Which liquid will occupy the greater volume, \(50 \mathrm{~g}\) of water or \(50 \mathrm{~g}\) of ethyl alcohol? Explain.

Density is a measure of how much mass is contained in a given volume. It’s like trying to figure out how tightly packed the particles are within a substance. The formula for density is simple: \( \rho = \frac{m}{V} \), where \( \rho \) represents density, \( m \) is mass, and \( V \) is volume.
For instance, water has a density of about \(1 \text{ g/cm}^3 \), meaning 1 gram of water fits into 1 cubic centimeter. Densities can vary vastly among different materials; solids are generally denser than liquids, and liquids are denser than gases. Understanding density is crucial because it helps in identifying substances and is fundamental in calculations involving mass and volume.
For example, if you have 50 grams of water (\text{density] = 1 \text{ g/cm}^3) and 50 grams of ethyl alcohol (\text{density} \approx 0.789 \text{ g/cm}^3), we use their densities to find out how much volume each will occupy.

Volume measures the amount of space an object or substance occupies. Imagine a container: the volume is the space inside that container. You can find the volume of a liquid by using the formula \( V = \frac{m}{\rho} \), where \( V \) is volume, \( m \) is mass, and \( \rho \) is the density.
For water with a mass of 50 grams and density of 1 \text{ g/cm}^3, the volume is \( \frac{50 \text{ g}}{1 \text{ g/cm}^3} = 50 \text{ cm}^3 \).
On the other hand, for ethyl alcohol with a mass of 50 grams and a lower density of about 0.789 \text{ g/cm}^3, the volume is \( \frac{50 \text{ g}}{0.789 \text{ g/cm}^3} \approx 63.38 \text{ cm}^3 \).
Here, the lower density of ethyl alcohol means it will occupy more space than water for the same mass.

Mass is a measure of the amount of matter in an object, usually measured in grams (g), kilograms (kg), etc. It differs from weight, which is the force exerted by gravity on that mass. In calculations involving density and volume, mass is a key component and is generally provided or can be measured easily.
In our exercise, we have a mass of 50 grams for both water and ethyl alcohol. This common mass allows us to compare how differently they behave due to their different densities.
With a known density and mass, we can straightforwardly determine the volume that each substance will occupy. Understanding the relations between mass, density, and volume is crucial for solving such problems effectively, providing insights into the material properties and their applications.