Problem 43 - Chemistry The Central Science

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 level of \(2.0 \times 10^{-6} \mathrm{g} / \mathrm{L}\) of vinyl chloride is equivalent to \(3.2 \times 10^{-8}\) moles per liter and \(1.928 \times 10^{16}\) molecules of vinyl chloride per liter.

Step 1: Calculate the molar mass of vinyl chloride

First, we need to find the molar mass of vinyl chloride (C2H3Cl). We can do this by summing the atomic masses of the elements in the molecule using the periodic table. The molar mass of carbon (C) is 12.01 g/mol, the molar mass of hydrogen (H) is 1.01 g/mol, and the molar mass of chlorine (Cl) is 35.45 g/mol. C2H3Cl = 2(12.01) + 3(1.01) + 35.45 = 24.02 + 3.03 + 35.45 = 62.50 g/mol

Step 2: Calculate the moles of vinyl chloride in each liter

Now that we have the molar mass, we can calculate the moles of vinyl chloride in each liter. We can use the formula: moles = (mass of substance)/(molar mass) The given mass of vinyl chloride is \(2.0 \times 10^{-6}\) g/L. Using the molar mass calculated in Step 1, we now have: moles = (\(2.0 \times 10^{-6}\) g/L) / (62.50 g/mol) moles = \(3.2 \times 10^{-8}\) mol/L

Step 3: Calculate the number of molecules per liter

To find the number of molecules per liter, we can multiply the moles per liter by Avogadro's number which is approximately \(6.022 \times 10^{23}\) molecules/mol. number of molecules = (moles per liter) × (Avogadro's number) number of molecules = (\(3.2 \times 10^{-8}\) mol/L) × (\(6.022 \times 10^{23}\) molecules/mol) number of molecules = \(1.928 \times 10^{16}\) molecules/L

Step 4: Present the final results

From our calculations, we find that the allowable concentration level of vinyl chloride in the atmosphere in a chemical plant, \(2.0 \times 10^{-6} \mathrm{g} / \mathrm{L}\), is equivalent to: 1. \(3.2 \times 10^{-8}\) moles of vinyl chloride per liter 2. \(1.928 \times 10^{16}\) molecules of vinyl chloride per liter

Key Concepts

Molar Mass Calculation

When calculating the molar mass of a compound, it's important to add up the atomic masses of all the atoms in the molecule. This allows chemists to determine how much one mole of a substance weighs. For the compound vinyl chloride, which has the formula \( \text{C}_2\text{H}_3\text{Cl} \), the molar mass can be found using atomic masses from the periodic table:

• Two carbon (C) atoms, with an atomic mass of about 12.01 g/mol each. Thus, \( 2 \times 12.01 \text{ g/mol} = 24.02 \text{ g/mol} \).
• Three hydrogen (H) atoms, each with an atomic mass of about 1.01 g/mol, totaling \( 3 \times 1.01 \text{ g/mol} = 3.03 \text{ g/mol} \).
• One chlorine (Cl) atom with an atomic mass of 35.45 g/mol.

By summing these up, the molar mass of vinyl chloride is \( 24.02 + 3.03 + 35.45 = 62.50 \text{ g/mol} \). Knowing the molar mass is crucial for converting between grams and moles, a common task in chemistry.

Avogadro's Number

Avogadro's number is a constant that reveals how many particles, such as atoms or molecules, are in one mole of a substance. This number is incredibly large: approximately \( 6.022 \times 10^{23} \). It allows scientists to convert moles into actual numbers of molecules or atoms. For instance, if you know the number of moles of vinyl chloride, you can easily determine how many molecules there are.Imagine you have \( 3.2 \times 10^{-8} \) moles of vinyl chloride in a liter. To find the number of molecules, multiply the moles by Avogadro's number:

• \( 3.2 \times 10^{-8} \) moles \( \times 6.022 \times 10^{23} \text{ molecules/mol} \)
• This equals approximately \( 1.928 \times 10^{16} \) molecules per liter.

This application of Avogadro's number is essential in fields like chemistry and physics, where understanding the microscopic scale is necessary.

Molecular Calculations

Molecular calculations often begin with a known amount of a substance, expressed in grams or concentration (e.g., grams per liter), and require conversion into moles or molecules. This process involves several steps, starting with the determination of the molar mass.After finding the molar mass, you can calculate the number of moles in a given sample. Using the concentration of vinyl chloride \( 2.0 \times 10^{-6} \text{ g/L} \), the number of moles per liter can be calculated as:

• Moles of vinyl chloride = \( \frac{2.0 \times 10^{-6} \text{ g/L}}{62.50 \text{ g/mol}} \).
• This simplifies to \( 3.2 \times 10^{-8} \text{ mol/L} \).

Next, converting moles to molecules using Avogadro's number gives a deeper insight into the quantity of the substance in terms we can visualize, even if it's only theoretically. This is key for understanding chemical reactions, which typically occur at the molecular level.