Problem 18 - General Chemistry: Principles and Modern Applications

Question

A water sample is found to have 9.4 ppb of chloroform, \(\mathrm{CHCl}_{3} .\) How many grams of \(\mathrm{CHCl}_{3}\) would be found in a glassful \((250 \mathrm{mL})\) of this water?

Step-by-Step Solution

Answer

There would be \(2.35 \times 10^{-6}\) grams of chloroform in a glassful (250 mL) of this water.

Step 1: Convert volume from mL to Liters

Given that \(1 \text{ L} = 1000 \text{ mL}\), we can convert the volume from mL to L by dividing by \(1000\). Hence, \(250 \text{ mL} = 250 / 1000 = 0.25 \text{ L}\).

Step 2: Calculate the mass of chloroform in the volume of the water

Using the equation \(Mass = \text{volume} × \text{concentration}\), substitute the values. Concentration of 1ppb chloroform in water implies there is \(1 \text{ gram}\) of chloroform in \(10^9 \text{ g}\) (or \(\10^9 \text{ mL}\)) of water. Hence, the mass of chloroform in \(0.25 \text{ L}\) of water is \(0.25 × 9.4 = 2.35 \times 10^{-6} \text{ g}\).

Key Concepts

Chloroform Concentration

Chloroform, or \( ext{CHCl}_3\), is a compound found in water, often in trace amounts. It's important to understand how its concentration in water is calculated and interpreted. In this context, 'concentration' refers to the amount of chloroform present in a given mass or volume of water. In environmental and chemical analysis, chloroform concentration is measured to ensure water safety and determine pollution levels.
When given in 'parts per billion' (ppb), the concentration indicates how many parts of chloroform exist in one billion parts of water. While this number might seem trivial, it is significant in environmental chemistry where even small quantities of pollutants can have ecological impacts.
Understanding how chloroform concentration is expressed is crucial for making sense of water chemistry studies and environmental safety assessments.

Parts per Billion (ppb)

Parts per billion (ppb) is a unit of measurement used to express extremely dilute concentrations of substances. It allows scientists to describe the presence of pollutants, like chloroform, in water.
- 1 part per billion (ppb) means one part substance for every \(10^9\) parts of the solution. This could mean the grams of a substance per billion grams of water.
- It is like having 1 drop of ink in a large ocean of water.
Using ppb helps in conveying very small amounts which are critical in pollution control and water safety evaluations.
Since we need to know how many grams of chloroform exist per 250 mL of water, understanding ppb helps us bridge the gap between concentration and mass.

Volume Conversion

When dealing with water chemistry, converting volumes is a common task. It's important to have a good grasp of how different units of volume relate to each other. For instance, water samples often measure volume in milliliters (mL) or liters (L).
In any conversion: - Remember that 1 L equals 1000 mL.
- To convert from mL to L, divide the number of mL by 1000.
For the problem at hand, converting 250 mL to liters, you divide 250 by 1000, resulting in 0.25 L. This conversion is crucial because concentration values, like ppb, need to be applied to volumes in a consistent unit like liters to make subsequent calculations manageable.

Mass Calculation

After understanding concentration and converting the necessary units, the next step is calculating mass. In this process, you're determining the total mass of chloroform present in a certain volume of water.
- Use the equation: \( ext{Mass} = ext{Volume} imes ext{Concentration}\)
- With the chloroform concentration known as ppb (grams per billion grams of water) and the converted volume in liters, determine how much chloroform is present.
For example, in a 0.25 L sample of water with a chloroform concentration of 9.4 ppb, you multiply 0.25 by 9.4 to find the mass of chloroform in grams. This operation gives a tiny mass when expressed in standard units, highlighting the minute concentration's real-world impact.