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Chapter 3: Problem 42

At least \(25 \mu \mathrm{g}\) of tetrahydrocannabinol (THC), the active ingredient in marijuana, is required to produce intoxication. The molecular formula of THC is \(\mathrm{C}_{21} \mathrm{H}_{30} \mathrm{O}_{2}\). How many moles of THC does this \(25 \mu \mathrm{g}\) represent? How many molecules?

Short Answer

Expert verified
25 µg of THC represents approximately \(7.95 \times 10^{-11}\) moles and \(4.79 \times 10^{13}\) molecules of THC.

Step by step solution

01

Calculate the molar mass of THC

First, we need to find the molar mass of THC. To do this, we'll use the molecular formula \(\mathrm{C}_{21} \mathrm{H}_{30} \mathrm{O}_{2}\) and the atomic masses of each element. We know the atomic masses of carbon (C), hydrogen (H), and oxygen (O) are approximately 12.01 g/mol, 1.01 g/mol, and 16.00 g/mol, respectively. So, the molar mass of THC is: Molar mass of THC = (21 × 12.01 g/mol) + (30 × 1.01 g/mol) + (2 × 16.00 g/mol) = 314.47 g/mol
02

Convert the given mass of THC to moles

Next, we will convert the given mass of THC, \(25 \mu \mathrm{g}\), to moles. To do this, we will use the molar mass of THC (314.47 g/mol) and the conversion factor: 1 g = 1,000,000 µg. Moles of THC = \(\frac{25 \mu \mathrm{g}}{314.47 \frac{\mathrm{g}}{\mathrm{mol}} \times 1,000,000 \frac{\mu \mathrm{g}}{\mathrm{g}}}\) = \(\frac{25}{314.47 \times 10^6}\) mol ≈ 7.95 × 10⁻¹¹ mol
03

Convert the number of moles to the number of molecules

Finally, we will convert the number of moles of THC (7.95 × 10⁻¹¹ mol) to the number of molecules. To do this, we will use Avogadro's number (6.022 × 10²³ molecules/mol): Number of molecules = (7.95 × 10⁻¹¹ mol) × (6.022 × 10²³ molecules/mol) ≈ 4.79 × 10¹³ molecules So, 25 µg of THC represents approximately 7.95 × 10⁻¹¹ moles and 4.79 × 10¹³ molecules of THC.

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Most popular questions from this chapter

Write the balanced chemical equations for (a) the complete combustion of acetic acid \(\left(\mathrm{CH}_{3} \mathrm{COOH}\right)\), the main active ingredient in vinegar; \((\mathbf{b})\) the decomposition of solid calcium hydroxide into solid calcium(II) oxide (lime) and water vapor; (c) the combination reaction between nickel metal and chlorine gas.

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?

A compound whose empirical formula is \(\mathrm{XF}_{3}\) consists of \(65 \%\) F by mass. What is the atomic mass of X?

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.

Why is it essential to use balanced chemical equations when determining the quantity of a product formed from a given quantity of a reactant?
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