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Chapter 8: Problem 43

"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?

Short Answer

Expert verified
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 by step solution

01

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: \[\mathrm{Ca}^{2+}(a q) + \mathrm{Na}_{2} \mathrm{B}_{4} \mathrm{O}_{7}(s) \rightarrow \mathrm{CaB}_{4} \mathrm{O}_{7}(s) + 2 \mathrm{Na}^{+}(a q)\]
02

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: \[\mathrm{Ca}^{2+}(a q) + \mathrm{B}_{4} \mathrm{O}_{7}^{2-}(a q) \rightarrow \mathrm{CaB}_{4} \mathrm{O}_{7}(s) \]
03

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: \[\mathrm{Mg}^{2+}(a q) + \mathrm{Na}_{2} \mathrm{B}_{4} \mathrm{O}_{7}(s) \rightarrow \mathrm{MgB}_{4} \mathrm{O}_{7}(s) + 2 \mathrm{Na}^{+}(a q)\]
04

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: \[\mathrm{Mg}^{2+}(a q) + \mathrm{B}_{4} \mathrm{O}_{7}^{2-}(a q) \rightarrow \mathrm{MgB}_{4} \mathrm{O}_{7}(s) \]
05

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.

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