A dioxin-contaminated water source contains \(0.085 \%\) dioxin by mass. How much dioxin is present in \(2.5\) L of this water? (Assume that the density of the solution is \(1.01 \mathrm{~g} / \mathrm{mL}\) )

Understanding the mass percentage of a component in a mixture is crucial when dealing with solutions, especially those containing contaminants like dioxin. Mass percentage is simply the mass of a given component divided by the total mass of the mixture, then multiplied by 100 to get a percentage.

When you're given a mass percentage, such as the 0.085% dioxin contamination in our water source example, you can envision this as 0.085 grams of dioxin per 100 grams of the solution. To determine the actual mass of dioxin in a different total mass, you would use the following formula:
\[\text{Mass of dioxin} = \text{Total mass of water} \times \left(\frac{\text{Percentage of dioxin}}{100}\right)\].

In this formula, the percentage of dioxin is expressed as a decimal (0.085% becomes 0.00085) to accurately calculate the mass of the dioxin. This is an essential step often missed, leading to incorrect results.

Solution density provides a connection between the volume of a liquid and its mass, and is crucial when you need to know how much mass is present in a given volume. Density is defined as mass per unit volume, usually expressed in grams per milliliter (g/ml) or kilograms per liter (kg/L).

Given the density, you can calculate the mass of a solution by multiplying the volume of the solution by its density, as shown in the original exercise. It is important to ensure that the units of volume match those used for density. For example, if density is in g/ml, the volume should be measured in milliliters.

Additionally, understanding solution density allows for comparison between different solutions or liquids. For instance, a higher density means that there’s more mass packed into the same volume compared to a solution with a lower density.

The process of converting volume to mass involves using the known density of a substance. This conversion is fundamental in science and engineering, as it allows for the determination of the amount of a substance present in a given space.

To convert volume to mass, you use the formula:
\[\text{Mass (g)} = \text{Volume (ml)} \times \text{Density (g/ml)}\].

This relationship means that if you know the volume of a liquid (in milliliters) and its density (in g/ml), you can find the mass directly. In the example given, because we are dealing with water, the density is close to 1 g/ml, simplifying the calculation somewhat. However, for other substances or mixtures, it's vital to use the accurate density to get the correct mass. Always remember to match the units to avoid common mistakes in the conversion process.