Problem 97 - General Chemistry: Principles and Modern Applications

Question

A public water supply was found to contain 1 part per billion (ppb) by mass of chloroform, \(\mathrm{CHCl}_{3}\) (a) How many \(\mathrm{CHCl}_{3}\) molecules would be present in a \(225 \mathrm{mL}\) glass of this water? (b) If the \(\mathrm{CHCl}_{3}\) in part (a) could be isolated, would this quantity be detectable on an ordinary analytical balance that measures mass with a precision of ±0.0001 g?

Step-by-Step Solution

Answer

The number of \(\mathrm{CHCl}_{3}\) molecules present in a \(225 \mathrm{mL}\) glass of this water is approximately \(1.13 \times 10^{15}\) and this quantity is not detectable on an ordinary analytical balance that measures mass with a precision of ±0.0001 g since the calculated mass of chloroform is far less than the balance precision.

Step 1: Calculate the mass of water

Determine the mass of the 225 mL glass of water. Since the density of water is approximately \(1 \mathrm{g/mL}\), the mass of this volume of water equals to the volume in mL. So, it would be approximately \(225 \mathrm{g}\).

Step 2: Calculate the mass of chloroform

Calculate the mass of chloroform in the water sample. Since there's 1 ppb (part-per-billion) by mass of chloroform, it means there's 1 gram of chloroform per billion grams of water. Hence, the amount of \(\mathrm{CHCl}_{3}\) in our sample is \(225 \cdot 10^{-9} \mathrm{g}\).

Step 3: Calculate the number of molecules

Find out the number of chloroform molecules in the given mass. First, we need to know the molar mass of \(\mathrm{CHCl}_{3}\) which is \(119.37 \mathrm{g/mol}\), then convert mass to moles using the molar mass. The quantity in moles is \((225 \cdot 10^{-9}) / 119.37\). In order to find out the number of molecules, multiply the mole quantity by Avogadro's number \(6.022 \times 10^{23} / \mathrm{mol}\).

Step 4: Comparison with balance precision

Check if the obtained mass of chloroform is detectable by the balance. Compare the calculated mass of \(\mathrm{CHCl}_{3}\) with the precision of the balance which is \(0.0001 \mathrm{g}\). If the mass of \(\mathrm{CHCl}_{3}\) is greater than or equal to the balance precision, it would be detectable.

Key Concepts

Mole Concept

The mole concept is a foundational principle in chemistry. It provides a method to count entities at the atomic level, such as atoms, molecules, or ions. A mole is a unit that represents a specific number of particles, typically atoms or molecules. This number is known as Avogadro's number,

• One mole of any substance contains exactly \[6.022 \times 10^{23} \] particles.
• This standard measurement allows chemists to use a single number to reference massive amounts of tiny entities in a convenient way.

To convert between the mass of a substance and the number of molecules, we refer to the substance's molar mass, which is expressed in grams per mole (g/mol). By using the molar mass, you can calculate how many moles are present in a certain mass of the substance.
For instance, if water contains 1 part per billion of chloroform, we can convert that tiny mass to moles and then to the number of molecules using the mole concept.

Density of Water

The density of water is a key factor in many chemical calculations. **Density** is defined as mass per unit volume. For water, the density is approximately 1 gram per milliliter (1 g/mL) at room temperature. This makes calculations involving the mass of water very straightforward.

• Since 1 mL of water corresponds to 1 gram, it means that the mass of any given volume of water in milliliters is numerically equal to the volume.
• In practical chemical calculations, such simple conversion allows us to easily determine how much mass we are dealing with when we know the volume.

For example, if we have 225 mL of water, it directly translates to 225 grams of water, simplifying the calculation needed to determine how much chloroform is present by mass.

Avogadro's Number

Avogadro's number is a fundamental constant that stands for the number of constituent particles, usually molecules or atoms, contained in one mole of a substance. It is an essential part in stoichiometry for converting between Atomic Scale and macroscopic measurements.

• The value of Avogadro's number is \[6.022 \times 10^{23} \] particles per mole.
• This number helps to translate between the mass, moles, and the actual count of molecules or atoms, providing a bridge from the mass that we can easily weigh, to the number of particles that we are interested in at a molecular level.

Using Avogadro's number in our calculations, we can determine how many molecules are present in a given mass of chloroform in water, particularly helpful when working with tiny concentrations, like parts per billion.

Analytical Chemistry

Analytical chemistry involves using tools and methods to measure properties of substances precisely and accurately analyze their composition.

• Tools such as analytical balances are influenced by precision limitations. A balance's precision dictates the minimum detectable mass. In our case, the balance's precision is \(0.0001 \mathrm{g}\).
• Analytical chemistry ensures insights into the type and quantity of substances present, which is essential in understanding complex mixtures.

For example, analytical balances are crucial when determining whether or not a small amount of substance like chloroform, present at extremely low concentrations in water, can be detected based on the sample's mass and the precision threshold of the balance.