Problem 50 - Chemistry: The Central Science

Question

(a) Which of the following ionic species could be responsible for hardness in a water supply: \(\mathrm{Ca}^{2+}, \mathrm{K}^{+}, \mathrm{Mg}^{2+}, \mathrm{Fe}^{2+}, \mathrm{Na}^{+}\)? (b) What properties of an ion determine whether it will contribute to water hardness?

Step-by-Step Solution

Answer

The ions responsible for hardness in a water supply are calcium ion (\(\mathrm{Ca}^{2+}\)) and magnesium ion (\(\mathrm{Mg}^{2+}\)). The properties that determine whether an ion will contribute to water hardness are: (1) charge of the ion, (2) ionic size, and (3) solubility of the ion and its compounds. Ions with a higher charge and smaller size, like calcium and magnesium, can strongly bind with negatively charged ions in water, forming insoluble compounds that cause hardness. Soluble compounds, like those formed by sodium and potassium ions, do not cause hardness as they remain dissolved in water.

Step 1: (a) Identifying responsible ions for water hardness

The ions that are responsible for hardness in a water supply are the calcium ion (\(\mathrm{Ca}^{2+}\)) and the magnesium ion (\(\mathrm{Mg}^{2+}\)). The other ions listed (\(\mathrm{K}^{+}\), \(\mathrm{Fe}^{2+}\), and \(\mathrm{Na}^{+}\)) do not significantly contribute to water hardness.

Step 2: (b) Properties of ions contributing to water hardness

The properties of an ion that determine whether it will contribute to water hardness are: 1. Charge of the ion: Ions with a higher charge, like Ca²⁺ and Mg²⁺, are more likely to cause water hardness because they can strongly bind with negatively charged ions in water, such as carbonate (\(\mathrm{CO_{3}}^{2-}\)) and sulfate (\(\mathrm{SO_{4}}^{2-}\)). These complex formations result in insoluble precipitates, which cause the water to be hard. 2. Ionic size: The size of the ion is also a contributing factor to water hardness. Smaller ions, like calcium and magnesium, have a higher affinity for negatively charged ions in water than larger ions like sodium and potassium. As a result, these smaller ions can form insoluble compounds more easily, further contributing to water hardness. 3. Solubility of the ion and its compounds: Hard water ions like calcium and magnesium generally form insoluble compounds with carbonate and sulfate ions, which precipitate out of the water and cause hardness. Ions that form highly soluble compounds, such as sodium and potassium, do not cause hardness because they remain dissolved in the water.

Key Concepts

Calcium Ion

Calcium ions, denoted as \( \mathrm{Ca}^{2+} \), play a significant role in contributing to water hardness. These ions originate primarily from the dissolution of calcium-containing minerals such as limestone, gypsum, and calcite in water. When calcium ions are present, they can combine with negatively charged ions like carbonate \( \mathrm{CO_{3}}^{2-} \) and sulfate \( \mathrm{SO_{4}}^{2-} \).

• The combination of \( \mathrm{Ca}^{2+} \) with carbonate, in particular, leads to the formation of insoluble calcium carbonate \( \mathrm{CaCO_{3}} \).
• As more of these insoluble precipitates accumulate, they cause the water to become hard.

The presence of calcium ions in water is crucial for various biological functions but can be problematic in household scenarios. This is because hard water can lead to the scaling of pipes, reducing appliance efficiency. Understanding calcium ions' role in water hardness helps in addressing the scaling issues through water softening techniques like ion exchange or reverse osmosis systems.

Magnesium Ion

Magnesium ions, expressed chemically as \( \mathrm{Mg}^{2+} \), are another key contributor to water hardness. Much like calcium, magnesium is found in a variety of minerals, such as dolomite and magnesite, and can be introduced into water through geologic processes.
Just as calcium ions do, magnesium ions in water react with negatively charged ions.

• These include carbonate \( \mathrm{CO_{3}}^{2-} \) and sulfate \( \mathrm{SO_{4}}^{2-} \), forming compounds like magnesium carbonate \( \mathrm{MgCO_{3}} \).
• These compounds tend to be less soluble, leading to precipitation and contributing to hard water formation.

Magnesium ions are crucial for health, providing essential nutrients the body needs. However, similar to calcium ions, in household water systems, they can cause mineral build-up in pipes and reduce the effectiveness of soaps and detergents. Using water softeners can help mitigate problems associated with high magnesium ion concentrations.

Ion Charge

The charge of an ion significantly influences its role in contributing to water hardness. In chemistry, ions are atoms or molecules that have gained or lost electrons, resulting in a net charge. For hardness, high-charge metal cations such as \( \mathrm{Ca}^{2+} \) and \( \mathrm{Mg}^{2+} \) are particularly important.
The charge of these ions is a critical property. It determines how ions interact with their environment:

• Highly charged ions, like \( \mathrm{Ca}^{2+} \) and \( \mathrm{Mg}^{2+} \), attract and bond more readily with negatively charged ions.
• This leads to the formation of stable, and often insoluble, compounds.

Higher ion charge increases the likelihood of precipitate formation, leading to hard water. Understanding ion charge helps in designing effective water treatment solutions and predicting the behavior of ions in various chemical contexts. Solutions often involve substituting these ions with ones that make soluble compounds, reducing hardness and related issues.