Question

The allowable concentration level of vinyl chloride, \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}\), in the atmosphere in a chemical plant is \(20 \times 10^{-6} \mathrm{~g} / \mathrm{L}\). How many moles of vinyl chloride in each liter does this represent? How many molecules per liter?

Short answer

The molar mass of vinyl chloride (\(C_2H_3Cl\)) is \(2 \times (12.01) + 3 \times (1.01) + (35.45) = 62.5\, g/mol\). To find the moles per liter, divide the concentration by the molar mass, which equals \(\frac{20 \times 10^{-6}\, g/L}{62.5\, g/mol} = 3.2 \times 10^{-7}\, mol/L\). To find the number of molecules per liter, multiply the moles per liter by Avogadro's number: \((3.2 \times 10^{-7}\, mol/L) \times (6.022 \times 10^{23}\, molecules/mol) = 1.93\times 10^{17}\) molecules per liter.

Step-by-step solution

Determine the molar mass of vinyl chloride

Using the periodic table, we find the atomic masses of each element in vinyl chloride (C, H, and Cl): - Carbon (C): 12.01 g/mol - Hydrogen (H): 1.01 g/mol - Chlorine (Cl): 35.45 g/mol Now we find the molar mass of vinyl chloride (\(C_2H_3Cl\)) using this formula: molar mass \(= 2 \times (C) + 3 \times (H) + (Cl)\)

Calculate the moles of vinyl chloride per liter of air

The given allowable concentration is \(20 \times 10^{-6}\, g/L\). Divide the concentration by the molar mass of vinyl chloride to find the number of moles per liter: moles per liter \(= \frac{20 \times 10^{-6}\, g/L}{\text{molar mass of } C_2H_3Cl (g/mol)}\)

Calculate the number of molecules of vinyl chloride per liter of air

We know that 1 mole contains Avogadro's number of molecules, which is approximately \(6.022 \times 10^{23}\) molecules per mole. Multiply the moles per liter by Avogadro's number to find the number of molecules per liter: molecules per liter \(= (\text{moles per liter}) \times (\text{ Avogadro's number (molecules/mol)})\)

Key concepts

Molar Mass

The molar mass is a crucial concept in chemistry relating the mass of a given substance to its amount in moles. It helps accurately link mass to the number of particles involved in chemical processes. To calculate the molar mass of a compound, you sum up the atomic masses of all the atoms that make up the compound. For vinyl chloride (\(C_2H_3Cl\)), we need to consider each element:

• Carbon (C) has an atomic mass of 12.01 g/mol
• Hydrogen (H) has an atomic mass of 1.01 g/mol
• Chlorine (Cl) has an atomic mass of 35.45 g/mol

Now, we calculate the molar mass as follows:\[\text{Molar Mass of } C_2H_3Cl = (2 \times 12.01) + (3 \times 1.01) + 35.45 = 62.50 \, \text{g/mol}\]This number (62.50 g/mol) tells us that there are 62.50 grams in every mole of vinyl chloride. Understanding molar mass enables us to convert given mass into moles, which is a step in various chemical calculations.

Avogadro's Number

Avogadro's number is a fundamental constant in chemistry, representing the number of entities in one mole. It is massive: approximately \(6.022 \times 10^{23}\). But what does this number really mean?

Avogadro's number allows chemists to talk about tiny particles—like atoms and molecules—in meaningful amounts. One mole of any substance contains this staggering number of molecules, atoms, or formula units, making it easier to perform calculations involving chemical reactions.

• This number provides a bridge between the macroscopic scale (grams, liters) and the molecular scale.
• It's essential for converting between moles and number of molecules.

In practice, once you have the number of moles of a substance and need to find the number of molecules, you multiply by Avogadro's number. Let's say you find the moles of vinyl chloride in a liter of air. By multiplying the moles by Avogadro's number, you obtain the number of molecules in that volume, which translates theory into practical, real-world application.

Chemical Calculations

Chemical calculations categorize the various arithmetic operations used to solve chemical problems. They encompass converting between moles, mass, and the number of particles—important skills for any chemist.

Let's explore some of these key calculations using vinyl chloride concentration:

• Given concentration in mass terms: \(20 \times 10^{-6} \, \text{g/L}\)
• To find moles from mass, divide by molar mass: \(\frac{20 \times 10^{-6} \, \text{g/L}}{62.50 \, \text{g/mol}}\)
• This provides moles of vinyl chloride per liter.

Once you've determined the moles per liter, the next step often involves calculating the number of molecules using Avogadro's number:

• Multiply the moles found by \(6.022 \times 10^{23} \, \text{molecules/mol}\)
• This yields the number of molecules per liter of air.

Through these systematic calculations, chemists predict and quantify chemical interactions, determining concentrations and reactions precisely. It's essential to grasp each step thoroughly, as these fundamental concepts underpin empirical work and theoretical models in chemistry.