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 allowable concentration level of vinyl chloride, \(C_2H_3Cl\), is \(3.202 \times 10^{-7}\) moles/L and \(1.927 \times 10^{17}\) molecules/L.

Step-by-step solution

Identify the given information

The allowable concentration level of vinyl chloride, \(C_2H_3Cl\), is given as \(20 \times 10^{-6} g/L\), which we need to convert into moles per liter and eventually to molecules per liter.

Find the molecular weight of vinyl chloride

In order to convert the allowable concentration from grams per liter to moles per liter, we need to find the molecular weight of vinyl chloride, \(C_2H_3Cl\). The molecular weight of: Carbon (C) = 12.01 g/mol, Hydrogen (H) = 1.008 g/mol, and Chlorine (Cl) = 35.45 g/mol. Using these values, we can calculate the molecular weight of vinyl chloride: Molecular weight (Vinyl chloride) = 2(C) + 3(H) + 1(Cl) = 2 x (12.01 g/mol) + 3 x (1.008 g/mol) + 1 x (35.45 g/mol) = 62.498 g/mol

Convert grams per liter to moles per liter

Now, we can convert the allowable concentration from grams per liter to moles per liter using the molecular weight of vinyl chloride. We'll use the formula: Moles per liter (n/V) = Concentration (g/L) / Molecular weight (g/mol) n/V = \(\frac{20 \times 10^{-6} g/L}{62.498 g/mol}\) = \(3.202 \times 10^{-7}\) moles/L So, the allowable concentration level in moles per liter is \(3.202 \times 10^{-7}\) moles/L.

Calculate the number of molecules per liter using Avogadro's number

Now that we have the concentration in moles per liter, we can use Avogadro's number (6.022 x 10^23 molecules/mol) to find the number of molecules per liter. We'll multiply the concentration in moles per liter by Avogadro's number: Molecules per liter = (Moles per liter) x (Avogadro's number) Molecules per liter = \(3.202 \times 10^{-7} moles/L\) x \(6.022 \times 10^{23} molecules/mol\) = \(1.927 \times 10^{17}\) molecules/L So, the allowable concentration level in molecules per liter is \(1.927 \times 10^{17}\) molecules/L.