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Chapter 3: Problem 44

At least \(25 \mu \mathrm{g}\) of tetrahydrocannabinol \((\mathrm{THC}),\) the active ingredient in marijuana, is required to produce intoxication. The molecular formula of \(\mathrm{THC}\) 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 \(7.95 \times 10^{-8}\) moles and \(4.79 \times 10^{16}\) molecules of THC.

Step by step solution

01

Convert the mass of THC into grams

To make the calculations easier, we need to first convert the mass of THC from micrograms (μg) to grams (g). To do this, use the following conversion factor: 1 g = 1,000,000 μg So, 25 μg = 25 × (1/1,000,000) g = 25 × 10⁻⁶ g
02

Calculate the molar mass of THC

We have the molecular formula for THC as C₂₁H₃₀O₂. So, let's find the molar mass for each element and sum them up. Molar mass of Carbon (C): 12.01 g/mol Molar mass of Hydrogen (H): 1.01 g/mol Molar mass of Oxygen (O): 16.00 g/mol Molar mass of C₂₁H₃₀O₂: = 21 × (12.01 g/mol) + 30 × (1.01 g/mol) + 2 × (16.00 g/mol) = 252.21 g/mol + 30.3 g/mol + 32 g/mol = 314.51 g/mol
03

Calculate the moles of THC

To calculate the number of moles, divide the mass of THC by its molar mass. Moles of THC = (Mass of THC)/(Molar mass of THC) = (25 × 10⁻⁶ g)/(314.51 g/mol) = 7.95 × 10⁻⁸ mol
04

Calculate the number of molecules of THC

Now, use Avogadro's constant to find the number of molecules in this amount of THC. Recall that Avogadro's constant is approximately 6.022 × 10²³ mol⁻¹. Number of molecules = (Moles of THC) × (Avogadro's constant) = (7.95 × 10⁻⁸ mol) × (6.022 × 10²³ mol⁻¹) = 4.79 × 10¹⁶ molecules So, 25 μg of THC represents 7.95 × 10⁻⁸ moles and 4.79 × 10¹⁶ molecules of THC.

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Most popular questions from this chapter

Write balanced chemical equations to correspond to each of the following descriptions: (a) When sulfur trioxide gas reacts with water, a solution of sulfuric acid forms. (b) Boron sulfide, \(\mathrm{B}_{2} \mathrm{~S}_{3}(s),\) reacts violently with water to form dissolved boric acid, $\mathrm{H}_{3} \mathrm{BO}_{3},$ and hydrogen sulfide gas. (c) Phosphine, \(\mathrm{PH}_{3}(g)\), combusts in oxygen gas to form water vapor and solid tetraphosphorus decaoxide. (d) When solid mercury(II) nitrate is heated, it decomposes to form solid mercury(II) oxide, gaseous nitrogen dioxide, and oxygen. (e) Copper metal reacts with hot concentrated sulfuric acid solution to form aqueous copper(II) sulfate, sulfur dioxide gas, and water.

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(a) The characteristic odor of pineapple is due to ethyl butyrate, a compound containing carbon, hydrogen, and oxygen. Combustion of \(2.78 \mathrm{mg}\) of ethyl butyrate produces \(6.32 \mathrm{mg}\) of \(\mathrm{CO}_{2}\) and $2.58 \mathrm{mg}\( of \)\mathrm{H}_{2} \mathrm{O}$. What is the empirical formula of the compound? (b) Nicotine, a component of tobacco, is composed of \(\mathrm{C}, \mathrm{H},\) and \(\mathrm{N}\). A \(5.250-\mathrm{mg}\) sample of nicotine was combusted, producing \(14.242 \mathrm{mg}\) of \(\mathrm{CO}_{2}\) and \(4.083 \mathrm{mg}\) of \(\mathrm{H}_{2} \mathrm{O} .\) What is the empirical formula for nicotine? If nicotine has a molar mass of $160 \pm 5 \mathrm{~g} / \mathrm{mol},$ what is its molecular formula?
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