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Chapter 3: Problem 43

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 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

01

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: \(Molar\ Mass\ of\ C_{2}H_{3}Cl = (2 \times Atomic\ Mass\ of\ C) + (3 \times Atomic\ Mass\ of\ H) + (Atomic\ Mass\ of\ Cl)\) \(Molar\ Mass\ of\ C_{2}H_{3}Cl = (2 \times 12.01\ g/mol) + (3 \times 1.008\ g/mol) + (35.45\ g/mol)\) \(Molar\ Mass\ of\ C_{2}H_{3}Cl = 62.498\ g/mol\)
02

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: \(Moles\ per\ liter\ of\ C_{2}H_{3}Cl = \frac{2.0 \times 10^{-6}\ g / L}{62.498\ g/mol}\) \(Moles\ per\ liter\ of\ C_{2}H_{3}Cl = 3.203 \times 10^{-8}\ mol / L\)
03

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: \(Molecules\ per\ liter\ of\ C_{2}H_{3}Cl = 3.203 \times 10^{-8}\ mol / L \times 6.022 \times 10^{23}\ molecules / mol\) \(Molecules\ per\ liter\ of\ C_{2}H_{3}Cl = 1.928 \times 10^{16}\ molecules / L\)
04

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

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Most popular questions from this chapter

Determine the empirical and molecular formulas of each of the following substances: (a) Ibuprofen, a headache remedy, contains \(75.69 \% \mathrm{C}\), \(8.80 \% \mathrm{H}\), and \(15.51 \% \mathrm{O}\) by mass, and has a molar mass of \(206 \mathrm{~g} / \mathrm{mol}\). (b) Cadaverine, a foul-smelling substance produced by the action of bacteria on meat, contains \(58.55 \% \mathrm{C}\), \(13.81 \% \mathrm{H}\), and \(27.40 \% \mathrm{~N}\) by mass; its molar mass is \(102.2 \mathrm{~g} / \mathrm{mol}\) (c) Epinephrine (adrenaline), a hormone secreted into the bloodstream in times of danger or stress, contains \(59.0 \%\) \(\mathrm{C}, 7.1 \% \mathrm{H}, 26.2 \% \mathrm{O}\), and \(7.7 \% \mathrm{~N}\) by mass; its \(\mathrm{MW}\) is about 180 amu.

Epsom salts, a strong laxative used in veterinary medicine, is a hydrate, which means that a certain number of water molecules are included in the solid structure. The formula for Epsom salts can be written as \(\mathrm{MgSO}_{4} \cdot x \mathrm{H}_{2} \mathrm{O}\), where \(x\) indicates the number of moles of \(\mathrm{H}_{2} \mathrm{O}\) per mole of \(\mathrm{MgSO}_{4}\). When \(5.061 \mathrm{~g}\) of this hydrate is heated to \(250^{\circ} \mathrm{C}\), all the water of hydration is lost, leaving \(2.472 \mathrm{~g}\) of \(\mathrm{MgSO}_{4}\). What is the value of \(x\) ?

What is the mass, in kilograms, of an Avogadro's number of people, if the average mass of a person is \(160 \mathrm{lb}\) ? How does this compare with the mass of Earth, \(5.98 \times 10^{24} \mathrm{~kg}\) ?

Solutions of sodium carbonate and silver nitrate react to form solid silver carbonate and a solution of sodium nitrate. A solution containing \(3.50 \mathrm{~g}\) of sodium carbonate is mixed with one containing \(5.00 \mathrm{~g}\) of silver nitrate. How many grams of sodium carbonate, silver nitrate, silver carbonate, and sodium nitrate are present after the reaction is complete?

Write a balanced chemical equation for the reaction that occurs when (a) titanium metal undergoes a combination reaction with \(\mathrm{O}_{2}(g) ;\) (b) silver(I) oxide decomposes into silver metal and oxygen gas when heated; (c) propanol, \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}(l)\) burns in air; (d) methyl tert-butyl ether, \(\mathrm{C}_{5} \mathrm{H}_{12} \mathrm{O}(l)\), burns in air.
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