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

Step-by-step solution

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: \(Molar\ Mass\ of\ C_{2}H_{3}Cl = (2 \times Atomic\ Mass\ of\ C) + (3 \times Atomic\ Mass\ of\ H) + (Atomic\ Mass\ of\ Cl)\) \(Molar\ Mass\ of\ C_{2}H_{3}Cl = (2 \times 12.01\ g/mol) + (3 \times 1.008\ g/mol) + (35.45\ g/mol)\) \(Molar\ Mass\ of\ C_{2}H_{3}Cl = 62.498\ g/mol\)

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: \(Moles\ per\ liter\ of\ C_{2}H_{3}Cl = \frac{2.0 \times 10^{-6}\ g / L}{62.498\ g/mol}\) \(Moles\ per\ liter\ of\ C_{2}H_{3}Cl = 3.203 \times 10^{-8}\ mol / L\)

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: \(Molecules\ per\ liter\ of\ C_{2}H_{3}Cl = 3.203 \times 10^{-8}\ mol / L \times 6.022 \times 10^{23}\ molecules / mol\) \(Molecules\ per\ liter\ of\ C_{2}H_{3}Cl = 1.928 \times 10^{16}\ molecules / L\)

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 \(1.928 \times 10^{16}\ molecules / L\).