Question

A dioxin-contaminated water source contains 0.085\(\%\) dioxin by mass. How much dioxin is present in 2.5 L of this water? Assume a density of 1.00 \(\mathrm{g} / \mathrm{mL} .\)

Short answer

There are approximately 2.125 grams of dioxin in 2.5 liters of the contaminated water.

Step-by-step solution

Convert Water Volume to Mass

Since the density of the water is given as 1.00 g/mL, the mass of 2.5 L of water can be found by converting liters to milliliters and multiplying by the density. There are 1000 mL in one liter, so multiply 2.5 L by 1000 mL/L to convert to milliliters. The mass of the water in grams will then be equivalent to the volume in milliliters because of the 1:1 density ratio.

Calculate the Mass of Dioxin in the Water

With 0.085% of the water's mass being dioxin by mass, we calculate the amount of dioxin by multiplying the total mass of the water by the percentage of dioxin (expressed as a decimal).

Final Calculation

Finally, use the mass of the water (found in step 1) and the percentage of dioxin to calculate the exact mass of dioxin in grams.

Key concepts

Percent by Mass

Understanding 'percent by mass' is crucial when dealing with mixtures or solutions in chemistry. This term describes the concentration of a component in a mixture and is calculated as the mass of that particular substance divided by the total mass of the mixture, multiplied by 100.

In a practical scenario, if a water source is contaminated with dioxin, knowing the percent by mass of dioxin allows us to calculate precisely how much of this contaminant is present in a given sample. In our exercise, the dioxin-contaminated water contains 0.085% dioxin by mass. This means that for every 100 grams of this water, there is 0.085 grams of dioxin. This is a relatively small amount, but dioxin is highly toxic, making the accuracy of this calculation extremely important for environmental and health-related assessments.

Density Calculations

Density is a fundamental concept in science, defined as mass per unit volume. It is a particularly useful measurement in chemistry for converting between the mass of a substance and its volume. The density of water, for example, is typically about 1.00 g/mL, meaning that 1 milliliter of water has a mass of 1 gram.

This principle is used in our exercise to find the mass of 2.5 liters of water.

Converting Volume to Mass

By knowing the density, we can easily convert the volume of water (in liters or milliliters) directly into mass (in grams), since the volume in milliliters is numerically equal to the mass in grams due to water's density. Therefore, calculating the mass of a volume of water is straightforward if the density is known. This step is vital because the percent by mass of dioxin is based on the mass of the water, not its volume.

Unit Conversion

Unit conversion is a ubiquitous necessity in science, allowing for the consistent comparison and calculation of measurements. It often requires converting between different systems, like metric and imperial, or between units within the same system, such as milliliters to liters.

Good practice mandates that units be treated as algebraic quantities that can cancel each other out when they're divided and multiply. In the exercise, we start with the volume in liters and need to convert this to milliliters to use the given density.

Practical Application

Since 1 liter equals 1000 milliliters, you multiply the volume in liters by 1000 to get the volume in milliliters. Only after this crucial conversion can the calculation proceed to use the density value effectively. This skill in converting units is essential for students as it is used throughout various scientific disciplines and practical applications, including the assessment of the concentration of contaminants in environmental science.