Problem 120 - Chemistry The Molecular Science

Question

When volumes of liquids are mixed, the resulting volume is not always equal to the sum of the volume of each liquid. For example, when \(50.0 \mathrm{~mL}\) of ethanol \((\mathrm{d}=\) \(0.789 \mathrm{~g} / \mathrm{mL}\) ) is mixed with \(50.0 \mathrm{~mL}\) of water \((0.998 \mathrm{~g} / \mathrm{mL})\) at \(25^{\circ} \mathrm{C}\), the resulting volume is only \(95.6 \mathrm{~mL}\). Calculate the density of the solution.

Step-by-Step Solution

Answer

The density of the solution is approximately 0.935 g/mL.

Step 1: Calculate Mass of Ethanol

Use the density formula to calculate the mass of ethanol: \[ \text{Mass} = \text{Volume} \times \text{Density} = 50.0 \ \text{mL} \times 0.789 \ \text{g/mL} = 39.45 \ \text{g} \]

Step 2: Calculate Mass of Water

Calculate the mass of water using the density formula: \[ \text{Mass} = \text{Volume} \times \text{Density} = 50.0 \ \text{mL} \times 0.998 \ \text{g/mL} = 49.90 \ \text{g} \]

Step 3: Calculate Total Mass of Solution

Add the mass of ethanol and the mass of water to find the total mass:\[ \text{Total Mass} = 39.45 \ \text{g} + 49.90 \ \text{g} = 89.35 \ \text{g} \]

Step 4: Use the Resulting Volume to Find Density of Solution

Density is mass divided by volume. Calculate the density of the solution:\[ \text{Density} = \frac{\text{Total Mass}}{\text{Resulting Volume}} = \frac{89.35 \ \text{g}}{95.6 \ \text{mL}} \approx 0.935 \ \text{g/mL} \]

Key Concepts

Volume

Volume is the amount of space that a substance or object occupies. In everyday situations, we often measure the volume of a liquid in milliliters (mL) or liters (L). It's important to note that when mixing liquids, the total volume may not simply be the sum of the individual volumes. This phenomenon occurs due to the interactions between the molecules of the substances being mixed.

For example, when mixing ethanol and water, the volume comes out to be less than the sum of their initial volumes. In the provided exercise, the volume of the solution is only 95.6 mL, despite mixing 50.0 mL of ethanol with 50.0 mL of water. Understanding this concept is crucial, particularly when you're calculating the density of mixtures.

Mixture

A mixture is a combination of two or more substances where each retains its properties and can usually be separated by physical means. Mixtures can be categorized into homogeneous and heterogeneous mixtures. A homogeneous mixture, like the solution of ethanol in water, has a uniform composition throughout.

When preparing mixtures, each component may influence the final properties of the mixture in different ways, such as altering its density, viscosity, or boiling point. With ethanol and water, their distinct molecular structures lead to interactions that affect the final volume and density. By understanding mixtures, we can predict and calculate important characteristics like density, which is crucial for many scientific and industrial applications.

Ethanol and Water

Ethanol and water are both common liquids with distinct properties, and when mixed, they form a widely studied solution due to its interesting characteristics. Ethanol is an alcohol, known chemically as C\(\_2\)H\(\_5\)OH, and is less dense than water. Water, with its unique molecular structure, is known for its high density and ability to dissolve many substances.

When ethanol is added to water, the polar nature of both molecules leads to strong hydrogen bonding, which causes the mixture to occupy a smaller volume than expected. This interaction results in the phenomenon where the sum of their individual volumes is not equal to the final volume. In the given example, this results in a smaller than expected total volume and, consequently, affects the density calculation of the resultant solution.

Thus, understanding the interactions between ethanol and water is essential in calculating properties like density, which depend heavily on the final volume of the mixture.