Problem 43 - Introductory Chemistry Atoms First

Question

"Hard" water is hard because it contains \(\mathrm{Ca}^{2+}(a q)\) and \(\mathrm{Mg}^{2+}(a q)\) ions. It can be softened by adding borax powder, which is sodium tetraborate, \(\mathrm{Na}_{2} \mathrm{~B}_{4} \mathrm{O}_{7} .\) Adding borax removes the \(\mathrm{Ca}^{2+}(a q)\) and \(\mathrm{Mg}^{2+}(a q)\) from solution. Write a net ionic equation for each of these two reactions. What ion replaces the \(\mathrm{Ca}^{2+}(a q)\) and \(\mathrm{Mg}^{2+}(a q)\) ions in the water?

Step-by-Step Solution

Answer

The net ionic equations for the reactions between calcium ions and sodium tetraborate, and magnesium ions and sodium tetraborate are: 1) \(\mathrm{Ca}^{2+}(a q) + \mathrm{B}_{4} \mathrm{O}_{7}^{2-}(a q) \rightarrow \mathrm{CaB}_{4} \mathrm{O}_{7}(s) \) 2) \(\mathrm{Mg}^{2+}(a q) + \mathrm{B}_{4} \mathrm{O}_{7}^{2-}(a q) \rightarrow \mathrm{MgB}_{4} \mathrm{O}_{7}(s) \) The ion that replaces the \(\mathrm{Ca}^{2+}(a q)\) and \(\mathrm{Mg}^{2+}(a q)\) ions in the water is the sodium ion \(\mathrm{Na}^{+}\).

Step 1: Write a balanced chemical equation for calcium ions and sodium tetraborate reaction

The chemical equation for the reaction between calcium ions and sodium tetraborate is: \[\mathrm{Ca}^{2+}(a q) + \mathrm{Na}_{2} \mathrm{B}_{4} \mathrm{O}_{7}(s) \rightarrow \mathrm{CaB}_{4} \mathrm{O}_{7}(s) + 2 \mathrm{Na}^{+}(a q)\]

Step 2: Find the net ionic equation for the reaction between calcium ions and sodium tetraborate

The net ionic equation for this reaction will include only the species that are involved in the reaction, i.e., the ions that change their states. Thus, we remove the spectator ions which are not participating in the reaction. The net ionic equation for the reaction between calcium ions and sodium tetraborate is: \[\mathrm{Ca}^{2+}(a q) + \mathrm{B}_{4} \mathrm{O}_{7}^{2-}(a q) \rightarrow \mathrm{CaB}_{4} \mathrm{O}_{7}(s) \]

Step 3: Write a balanced chemical equation for magnesium ions and sodium tetraborate reaction

The chemical equation for the reaction between magnesium ions and sodium tetraborate is: \[\mathrm{Mg}^{2+}(a q) + \mathrm{Na}_{2} \mathrm{B}_{4} \mathrm{O}_{7}(s) \rightarrow \mathrm{MgB}_{4} \mathrm{O}_{7}(s) + 2 \mathrm{Na}^{+}(a q)\]

Step 4: Find the net ionic equation for the reaction between magnesium ions and sodium tetraborate

As before, we write the net ionic equation by removing the spectator ions and focusing on the species that are involved in the reaction. The net ionic equation for the reaction between magnesium ions and sodium tetraborate is: \[\mathrm{Mg}^{2+}(a q) + \mathrm{B}_{4} \mathrm{O}_{7}^{2-}(a q) \rightarrow \mathrm{MgB}_{4} \mathrm{O}_{7}(s) \]

Step 5: Determine the ion that replaces calcium and magnesium ions

Comparing both reactions we can see that the ion that replaces both calcium and magnesium ions is the sodium ion, \(\mathrm{Na}^{+}\). This happens as sodium tetraborate dissociates into sodium ions and tetraborate ions, and the sodium ions are left unreacted in the water, replacing the \(\mathrm{Ca}^{2+}(a q)\) and \(\mathrm{Mg}^{2+}(a q)\) ions that were removed during the reactions.

Key Concepts

Ion Exchange

In the process of ion exchange, we swap ions of similar charge between two substances. This is a crucial principle in many chemical reactions, especially in water treatment systems.
This process helps us remove unwanted ions from solutions by replacing them with more desirable ions.
In our problem with "hard water," the undesirable ions are calcium (\(\text{Ca}^{2+}\)) and magnesium (\(\text{Mg}^{2+}\)).

• These ions are known to cause water hardness, leading to issues such as scale buildup in pipes.
• By introducing sodium tetraborate (\(\text{Na}_2\text{B}_4\text{O}_7\)), ion exchange occurs.
• Sodium ions (\(\text{Na}^{+}\)) swap places with calcium and magnesium ions in the water.

Through this exchange, the hard water becomes "softened," resulting in fewer mineral deposits and better water quality.

Chemical Reactions

Chemical reactions involve transformations where reactants convert to products. This requires breaking and forming new chemical bonds.
The example in our problem highlights a chemical reaction where calcium and magnesium ions interact with sodium tetraborate.

• In this chemical process, calcium and magnesium ions are removed in the form of insoluble solids, called precipitates, namely \(\text{CaB}_4\text{O}_7(s)\) and \(\text{MgB}_4\text{O}_7(s)\).
• The process demonstrates the formation of compounds, showing how elements combine and transform in reactions.

Through these reactions, the chemistry of the water changes, as shown in net ionic equations that reflect only participating ions and their transformations.

Water Softening

Water softening is the method of removing calcium and magnesium ions from hard water to improve its quality. Hard water can cause scaling and reduces appliance efficiency.
This process is essential in both domestic and industrial systems.
The use of sodium tetraborate helps in this context by promoting reactions with hard water ions.

• Water softening prevents issues with soap performance and buildup of limescale.
• The softened water has \(\text{Na}^{+}\) ions taking place of the harder \(\text{Ca}^{2+}\) and \(\text{Mg}^{2+}\) ions.

The result is water that interacts better with soap and detergents, improving cleaning efficiency and reducing costs.

Spectator Ions

Spectator ions are ions present during chemical reactions but do not participate in the actual chemical change. They remain unchanged from reactants to products. In a net ionic equation, these ions are omitted.

• In the reactions of calcium and magnesium with sodium tetraborate, the \(\text{Na}^{+}\) does not contribute directly to forming \(\text{CaB}_4\text{O}_7(s)\) or \(\text{MgB}_4\text{O}_7(s)\).
• However, these ions are crucial for \(\text{Ca}^{2+}\) and \(\text{Mg}^{2+}\) replacement, as the overall reaction continues without their involvement.

Proper understanding of spectator ions helps in accurately writing net ionic equations indicating ions undergoing change during reactions.

Hard Water

Hard water contains high mineral content, particularly calcium and magnesium ions. This type of water poses challenges in both household and industrial applications.

• Scale formation in pipes, boilers, and heating systems is a common result of using hard water.
• It also reduces the efficiency of soaps and detergents, making cleaning processes less effective.

By treating hard water with substances such as sodium tetraborate, we can alleviate these issues.
Removing calcium and magnesium ions results in "softer" water, thus enhancing numerous benefits for daily use.