric relationship here, which dictates the proportion of ions in the solution.

Dissolution of Ca5(PO4)3OH

In the dissolution of hydroxyapatite, Ca5(PO4)3OH, key processes occur:

• Initial Solid: Ca5(PO4)3OH(s) — Start with the solid mineral often found in bone and teeth.
• Process: Under acidic conditions, it can dissolve into aqueous ions.
• Resulting Ions: 5Ca^{2+}(aq) + 3PO4^{3-}(aq) + OH^{-}(aq) — This illustrates the stoichiometry of the substance where multiple ions are produced from each unit of solid dissolved.

The balance of calcium, phosphate, and hydroxide ions is crucial for biological systems as well as in chemical stoichiometry.

Stoichiometry

Stoichiometry is the calculation of reactants and products in a chemical reaction. It governs how the dissolution of compounds like AgI or CaCO3 occurs. In stoichiometry:

• Mole Ratios: The coefficients in a balanced equation represent the exact mole ratios of each substance involved.
• Conservation: Matter is conserved, meaning the number of atoms of each element is the same on both sides of the reaction.
• Predictive tool: Stoichiometry predicts the amounts of substances consumed and formed in a reaction.

In the dissolution processes we've discussed, stoichiometry helps us understand the quantitative relationships between solid substances and their resulting ions.

Chemical Equations

Chemical equations are symbolic representations of chemical reactions. They demonstrate the following:

• Reactants and Products: What is consumed and produced in the reaction.
• The Law of Conservation of Mass: Mass does not change in a chemical reaction; therefore, both sides of the equation must be balanced.
• Phases of Matter: Indicated by (s) for solid, (l) for liquid, (g) for gas, and (aq) for aqueous.

For all of the dissolution reactions, writing a balanced chemical equation is the first step in understanding the process and is key in grasping the stoichiometry involved.

Aqueous Solutions

Aqueous solutions are formed when substances like salts, acids, or bases dissolve in water:

• Hydration: Water molecules surround and interact with the ions or molecules of the dissolved substance.
• Solubility: This term describes how much of a substance can dissolve in water at a given temperature.
• Electrolytes: Many common ionic compounds, when dissolved, turn the solution into an electrolyte that can conduct electricity.

In the context of the dissolution reactions detailed above, each produces an aqueous solution where ions are uniformly distributed and can freely move, displaying the characteristic properties of such solutions.