Question

The following cylinder contains three liquids that do not mix with one another: water (density \(=1.0 \mathrm{~g} / \mathrm{mL}\) ), vegetable oil (density \(=0.93 \mathrm{~g} / \mathrm{mL})\), and mercury (density \(=13.5 \mathrm{~g} / \mathrm{mL})\). Which liquid is which?

Short answer

Mercury is at the bottom, water in the middle, and vegetable oil at the top.

Step-by-step solution

Understand the Densities

The densities of the liquids are given as follows: water is 1.0 g/mL, vegetable oil is 0.93 g/mL, and mercury is 13.5 g/mL. The liquid with the highest density will be at the bottom, and the one with the lowest density will be at the top, as denser liquids sink below less dense liquids.

Identify the Order of the Liquids

Since mercury has the highest density (13.5 g/mL), it will settle at the bottom of the cylinder. Water, with a density of 1.0 g/mL, is less dense than mercury but denser than vegetable oil. Vegetable oil, with the lowest density of 0.93 g/mL, will float on top of the water.

Conclusion

The order from bottom to top in the cylinder is mercury (bottom), water (middle), and vegetable oil (top). This layering occurs because denser liquids sit below the less dense ones.

Key concepts

Liquid Layers

When dealing with liquids, understanding how they layer upon each other is essential in the study of density and buoyancy. In scenarios where you have multiple liquids like water, oil, and mercury that do not mix, they naturally arrange in a formation if they are in a container. This arrangement is primarily determined by their densities.

In a cylinder or any similar container, liquids form distinct layers based on density. Liquids that do not mix with each other form clear boundaries, allowing us to visually distinguish different layers. When placed in a container:

• The liquid with the highest density sinks to the bottom.
• The liquid with the next highest density will form a layer above the densest liquid.
• The liquid with the lowest density will float on top of the others.

This is a common property utilized in various scientific applications, such as in separating liquids in laboratory settings or in understanding geological formations where liquid layers can be found underground.

Properties of Matter

The concept of density is intricately linked to the properties of matter. Each type of matter, be it a solid, a liquid, or a gas, has unique properties that define how it behaves in different environments.

Density is defined as the mass of a substance divided by its volume. It tells us how much matter is packed into a specific volume, and it is one of the key factors that determine the behavior of substances in liquid form. For example:

• High-density substances are typically heavier and will often settle below less dense substances when placed in the same container.
• Low-density substances, being lighter, have a tendency to float above higher density substances.

Additionally, the properties that determine whether different substances mix, also play a crucial role. Some substances remain immiscible due to molecular interactions that prevent mixing. Understanding these properties allows scientists to predict and manipulate material behavior in practical applications like oil spill cleanup or formulating cosmetics.

Density Comparison

Density comparison involves evaluating the densities of different materials to predict their behavior when combined or layered. In the exercise, we compare the densities of water, oil, and mercury to determine their positioning in a container.

The step-by-step solution demonstrates that:

• Mercury, with the highest density (13.5 g/mL), settles at the bottom.
• Water, denser than oil but less than mercury (1.0 g/mL), situates in the middle.
• Vegetable oil, being the least dense (0.93 g/mL), floats on top.

These layers form naturally as a consequence of gravitational pull acting on the denser liquid, causing it to settle below those with lower density. By comparing densities, we can also predict how liquids will behave in certain environments and can use this knowledge in engineering, food industry, and even in nature for understanding various natural phenomena.