Question

Mercury is the only metal that is a liquid at room temperature. Its density is \(13.6 \mathrm{~g} / \mathrm{mL}\). How many grams of mercury will occupy a volume of \(95.8 \mathrm{~mL} ?\)

Short answer

To find the answer: Perform the multiplication \(mass = 13.6 \mathrm{g/mL} \times 95.8 \mathrm{mL}\). The unit of mL is cancelled, leaving grams as the unit for the mass.

Step-by-step solution

Write down given information

The problem provides the density of mercury, \(13.6 \mathrm{~g} / \mathrm{mL}\), and the volume of \(95.8 \mathrm{mL}\) which it will occupy.

Identify correct formula

We need to calculate the mass, which can be found using the formula \(mass = density \times volume\). This comes from the definition of density.

Plug in values into formula

Replace the density and volume in the formula with the values that are given: \(mass = 13.6 \mathrm{g/mL} \times 95.8 \mathrm{mL}\).

Calculate the mass

Multiply the values together to get the mass. A calculator may be needed for this step.

Key concepts

Understanding Mass and Volume

In the realm of physics, mass and volume are two foundational concepts that enable us to describe the properties of substances. Mass refers to the amount of matter in an object and is typically measured in grams or kilograms. Volume, on the other hand, refers to the space that an object occupies and is commonly measured in milliliters or liters for liquids. In the context of the exercise, we are dealing with mercury, which is measured in milliliters (mL) for volume because it is a liquid at room temperature.

To perform density calculations, it's important to firmly grasp the relationship between mass and volume. This relationship is crucial because density is defined as the mass per unit volume of a substance. The formula to calculate an object's mass when its density and volume are known is straightforward: \( mass = density \times volume \). By understanding this basic concept, one can easily solve for mass when given the density and volume, just as we did with the mercury example.

In practice, if we have a specified volume of a substance, we can calculate the mass by multiplying this volume by the substance's density. This calculation is pivotal in fields such as chemistry and engineering, where precise measurements are necessary for experiments and designs.

The Density of Mercury

Mercury, with the chemical symbol Hg, stands out in the periodic table due to its unique characteristic of being a liquid metal at room temperature. Its density is quite high at \(13.6 \mathrm{g/mL}\), a fact that plays a significant role in many of its applications, such as in barometers and thermometers.

The density of a substance can tell us a lot about its properties. For instance, a high-density material like mercury means that a relatively small volume of it will have a considerable mass. This property of mercury is critical for understanding the step-by-step solution to the textbook exercise. Knowing that mercury's density is \(13.6 \mathrm{g/mL}\), one can predict that a small volume would weigh a lot compared to the same volume of a less dense substance, like water, which has a density of about \(1 \mathrm{g/mL}\).

Facts like these are not just useful for solving problems in physics and chemistry; they also have practical implications. For example, because mercury has a high density, it is used in applications that require a dense material to occupy a small space while providing significant weight or force.

Chemical Properties of Substances

In chemistry, understanding the chemical properties of a substance is essential as these properties define how a substance reacts under different conditions and with other substances. Chemical properties are intrinsic to the substance and include reactivity, flammability, and acidity, among others.

While the focus of our mercury exercise is on physical properties, specifically density, it's beneficial to be aware of the chemical properties as well. Mercury, for instance, has a relatively low reactivity compared to other metals. This means it does not readily react with many substances, which is why it can stay in liquid form at room temperature without reacting with the oxygen in the air. It is also toxic, meaning that its interactions with living organisms can lead to adverse health effects - this is a vital aspect of its chemical property profile.

Understanding the chemical properties play a crucial role in safe handling and usage of substances. And while they may not be the main attraction in a problem about density, they lay the foundation for why materials behave the way they do, further deepening one's comprehension of science as a whole.