Problem 161 - General Chemistry

Question

A solution is prepared by dissolving table salt, sodium chloride, in water at room temperature. a Assuming there is no significant change in the volume of water during the preparation of the solution, how would the density of the solution compare to that of pure water? b If you were to boil the solution for several minutes and then allow it to cool to room temperature, how would the density of the solution compare to the density in part a? c If you took the solution prepared in part a and added more water, how would this affect the density of the solution?

Step-by-Step Solution

Answer

a) Increased density; b) Increased density; c) Decreased density.

Step 1: Understanding Density in Part a

In part a, when table salt is dissolved in water, the number of particles in the solution increases but the volume of the water remains approximately the same. Since density is defined as mass divided by volume and the mass of dissolved salt adds to the total mass of the solution, the density of the solution will be greater than that of pure water.

Step 2: Effect of Boiling on Density in Part b

When the solution is boiled, some of the water will evaporate, leaving behind less water but the same amount of salt. This decreases the volume more than the mass, increasing the density of the remaining solution compared to the initial solution in part a.

Step 3: Adding Water in Part c

In part c, adding more water to the solution increases the total volume while the mass of the initially dissolved salt remains unchanged. This results in a decrease in density because density is mass divided by an increased volume. Thus, the density of the new solution will be less than the density of the original solution prepared in part a.

Key Concepts

Sodium Chloride Solution

A sodium chloride solution, commonly referred to as saltwater, is made by dissolving table salt (sodium chloride) in water. This process is familiar, yet it involves some interesting scientific principles. When salt is added to water, the individual sodium (Na⁺) and chloride (Cl⁻) ions separate and disperse evenly throughout the water.
This formation of ions in water is what makes the solution conductive and is a basic example of the solubility concept in chemistry.

• The ions are surrounded by water molecules, a process known as hydration, which helps them to dissolve.
• Because sodium chloride dissociates completely in water, it is categorized as a strong electrolyte.

Solutions like these are important in various fields, from culinary to industrial applications, due to their ability to alter several properties of pure substances.

Effect of Temperature on Density

The density of a solution is sensitive to temperature changes. When the temperature of a liquid increases, the molecules move more vigorously, making the liquid expand and the volume increase while the mass remains constant.
This leads to a decrease in density, as density is calculated by dividing mass by volume. However, when we look specifically at a sodium chloride solution, boiling plays a significant role.

• Boiling causes water, but not the salt, to evaporate. This decreases the volume of the liquid more than it decreases the mass.
• Once the boiled solution cools to room temperature, the density becomes higher than it was initially, because there's now the same amount of salt in a smaller amount of water.

This phenomenon is essential, particularly in industrial processes that involve concentration of solutions by evaporating solvents.

Dilution and Concentration

Dilution and concentration are opposite processes that describe how the amount of solute in a solution is altered. Dilution refers to adding more solvent, typically water, to decrease the solution's concentration.
By doing this, you lower the number of solute particles per unit volume, which directly affects the density of the solution.

• With dilution, the mass of the solute remains constant while the volume increases, leading to a lower density, because density is mass divided by volume.
• Concentration, on the other hand, involves removing some solvent or adding more solute, increasing the density of the solution.

Understanding these concepts is crucial for tasks requiring precise chemical measurements, such as pharmaceuticals or food flavoring.

Mass and Volume Relationship

The relationship between mass and volume is fundamental to understanding the concept of density, defined by the equation \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). This equation shows that density depends on how much matter there is (mass) in a given space (volume).
For solutions, any process that changes either mass or volume will affect density.

• For example, dissolving sodium chloride in water increases the mass while the volume remains nearly constant, resulting in a higher density than pure water.
• Conversely, adding more water to the same solution increases the volume, reducing the density.

This relationship helps explain how and why density varies with different solution preparations, making it a vital concept in chemistry education.