Density and Volume Calculation of Alcohol in a Plastic Container: A Detailed Guide

Guide to Calculating the Volume and Density of Alcohol in a Container

Understanding the Problem

Let's start with a basic problem: a plastic container with a mass of 55 grams when empty and 175 grams when filled with alcohol. Given that the density of the alcohol is 0.79 grams per milliliter (g/mL), we will calculate the volume of the alcohol in the container. The objective is to understand the relationship between mass, density, and volume in a real-world scenario.

Calculating the Mass of Alcohol

The first step is to find out how much mass is taken up by the alcohol. This can be done by subtracting the mass of the empty container from the total mass when the container is filled with alcohol. Using the given values:

Mass of Alcohol Mass of container with alcohol - Mass of empty container

Substituting the given values:

Mass of Alcohol 175 g - 55 g 120 g

Calculating the Volume of Alcohol Using Density

Next, we use the formula for density:

Density Mass / Volume

Rearranging the formula to solve for volume:

Volume Mass / Density

Substituting the known values:

Volume 120 g / 0.79 g/mL approximately 152 mL

Thus, the volume of alcohol in the container is approximately 152 mL.

Converting Milliliters to Liters for Larger Volumes

Since 1 liter (L) is equal to 1000 milliliters (mL), we can convert our volume from milliliters to liters to make the number more manageable, especially for larger volumes of alcohol. To convert:

Volume in Liters Volume in Milliliters / 1000

Substituting the value:

Volume in Liters 152 mL / 1000 0.152 L

Hence, the volume of alcohol in the container is approximately 0.152 liters or 152 milliliters.

Using Density for Volume Calculation

Another approach to finding the volume involves using the density formula directly. Given the density of alcohol (0.79 g/mL) and the added mass of the alcohol (175 g - 55 g 120 g), we can calculate the volume using the formula:

Density Mass / Volume

Manipulating the formula to solve for volume:

Volume Mass / Density

Substituting the known values:

Volume 120 g / 0.79 g/mL 0.152 L

Converting to milliliters:

Volume 0.152 L * 1000 mL/L 152 mL

Conclusion and Real-World Application

In conclusion, by understanding the relationship between mass, density, and volume, we can accurately calculate the volume of liquids within a given container. This method is not only useful for academic purposes but also for industries such as manufacturing, pharmaceuticals, and food service, where precise measurements are crucial.

Key Takeaways:

Density is calculated as Mass divided by Volume. Volume can be calculated by dividing Mass by Density. For larger volumes, convert milliliters to liters by dividing by 1000.

By mastering these calculations, you can solve similar problems with ease and accuracy, making your work in any field more reliable and precise.