Question

A \(375.0\)-g sample of river water taken near an industrial plant contains \(37 \mathrm{mg}\) of chromium. What is the mass percent of chromium in the river? How many parts per million of chromium are in the river? How many parts per billion?

Short answer

The mass percent of chromium in the river water is 0.00987%. The number of parts per million (ppm) is 98.7 ppm, and the number of parts per billion (ppb) is 98,700 ppb.

Step-by-step solution

Calculate the mass percent of chromium

The mass percent is calculated by dividing the mass of the solute (chromium) by the mass of the solution (river water) and multiplying by 100. The mass of chromium is 37 mg and the mass of the water sample is \(375.0 g = 375,000 mg\). Therefore, the mass percent of chromium is given by: \[\frac{37 \, mg}{375,000 \, mg} \times 100\%.\]

Convert mass percent to ppm and ppb

To convert the mass percent to ppm, we multiply by 10,000. This is because 1% is equivalent to 10,000 ppm. The calculation is thus: \[\text{Mass percent of chromium} \times 10,000 .\] To convert the mass percent to ppb, we multiply by 10,000,000, since 1% is equivalent to 10,000,000 ppb. The calculation is thus: \[\text{Mass percent of chromium} \times 10,000,000 .\]

Key concepts

Understanding River Water

River water is a body of flowing surface water that travels from higher to lower elevations, and it plays a crucial role in the ecosystem. Its composition can vary significantly depending on several factors such as upstream conditions, tributaries, and surrounding soil and rock. The quality of river water often needs monitoring, especially near industrial areas, because factories may discharge pollutants, including heavy metals like chromium, into the water sources.

Rivers supply water for various uses like irrigation, drinking, and industrial activities. Hence, regular testing is essential to ensure water safety and quality. Factors like pH, dissolved oxygen, and metal ions concentration are monitored, and high levels of these substances can affect health and the environment. Understanding river water quality can help in formulating strategies to reduce pollution.

In our problem, we are investigating a scenario where river water is contaminated with chromium. Understanding how to measure and interpret these levels helps in assessing the safety of the water.

Chromium Concentration in Water

Chromium is a metal that can exist in several forms (or valences), primarily as trivalent chromium (Cr(III)) and hexavalent chromium (Cr(VI)). Hexavalent chromium is considered more toxic and is a concern due to its potential health effects when present in drinking water.

• Cr(III) is an essential dietary element for people in trace amounts, but Cr(VI) can be harmful if ingested in larger amounts.
• Industries commonly use chromium compounds in manufacturing, where improper waste disposal can result in contamination of nearby water bodies.

To determine chromium concentration, we need to measure the mass of chromium in a specific mass of water sample. This approach allows us to express the amount of chromium as a ratio, which helps convey its concentration. In this exercise, we are interested in the mass percent and parts per million (ppm), which provide insight into how much chromium is present relative to the entire water sample.

Given that the water sample contains 37 mg of chromium and the total water mass is 375,000 mg, these measures allow a detailed understanding of the level of contamination and necessary steps to mitigate its impact.

Parts Per Million (PPM) Explained

Parts per million (PPM) is a unit of measurement used to describe the concentration of a contaminant in a solution. It signifies one part of a solute per one million parts of the total solution. This level of precision is crucial in environmental sciences and industry to understand how diluted or concentrated a substance is within water or air.

• 1 ppm means that there is one gram of solute in one million grams of solution.
• For water, since 1 ml approximately equals 1 g, ppm can also refer to one milligram per liter (mg/L).

In the context of our exercise, converting mass percent to ppm involves a straightforward multiplication by 10,000, showing that a very small concentration of chromium can still be significant from a health perspective.

Understanding PPM and how to calculate it from mass percent helps in comparing various substances' concentrations in different contexts, such as regulatory compliance in environmental standards or diagnosing potential pollution issues.