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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 of \(2.0 \times 10^{-6} \mathrm{~g} / \mathrm{L}\) of vinyl chloride represents \(3.2 \times 10^{-8}\) moles per liter and \(1.93 \times 10^{16}\) molecules per liter.

Step by step solution

01

Calculate the molar mass of vinyl chloride

Vinyl chloride has a chemical formula of \(\mathrm{C}_{2}\mathrm{H}_{3}\mathrm{Cl}\). To calculate its molar mass, we can check the periodic table for the atomic masses of each element: - Carbon (C): 12.01 g/mol - Hydrogen (H): 1.01 g/mol - Chlorine (Cl): 35.45 g/mol Now, we can calculate the molar mass of \(\mathrm{C}_{2}\mathrm{H}_{3}\mathrm{Cl}\): Molar mass = (2 × 12.01 g/mol) + (3 × 1.01 g/mol) + (1 × 35.45 g/mol) = 62.50 g/mol
02

Calculate the moles of vinyl chloride per liter

We are given the concentration of vinyl chloride in the atmosphere, which is \(2.0 \times 10^{-6} \mathrm{~g} / \mathrm{L}\). To calculate the moles per liter, we can use the following formula: moles per liter = (mass per liter) / (molar mass) moles per liter = (2.0 × 10^{-6} g/L) / (62.50 g/mol) = 3.2 × 10^{-8} mol/L
03

Calculate the number of molecules per liter

To calculate the number of molecules per liter, we can use Avogadro's number, which states that 1 mole contains \(6.022 \times 10^{23}\) entities. Hence, the number of molecules per liter can be determined as follows: molecules per liter = (moles per liter) × (Avogadro's number) molecules per liter = (3.2 × 10^{-8} mol/L) × (6.022 × 10^{23} molecules/mol) = 1.93 × 10^{16} molecules/L To summarize, the allowable concentration of \(2.0 \times 10^{-6} \mathrm{~g} / \mathrm{L}\) of vinyl chloride represents \(3.2 \times 10^{-8}\) moles per liter and \(1.93 \times 10^{16}\) molecules per liter.

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Most popular questions from this chapter

Determine the empirical formulas of the compounds with the following compositions by mass: (a) \(42.1 \% \mathrm{Na}, 18.9 \% \mathrm{P}\), and \(39.0 \% \mathrm{O}\) (b) \(18.7 \% \mathrm{Li}, 16.3 \% \mathrm{C},\) and \(65.0 \% \mathrm{O}\) (c) \(60.0 \% \mathrm{C}, 4.4 \% \mathrm{H},\) and the remainder \(\mathrm{O}\)

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