Question

A \(250.0-\mathrm{g}\) sample of pond water contains \(2.4 \mathrm{mg}\) arsenic. What is the mass percent of arsenic in the pond? How many parts per million of arsenic are in the pond? How many parts per billion?

Short answer

The mass percent of arsenic in the pond is approximately 0.00096%, the parts per million concentration is 9.6 ppm and parts per billion concentration is 9600 ppb.

Step-by-step solution

Convert grams to milligrams

First off, we must convert the total sample mass from grams to milligrams to align with the units of arsenic's mass. Since 1g = 1000mg, so the sample mass is \(250.0 \times 1000 = 250000.0\) milligrams.

Calculate the mass percent

Mass percent can be calculated using the formula: mass percent = (mass of solute/mass of solution) x 100%. So, the mass percentage of arsenic = \(\frac{2.4}{250000.0} \times 100 = 0.00096 \%\)

Calculate the parts per million (ppm)

Parts per million (ppm) can be calculated using the conversion: 1% = 10,000 ppm. Therefore, the number of ppm of arsenic = \(0.00096 \times 10000 = 9.6\) ppm.

Calculate the parts per billion (ppb)

Parts per billion (ppb) can be calculated using the conversion: 1 ppm = 1000 ppb. Thus, the number of ppb of arsenic = \(9.6 \times 1000 = 9600\) ppb.

Key concepts

Arsenic Concentration

When discussing arsenic concentration in a sample, it's important to understand what we mean by concentration. It's all about how much arsenic is present in a certain amount of pond water. In this exercise, we deal with a sample of pond water weighing 250 grams, containing 2.4 milligrams of arsenic.
To find the arsenic concentration effectively, we first need to convert the total sample weight into the same unit as the arsenic amount. Since arsenic is measured in milligrams, we convert the water from grams to milligrams (1 gram = 1000 milligrams). This helps us get precise measurements.
Once we have everything in milligrams, we can calculate the mass percent of arsenic. Mass percent gives us an idea of how many grams of arsenic are present in 100 grams of pond water. It's calculated by dividing the mass of arsenic by the mass of the total solution and multiplying by 100%. This percentage helps us understand arsenic concentration in terms of weight.

Parts Per Million

Parts per million, abbreviated as ppm, is a unit of measurement used to describe the concentration of a substance in a million parts of another substance. One ppm means that there is one part of the solute in one million parts of the solution.
It's a very useful unit when dealing with very tiny concentrations, like the arsenic in this pond water. For example, our calculation of arsenic in parts per million uses the percentage value found earlier.

• Since 1% equals 10,000 ppm, a small percentage like 0.00096% translates to 9.6 ppm.

Again, this number indicates how many milligrams of arsenic are there for every million milligrams of pond water, allowing a clearer understanding of the arsenic's concentration in the water sample.

Parts Per Billion

Parts per billion, or ppb, takes concentration measurement to an even finer level than parts per million. While ppm deals with one part in a million, ppb deals with one part in a billion, which is handy when concentrations are very tiny, as is often the case in environmental samples.
In essence, converting from ppm to ppb involves multiplying the ppm value by 1000.

• In our example, the arsenic concentration was determined to be 9.6 ppm, which translates to 9600 ppb.

This result gives us a much more detailed perspective on the arsenic concentration in the pond water, providing a clearer picture for assessing safety and regulatory compliance, especially critical in ecological and health contexts.