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Ch.13 - Properties of Solutions
Chapter 13, Problem 91e

The 'free-base' form of cocaine (C17H21NO4) and its protonated hydrochloride form (C17H21NO4) are shown below; the free-base form can be converted to the hydrochloride form with one equivalent of HCl. For clarity, not all the carbon and hydrogen atoms are shown; each vertex represents a carbon atom with the appropriate number of hydrogen atoms so that each carbon makes four bonds to other atoms (e) How many mL of a concentrated 18.0 M HCl aqueous solution would it take to convert 1.00 kilograms (a 'kilo') of the free-base form of cocaine into its hydrochloride form?

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1
Determine the molar mass of the free-base form of cocaine (C_{17}H_{21}NO_{4}) by adding the atomic masses of all the atoms in the formula.
Calculate the number of moles of cocaine in 1.00 kg by dividing the mass (1000 g) by the molar mass of cocaine.
Since the conversion requires one equivalent of HCl per mole of cocaine, the number of moles of HCl needed is equal to the number of moles of cocaine.
Use the concentration of the HCl solution (18.0 M) to find the volume of HCl solution needed. Use the formula: \( \text{Volume (L)} = \frac{\text{moles of HCl}}{\text{concentration (M)}} \).
Convert the volume from liters to milliliters by multiplying by 1000, as there are 1000 mL in a liter.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Molarity

Molarity (M) is a measure of concentration defined as the number of moles of solute per liter of solution. In this context, the concentration of HCl is given as 18.0 M, meaning there are 18 moles of HCl in every liter of solution. Understanding molarity is essential for calculating the volume of HCl needed to react with a specific amount of cocaine.
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Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions based on balanced chemical equations. In this case, the conversion of free-base cocaine to its hydrochloride form requires one equivalent of HCl per mole of cocaine. Knowing the stoichiometric relationship allows for the determination of how much HCl is needed for the complete conversion of 1.00 kg of cocaine.
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Molecular Weight

Molecular weight is the mass of one mole of a substance, expressed in grams per mole (g/mol). For cocaine, the molecular weight can be calculated from its chemical formula (C17H21NO4), which is necessary to convert the mass of cocaine (1.00 kg) into moles. This conversion is crucial for applying stoichiometry to find the required volume of HCl.
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