Problem 43 - Chemistry: The Central Science in SI Units, Global Edition

Question

The allowable concentration level of vinyl chloride, \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl},\) in the atmosphere in a chemical plant is \(2.0 \times 10^{-6} \mathrm{~g} / \mathrm{L}\). How many moles of vinyl chloride in each liter does this represent? How many molecules per liter?

Step-by-Step Solution

Answer

The allowable concentration of \(2.0 \times 10^{-6} \mathrm{~g} / \mathrm{L}\) of vinyl chloride represents \(3.2 \times 10^{-8}\) moles per liter and \(1.93 \times 10^{16}\) molecules per liter.

Step 1: Calculate the molar mass of vinyl chloride

Vinyl chloride has a chemical formula of \(\mathrm{C}_{2}\mathrm{H}_{3}\mathrm{Cl}\). To calculate its molar mass, we can check the periodic table for the atomic masses of each element: - Carbon (C): 12.01 g/mol - Hydrogen (H): 1.01 g/mol - Chlorine (Cl): 35.45 g/mol Now, we can calculate the molar mass of \(\mathrm{C}_{2}\mathrm{H}_{3}\mathrm{Cl}\): Molar mass = (2 × 12.01 g/mol) + (3 × 1.01 g/mol) + (1 × 35.45 g/mol) = 62.50 g/mol

Step 2: Calculate the moles of vinyl chloride per liter

We are given the concentration of vinyl chloride in the atmosphere, which is \(2.0 \times 10^{-6} \mathrm{~g} / \mathrm{L}\). To calculate the moles per liter, we can use the following formula: moles per liter = (mass per liter) / (molar mass) moles per liter = (2.0 × 10^{-6} g/L) / (62.50 g/mol) = 3.2 × 10^{-8} mol/L

Step 3: Calculate the number of molecules per liter

To calculate the number of molecules per liter, we can use Avogadro's number, which states that 1 mole contains \(6.022 \times 10^{23}\) entities. Hence, the number of molecules per liter can be determined as follows: molecules per liter = (moles per liter) × (Avogadro's number) molecules per liter = (3.2 × 10^{-8} mol/L) × (6.022 × 10^{23} molecules/mol) = 1.93 × 10^{16} molecules/L To summarize, the allowable concentration of \(2.0 \times 10^{-6} \mathrm{~g} / \mathrm{L}\) of vinyl chloride represents \(3.2 \times 10^{-8}\) moles per liter and \(1.93 \times 10^{16}\) molecules per liter.

Key Concepts

Vinyl Chloride Concentration

Vinyl chloride is an important chemical used in the production of polyvinyl chloride (PVC), and understanding its concentration is crucial for safety in industrial settings. In this context, concentration is expressed in terms of mass per unit volume, specifically grams per liter (g/L). In our example, the concentration is given as \(2.0 \times 10^{-6} \text{ g/L}\). This means that for every liter of air, there are \(2.0 \times 10^{-6}\) grams of vinyl chloride.

Such concentration levels are crucial to maintaining safe working environments. Vinyl chloride is a human carcinogen, meaning it can contribute to cancer risk in high concentrations. Therefore, chemical plants often monitor these levels closely to ensure they do not exceed safety limits. This understanding is not only vital for safety compliance but also for performing subsequent calculations, like finding the number of moles or molecules present in a given volume.

Moles Calculation

The mole is a fundamental unit in chemistry that allows scientists to count particles at the atomic scale. To convert the concentration of vinyl chloride from grams per liter to moles per liter, you need its molar mass. The molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol).

• For vinyl chloride \(\text{C}_2\text{H}_3\text{Cl}\), the molar mass is calculated by adding up the atomic masses of all atoms in the molecule.
• Based on the periodic table: Carbon (C) is \(12.01\text{ g/mol}\), Hydrogen (H) is \(1.01\text{ g/mol}\), and Chlorine (Cl) is \(35.45\text{ g/mol}\).

Thus, the molar mass of vinyl chloride is \((2 \times 12.01) + (3 \times 1.01) + (35.45) = 62.50 \text{ g/mol}\).

This allows us to calculate the moles per liter using the formula:
\[ \text{moles per liter} = \frac{\text{mass per liter}}{\text{molar mass}} \]
For our case, \(\frac{2.0 \times 10^{-6} \text{ g/L}}{62.50 \text{ g/mol}} = 3.2 \times 10^{-8} \text{ mol/L}\). This conversion is key to understanding how concentration levels can be expressed in different units based on what is more useful for the task at hand.

Molecules Calculation

Once you know how many moles of vinyl chloride are present in each liter, you can find the number of molecules using Avogadro's number, which is \(6.022 \times 10^{23}\), a constant that represents the number of units (atoms, molecules, etc.) in one mole of a substance.

This step involves a simple multiplication of the number of moles by Avogadro's number:

• Use \(3.2 \times 10^{-8} \text{ mol/L}\) from the previous calculation.
• Multiply this by Avogadro's number: \(3.2 \times 10^{-8} \text{ mol/L} \times 6.022 \times 10^{23} \text{ molecules/mol} = 1.93 \times 10^{16} \text{ molecules/L}\).

Therefore, in each liter of air, there are \(1.93 \times 10^{16}\) molecules of vinyl chloride.

Understanding molecules on such a massive scale is important because it allows chemists to predict how substances will behave in reactions or understand the potential risks in certain concentrations, insights that are critical for both laboratory and industrial applications.