Question

When dealing with percent-by-volume concentrations of solutions composed of two liquids, why must the total volume be measured instead of using the sum of the volumes of the component liquids?

Short answer

The total volume of an liquid mixture must be measured rather than simply adding the volumes of the component liquids because of the molecular interactions that happen when the liquids are mixed together, which can cause a decrease in total volume. Measuring the total volume after mixing ensures an accurate calculation of percent-by-volume concentrations.

Step-by-step solution

Understand the properties of liquid mixtures

When two liquids are mixed together, the resultant mixture doesn't have a volume equal to the sum of the individual volumes of the two liquids. This phenomenon occurs because the molecules of the two liquids interact when mixed together.

Explain molecular interactions in liquid mixtures

In a liquid, the molecules are constantly moving and interacting with each other. When two liquids are mixed together, the molecules of each liquid interact with each other. These interactions can cause the molecules to pack together more efficiently, resulting in a decrease in total volume.

Relate molecular interactions to percent-by-volume concentrations

Percent-by-volume concentrations are calculated as the volume of the solute divided by the total volume of the solution, multiplied by 100%. If the total volume was calculated by simply adding the volumes of the two liquids, it would not take into account the decrease in volume due to molecular interactions. Therefore, to get an accurate percent-by-volume concentration, you must measure the total volume after the two liquids are mixed together.

Key concepts

Properties of Liquid Mixtures

Understanding the properties of liquid mixtures is essential in many areas of chemistry and everyday applications like pharmacy compounding or mixing beverages. A liquid mixture is formed when two or more liquids are combined together. What's fascinating is that when liquids mix, the rules of simple arithmetic don't always apply. In particular, the total volume of a liquid mixture is often not equal to the sum of the individual volumes of the liquids involved.

This non-additive volume property is attributed to the concept of 'excess volume.' Excess volume represents the difference between the ideal mixture volume (obtained by summing the pure components' volumes) and the actual mixture volume. When liquids mix, they might take up more space due to less efficient packing, resulting in positive excess volume, or they might occupy less space if the molecular interactions lead to a more efficient packing, leading to negative excess volume.

When making solutions or mixtures, it's crucial to recognize that the properties such as density, viscosity, and boiling point also change. These changes are consequences of the new intermolecular forces established between the different molecules of the liquids involved. For example, alcohol and water mix to form a liquid mixture with a volume less than the sum of their separate volumes, which illustrates the importance of these underlying molecular interactions.

Molecular Interactions in Liquid Mixtures

Diving deeper into the molecular interactions in liquid mixtures can provide insight into the anomalous volume changes observed. In the microscopic world, molecules are not static; they are dynamic and in constant motion, which leads to various interactions with one another. These interactions are dependent on the nature of the molecules involved.

When two miscible liquids (i.e., liquids that can mix in any proportion) come into contact, their molecules start to interact through forces such as hydrogen bonds, van der Waals forces, or dipole-dipole interactions. For instance, if we consider mixing ethanol and water, the strong hydrogen bonds between water molecules can be disrupted by ethanol, which can form its own hydrogen bonds with water.

Synergistic and Antagonistic Effects

These interactions can be synergistic, where molecules pack more efficiently, resulting in a mixture with a volume less than expected. Conversely, some interactions are antagonistic, causing the mix to have a volume greater than expected. These molecular dynamics profoundly affect the resultant mixture's properties, such as solubility, boiling point elevation, or freezing point depression.

Calculating Percent-by-Volume

Calculating percent-by-volume is a common practice in laboratories for expressing the concentration of a solution. The percent-by-volume formula is straightforward: it's the volume of the solute (the substance being dissolved) divided by the total volume of the solution, then multiplied by 100%. This comes down to a relatively simple mathematical expression: \[ \text{Percent-by-volume} = \left(\frac{\text{Volume of solute}}{\text{Total volume of solution}}\right) \times 100% \]

An accurate percent-by-volume calculation is crucial because it can affect formulation strength in pharmacology, the taste of food products, or the reproducibility of experimental results in research. As detailed previously, since the final mixture volume isn't necessarily the sum of individual liquid volumes due to molecular interactions, it is imperative to measure the final mixture volume to calculate percent-by-volume concentrations correctly. Not doing so could result in significant errors, leading to incorrect concentration values which might have dire consequences in precision-dependent fields. Moreover, understanding this calculation aids students and professionals alike in ensuring that their mixtures meet the desired criteria for various applications.