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?

Short answer

The allowable concentration level of vinyl chloride, \(\mathrm{C}_{2}\mathrm{H}_{3} \mathrm{Cl}\), in the atmosphere represents approximately \(3.20 \times 10^{-8}\) moles per liter and approximately \(1.93 \times 10^{16}\) molecules per liter.

Step-by-step solution

Find the molecular weight of vinyl chloride

We are given the formula for vinyl chloride as \(\mathrm{C}_{2}\mathrm{H}_{3} \mathrm{Cl}\). To find the molecular weight, we'll add the atomic weights of the constituent elements: - Carbon (C) has an atomic weight of 12.01 g/mol - Hydrogen (H) has an atomic weight of 1.008 g/mol - Chlorine (Cl) has an atomic weight of 35.45 g/mol So, the molecular weight of vinyl chloride is: (2 x 12.01) + (3 x 1.008) + 35.45 = 24.02 + 3.024 + 35.45 = 62.494 g/mol

Calculate the moles of vinyl chloride per liter

We know that the maximum allowable concentration of vinyl chloride is \(2.0 \times 10^{-6} \ \mathrm{g}/\mathrm{L}\). To get the number of moles per liter, we will divide the mass of vinyl chloride by its molecular weight: \[\text{Moles per liter} = \frac{2.0 \times 10^{-6}\ \mathrm{g}}{62.494\ \mathrm{g/mol}}\] Calculate the division: \[\text{Moles per liter} \approx 3.20 \times 10^{-8}\ \mathrm{mol/L}\]

Calculate the number of molecules per liter

To find the number of molecules per liter, we'll use Avogadro's number, which is approximately \(6.022 \times 10^{23}\ \mathrm{molecules/mol}\). Multiply this by the number of moles per liter: \[\text{Molecules per liter} = (3.20 \times 10^{-8}\ \mathrm{mol/L}) \times (6.022 \times 10^{23}\ \mathrm{molecules/mol})\] Calculate the multiplication: \[\text{Molecules per liter} \approx 1.93 \times 10^{16}\ \mathrm{molecules/L}\]

Final answers

To summarize, the allowable concentration level of vinyl chloride \(\mathrm{C}_{2}\mathrm{H}_{3} \mathrm{Cl}\) in the atmosphere represents: 1. Approximately \(3.20 \times 10^{-8}\) moles per liter 2. Approximately \(1.93 \times 10^{16}\) molecules per liter.

Key concepts

Molecular Weight Calculation

The molecular weight of a compound is the sum of the atomic weights of all the atoms in its molecular formula. In our case, we are looking at vinyl chloride, which has the molecular formula \(\mathrm{C}_{2}\mathrm{H}_{3}\mathrm{Cl}\). To find the molecular weight, simply add up the atomic weights of each element in the formula, multiplied by the number of atoms of that element present:

• Carbon (\(\mathrm{C}\)) has an atomic weight of 12.01 g/mol and there are 2 atoms of it, so \(2 \times 12.01 = 24.02 \) g/mol.
• Hydrogen (\(\mathrm{H}\)) has an atomic weight of 1.008 g/mol and there are 3 atoms, so \(3 \times 1.008 = 3.024 \) g/mol.
• Chlorine (\(\mathrm{Cl}\)) has an atomic weight of 35.45 g/mol and there is 1 atom, so \(1 \times 35.45 = 35.45 \) g/mol.

By adding these values together, we get the molecular weight: \(24.02 + 3.024 + 35.45 = 62.494 \) g/mol. Understanding how to calculate molecular weight is crucial in chemistry as it helps in converting between grams and moles, which are essential for quantitative chemical analysis.

Avogadro's Number

Avogadro's number is a fundamental constant that helps us understand the scale at which chemical processes operate. It is approximately \(6.022 \times 10^{23}\), and it represents the number of atoms, ions, or molecules contained in one mole of a substance. This number is named after the Italian scientist Amedeo Avogadro.Why is Avogadro's number important? It allows chemists to "count" very large numbers of tiny particles by relating the macroscopic measurements we can make in the lab to the microscopic count of individual molecules or atoms:

• When you know the number of moles of a substance, you can multiply it by Avogadro's number to find the number of particles.
• Conversely, if you know how many molecules you have, you can divide by Avogadro's number to get the number of moles.

This immense figure portrays the size of even tiny quantities of substances, providing an essential bridge from the tangible world to the molecular scale, allowing calculations that make practical chemistry possible.

Mole-to-Molecule Conversion

Converting from moles to molecules (or vice versa) is an essential skill in chemistry, as it helps you quantify the number of particles in a given amount of substance. To make this conversion, Avogadro's number is the key factor.For example, if you think of moles as the "scientific dozen," then just like a dozen represents 12 objects, a mole represents \(6.022 \times 10^{23}\) molecules. Here's how you can use it:

• **Convert from moles to molecules**: Multiply the number of moles by Avogadro's number. For instance, with vinyl chloride, if you have \(3.20 \times 10^{-8}\) moles, you calculate the number of molecules by multiplying \((3.20 \times 10^{-8} \times 6.022 \times 10^{23})\) to get approximately \(1.93 \times 10^{16}\) molecules.
• **Convert from molecules to moles**: Divide the number of molecules by Avogadro's number.

This step is crucial when you need to understand the proportion of molecules involved in reactions or the concentration levels in solutions. Mastery of this conversion allows for deeper comprehension of chemical reactions on a molecular level.