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Chapter 3: Problem 41

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

Expert verified
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

01

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
02

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: \[\text{Moles per liter} \approx 3.20 \times 10^{-8}\ \mathrm{mol/L}\]
03

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: \[\text{Molecules per liter} \approx 1.93 \times 10^{16}\ \mathrm{molecules/L}\]
04

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.

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Most popular questions from this chapter

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Calculate the percentage by mass of oxygen in the following compounds: (a) morphine, \(\quad \mathrm{C}_{17} \mathrm{H}_{19} \mathrm{NO}_{3}\); (b) codeine, \(\mathrm{C}_{18} \mathrm{H}_{21} \mathrm{NO}_{3} \quad\) (c) cocaine, \(\mathrm{C}_{17} \mathrm{H}_{21} \mathrm{NO}_{4}\); (d) tetracycline, \(\mathrm{C}_{22} \mathrm{H}_{24} \mathrm{~N}_{2} \mathrm{O}_{8} ;\) (e) digitoxin, \(\mathrm{C}_{41} \mathrm{H}_{64} \mathrm{O}_{13} ;\) (f) vancomycin, \(\mathrm{C}_{66} \mathrm{H}_{75} \mathrm{Cl}_{2} \mathrm{~N}_{9} \mathrm{O}_{24}\)

Write a balanced chemical equation for the reaction that occurs when (a) \(\mathrm{Mg}(s)\) reacts with \(\mathrm{Cl}_{2}(g) ;\) (b) barium carbonate decomposes into barium oxide and carbon dioxide gas when heated; \((\mathbf{c})\) the hydrocarbon styrene, \(\mathrm{C}_{8} \mathrm{H}_{8}(l)\), is combusted in air; (d) dimethylether, \(\mathrm{CH}_{3} \mathrm{OCH}_{3}(g)\), is combusted in air.
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