Question

If you mix olive oil with water, the olive oil will float on top of the water. The density of water is \(1.00 \mathrm{~g} / \mathrm{cm}^{3}\) at room temperature. (a) Is the density of olive oil more or less than \(1.00 \mathrm{~g} / \mathrm{cm}^{3} ?\) (b) The density of olive oil in its liquid phase does vary with temperature. Do you think olive oil would be more dense or less dense at higher temperatures? Explain.

Short answer

(a) The density of olive oil is less than 1.00 g/cm³, as it floats on top of water. (b) Olive oil would be less dense at higher temperatures, as its molecules gain kinetic energy and move apart from each other, occupying more space and thus decreasing its density.

Step-by-step solution

Determine the density of olive oil relative to water

Since olive oil floats on top of the water, it means that it is lighter than the water. This implies that its density must be less than that of water. Therefore, the density of olive oil is less than 1.00 g/cm³.

Find out whether olive oil becomes more or less dense with increasing temperature

When substances are heated, their molecules move faster and usually spread apart, thus occupying more space. This makes most liquids less dense at higher temperatures. Although olive oil is a different substance, it should also follow this general trend and its density should decrease when heated. So, olive oil would be less dense at higher temperatures.

Explain the reason behind the temperature dependence of olive oil density

The reason behind this behavior is the molecular structure of olive oil and the interactions between its molecules. As the temperature increases, the molecules of olive oil gain more kinetic energy and start moving faster. This causes the molecules to move apart from each other, increasing the volume occupied by a certain mass of olive oil. Since the density is defined as the mass divided by volume, an increase in volume with no change in mass will result in a decrease in density. Therefore, the density of olive oil becomes less at higher temperatures.

Key concepts

Density and Temperature

Density is a measure of how much mass is contained in a given volume. As temperature changes, the density of a substance can change as well. This is because temperature affects the speed at which molecules move.
When substances are heated, their molecules gain kinetic energy, causing them to move faster and spread further apart. This expansion increases the volume the substance occupies while the mass stays constant, leading to a decrease in density. For most liquids, including olive oil, an increase in temperature results in a decrease in density. Thus, when olive oil is heated, its molecules move apart, and its density decreases. This is a common trait seen in many liquids and even gases as they are heated.

Liquids

Liquids are a state of matter that have a definite volume but no definite shape. They take the shape of their container but maintain a consistent volume. This is because the particles in a liquid are not as tightly packed as in solids, but are less free-moving than gases.
In a liquid, molecules are close enough to be affected by intermolecular forces, such as Van der Waals forces, but they can still move around and slide past one another. This allows liquids to flow and take the shape of their container. The density of liquids is an important property. It is influenced by factors like temperature and pressure. In the case of olive oil mixed with water, olive oil floats because it is less dense. This simple observation highlights how density plays a crucial role in determining the behavior of liquids when mixed.

Buoyancy

Buoyancy is the force that allows objects to float in a liquid or gas. It occurs because of the pressure exerted by the fluid on the object it is submerged in. The upward buoyant force is equal to the weight of the fluid displaced by the object, as stated by Archimedes' principle. When olive oil is mixed with water, it floats on top because its density is less than that of water. This means the water exerts an upward buoyant force that is greater than the weight of the olive oil, allowing it to float. Buoyancy is a critical concept in understanding why objects behave differently in various fluids based on their densities. Understanding the principle of buoyancy is crucial in various applications, from designing ships to understanding how fish control their depth in water. It also explains everyday phenomena, like the floating of olive oil on water.