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 vinyl chloride in the atmosphere in the chemical plant represents \(3.203 \times 10^{-8}\ mol / L\) and \(1.928 \times 10^{16}\ molecules / L\).

Step 1: Calculate the molar mass of vinyl chloride

First, we need to determine the molar mass of vinyl chloride (C\(_{2}\)H\(_{3}\)Cl). Vinyl chloride is composed of 2 carbon atoms (C), 3 hydrogen atoms (H), and 1 chlorine atom (Cl). Using the periodic table, we can find the atomic masses for each element and then add them up to find the molar mass: \(Molar\ Mass\ of\ C_{2}H_{3}Cl = (2 \times Atomic\ Mass\ of\ C) + (3 \times Atomic\ Mass\ of\ H) + (Atomic\ Mass\ of\ Cl)\) \(Molar\ Mass\ of\ C_{2}H_{3}Cl = (2 \times 12.01\ g/mol) + (3 \times 1.008\ g/mol) + (35.45\ g/mol)\) \(Molar\ Mass\ of\ C_{2}H_{3}Cl = 62.498\ g/mol\)

Step 2: Convert concentration to moles per liter

We know that the allowable concentration of vinyl chloride is \(2.0 \times 10^{-6}\ g / L\). To convert this concentration to moles per liter, we'll divide the concentration by the molar mass of vinyl chloride: \(Moles\ per\ liter\ of\ C_{2}H_{3}Cl = \frac{2.0 \times 10^{-6}\ g / L}{62.498\ g/mol}\) \(Moles\ per\ liter\ of\ C_{2}H_{3}Cl = 3.203 \times 10^{-8}\ mol / L\)

Step 3: Convert moles per liter to molecules per liter

Finally, we'll use Avogadro's number (6.022 x 10^23 molecules/mol) to convert the moles per liter of vinyl chloride to molecules per liter: \(Molecules\ per\ liter\ of\ C_{2}H_{3}Cl = 3.203 \times 10^{-8}\ mol / L \times 6.022 \times 10^{23}\ molecules / mol\) \(Molecules\ per\ liter\ of\ C_{2}H_{3}Cl = 1.928 \times 10^{16}\ molecules / L\)

Step 4: Final Answer

The allowable concentration level of vinyl chloride in the atmosphere in the chemical plant represents \(3.203 \times 10^{-8}\ mol / L\) and \(1.928 \times 10^{16}\ molecules / L\).