Problem 25 - Chemistry: The Central Science

Question

By referring to Figure 13.15, determine whether the addition of \(40.0 \mathrm{~g}\) of each of the following ionic solids to \(100 \mathrm{~g}\) of water at \(40^{\circ} \mathrm{C}\) will lead to a saturated solution: (a) \(\mathrm{NaNO}_{3}\), (b) \(\mathrm{KCl}_{\text {, }}\) (c) \(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\), (d) \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}\)

Step-by-Step Solution

Answer

Referring to Figure 13.15 at 40°C, the solubility of each ionic solid in 100 g of water is as follows: a) NaNO3: 100 g b) KCl: 50 g c) K2Cr2O7: 10 g d) Pb(NO3)2: 65 g Given that 40.0 g of each solid is added: a) NaNO3: NOT saturated b) KCl: NOT saturated c) K2Cr2O7: saturated d) Pb(NO3)2: NOT saturated Therefore, only the K2Cr2O7 solution will be saturated.

Step 1: Find the solubility of each ionic solid at 40°C

To solve this exercise, we will refer to the solubility graph (Figure 13.15) provided in the question. The graph will give us the solubility of each ionic solid in 100 g of water at 40°C. a) Sodium Nitrate (NaNO3): From the graph, at 40°C, the solubility of NaNO3 is approximately 100 g/100 g of water. b) Potassium Chloride (KCl): From the graph, at 40°C, the solubility of KCl is approximately 50 g/100 g of water. c) Potassium Dichromate (K2Cr2O7): From the graph, at 40°C, the solubility of K2Cr2O7 is approximately 10 g/100 g of water. d) Lead Nitrate (Pb(NO3)2): From the graph, at 40°C, the solubility of Pb(NO3)2 is approximately 65 g/100 g of water.

Step 2: Compare the solubility with the amount of ionic solid being added

Now, we will compare the solubility of each ionic solid at 40°C with the amount of solid being added (40.0 g). a) Sodium Nitrate (NaNO3): The solubility is 100 g, and we are adding 40.0 g. As the amount being added is less than the solubility at 40°C, it will NOT lead to a saturated solution. b) Potassium Chloride (KCl): The solubility is 50 g, and we are adding 40.0 g. As the amount being added is less than the solubility at 40°C, it will NOT lead to a saturated solution. c) Potassium Dichromate (K2Cr2O7): The solubility is 10 g, and we are adding 40.0 g. As the amount being added is more than the solubility at 40°C, it will lead to a saturated solution. d) Lead Nitrate (Pb(NO3)2): The solubility is 65 g, and we are adding 40.0 g. As the amount being added is less than the solubility at 40°C, it will NOT lead to a saturated solution.

Step 3: Conclusion

Based on our analysis, the addition of 40.0 g of each of the following ionic solids to 100 g of water at 40°C will lead to a saturated solution only for (c) potassium dichromate (K2Cr2O7).

Key Concepts

Saturated Solution

A saturated solution occurs when a solvent, such as water, holds the maximum amount of solute it can dissolve at a given temperature. Any additional solute added beyond this point will not dissolve and will remain in its solid form.
This concept is vital in understanding solubility because it defines the limit of how much solute can be dissolved in a solvent under specific conditions.

For example, if 100 g of water at 40°C can dissolve 50 g of a solute, adding more than 50 g will result in a saturated solution. Any additional solute will settle at the bottom as it cannot be absorbed into the water anymore.

• Aqueous solutions become saturated when the kinetic energy of water molecules cannot break apart additional solute particles.
• Saturation points vary with substances due to their unique interactions with water molecules.
• Temperature plays a crucial role; higher temperatures usually increase solubility as they provide more energy for solute particles to dissolve.

Understanding saturation helps in predicting and controlling reactions and processes in various industries, such as food preservation, pharmaceuticals, and chemical manufacturing.

Ionic Solids

Ionic solids are large structures composed of ions held together by strong electrostatic forces known as ionic bonds. These solids are formed when metals and nonmetals react, transferring electrons from one to the other, creating positive and negative ions.
The strong bonds require a significant amount of energy to break, giving ionic solids high melting and boiling points.
This also means they are typically hard and brittle.

These properties influence their solubility in water:

• Many ionic solids dissolve in water as polar water molecules surround and pull the ions apart.
• The solubility varies with the specific ions involved and the temperature.
• Some ionic solids may only be slightly soluble, forming saturated solutions with a small amount of solute.

For example, while sodium chloride (table salt) readily dissolves in water, calcium sulfate has limited solubility. The study of ionic solids aids in understanding chemical universality as they are fundamental in many biological and chemical processes.

Chemistry Education

Chemistry education serves as a foundation for understanding the world at a molecular level and provides essential skills for scientific investigation and innovation. In the context of solubility and saturated solutions, students learn vital concepts such as solutes, solvents, dissolution, and precipitation processes.

These topics in chemistry education involve:

• Developing critical thinking by solving problems and conducting experiments.
• Building practical skills through laboratory work, such as accurately measuring solubility limits.
• Encouraging collaborative work when exploring saturated solutions and solubility graphs.

This education is crucial for preparing students to enter fields such as medicine, environmental science, and engineering. It also enhances everyday life understanding, helping people make informed decisions about consumer products, environmental issues, and health. Overall, chemistry education is not just about learning facts; it’s about cultivating a mindset for analytical reasoning and problem-solving.