Density — Definition & Calculation

Density is a measurement of how much of something there is in a given volume. The term "density" most often refers to $\color{#c61a4d}{\text{mass density}}$, which is mass per volume. In chemistry, mass density is typically expressed in units of grams per milliliter ($\frac{\text{g}}{\text{mL}}$). For the remainder of this explanation, the type of density will always be specified, but moving forward it is safe to assume "density" refers to mass density.

Calculating Mass Density

Calculating mass density is a simple task regarding a simple calculation. First determine the mass of the sample, then the volume, then divide the mass by the volume. As an example, lets say we have $10\text{ mL}$ of an unknown substance. We place it on a scale and determine it to have a mass of $23\text{ g}$. The mass density ($\rho$) is calculated as follows. $$\rho=\frac{23\text{ g}}{10\text{ mL}}=2.3\frac{\text{ g}}{\text{ mL}}$$

To find the mass density of our substance we must first determine the volume in milliliters. We are given that the volume is half of a 1 liter. $$\begin{align} V&=\frac{1}{2}\text{ L} \\ &=0.5\cancel{\text{ L}} \cdot \frac{1000 \text{ mL}}{\cancel{\text{L}}} \\ &=500 \text{mL} \end{align}$$ Now we can divide our mass by our volume to find mass density. $$\rho=\frac{847\text{ g}}{500\text{ mL}}=1.694\frac{\text{ g}}{\text{ mL}}$$

Mass Density of Water and other materials

Much of the metric system is based around the properties of water. As it happens, the original definition of a gram is the amount of mass in $1$ milliliter of water. What this means is that water has a mass density of $1\frac{\text{ g}}{\text{ mL}}$. Over time these definitions have changed, and this relationship is no longer exact, but it is still close enough for all practical purposes.

The fact that the mass density of pure water is always $1\frac{\text{ g}}{\text{ mL}}$ brings up an interesting fact: the mass density of a pure substance is always the same. What this means is that if we have a block of pure material, it doesn't matter where or how many times we cut it, the pieces will always have the same mass density as each other and as the original block. This is because mass density is a physical property. Be careful with this though. If we were to make a hollow aluminum sphere, the sphere would be less dense than aluminum since it is hollow. Only the outer shell would have the mass density of aluminum.

Other Types of Density

Mass density is by and far the most commonly used type of density. However, in chemistry it is useful to understand two other types of density: $\color{red}{\text{charge density}}$ and $\color{red}{\text{number density}}$. $\\$ Charge density is a measurement of how much electric charge there is in a given volume. It is uncommon in chemistry to numerically evaluate charge density, but rather they are qualitatively compared. As an example, we may say that the charge density of a lithium nucleus is more positive than the charge density of a helium nucleus, but the actual values would not be calculated. Charge density has a strong relation to electronegativity. $\\$ Number density is a measurement of how many countable units there are in a given volume. For example, we might say that there are $4$ moles of glucose in a liter. Each molecule of glucose is a countable unit, and we are counting $4$ moles. Number density is often addressed by a different name: concentration $$\color{red}{\text{Review}}$$ $\color{red}{\text{Mass Density}}$: The amount of mass in a specified volume. Typically expressed in units of grams per milliliter. $\\$ $\color{red}{\text{Charge Density}}$: The amount of electric charge in a specified volume. This is usually not explicitly evaluated. $\\$ $\color{red}{\text{Number Density}}$: The amount of countable units in a specified volume. This is often referred to as concentration.

Density

One property of matter that chemists frequently use to identify a substance is density.

Density is defined as the substance's mass per unit of the substance's volume.

To simplify this definition, we can write density using a formula: $Density = \frac{Mass}{Volume}$. This is commonly written as

$\rho = \frac{m}{V}$, where $\rho$, $m$, and $V$ are the density, mass, and volume of the substance, respectively.

Example

In this example, we will determine the density of a liquid.

A chemist measures out 67.3 cm$^3$ of ethanol and finds that it has a mass of 53.1 grams. What is the density of ethanol?

We can solve for density by using its definition. \begin{array} $\rho &= \frac{m}{V} \
&= \frac{53.1 ; g}{67.3 ; cm ^3} \
&= \boxed{0.789 ; g/cm ^3} \end{array}

Density is simply the amount of "stuff" per volume. Here, we'll use "density" to refer to mass density, or the amount of mass per volume in a material, though other types of density, like charge density, exist as well.

Mass density is measured in mass/volume, or grams/cm$^{3}$.

There's a number of reasons why it's important for chemists to know the density of a material. Mass is basically a measurement of the amount of matter in something. The amount of matter in something can tell us how many atoms there are in it, and therefore how much it can react with something else.

In everyday life, density is important when swimming. Buoyant force, or the ability to float, depends on whether you are less dense than the water around you. This same principle applies to the ability of helium balloons to rise through the air.

(Video) What Is Density?

by The Science Classroom

Density is a measure of mass per given volume. In this video, you will learn how to calculate density using the formula $density=\frac{\text{mass}}{\text{volume}}$.