Cocaine \(\left(\mathrm{C}_{17} \mathrm{H}_{21} \mathrm{O}_{4} \mathrm{~N}\right)\) is a natural substance found in \(\operatorname{coca}\) leaves, which have been used for centuries as a local anesthetic and stimulant. Illegal cocaine arrives in the United States either as the pure compound or as the hydrochloride salt \(\left(\mathrm{C}_{17} \mathrm{H}_{21} \mathrm{O}_{4} \mathrm{NHCl}\right)\). At \(25^{\circ} \mathrm{C},\) the salt is very soluble in water \((2.50 \mathrm{~kg} / \mathrm{L}),\) but cocaine is much less so \((1.70 \mathrm{~g} / \mathrm{L})\) (a) What is the maximum mass (g) of the hydrochloride salt that can dissolve in \(50.0 \mathrm{~mL}\) of water? (b) If the solution from part (a) is treated with \(\mathrm{NaOH}\), the salt is converted to cocaine. How much more water (L) is needed to dissolve it?

Understanding molar mass conversion is crucial for solving many chemistry problems, including those involving solubility calculations.
The molar mass is the mass of one mole of a substance, typically measured in grams per mole (g/mol).
To perform molar mass conversion, you often need the molecular weight of the substances involved.

For example, in the exercise, we need to convert the mass of cocaine hydrochloride to pure cocaine.
First, identify the molar masses of both compounds: Cocaine hydrochloride (C17H21O4NHCl) has a molar mass of 339.82 g/mol, and pure cocaine (C17H21O4N) has a molar mass of 303.36 g/mol.

To find the mass of pure cocaine from the hydrochloride salt, we used the ratio of their molar masses. This ratio helps us understand the proportionate weights between the salt and the pure compound.
By multiplying this ratio with the given mass of the hydrochloride salt, we obtain the corresponding mass of pure cocaine.

Solubility tells us how much of a substance can dissolve in a solvent at a specific temperature.
It is usually expressed in terms of grams per liter (g/L) or kilograms per liter (kg/L).
Solubility product (Ksp) is different; it applies to sparingly soluble salts and pertains to their ionic components in a saturated solution.

In this exercise, we dealt with the solubility of cocaine hydrochloride and pure cocaine. The solubility of cocaine hydrochloride is given as 2.50 kg/L, and for pure cocaine, it is 1.70 g/L.
Because we're dealing with large quantities for the hydrochloride salt, the mass was initially given in kilograms, necessitating a conversion to grams for better precision in our calculations.

Procedurally, knowing that we had 50.0 mL (or 0.050 L) of water helped us to calculate the maximum mass of hydrochloride salt that can dissolve using its solubility. By multiplying the solubility by the volume of water, we determine the maximum mass capable of dissolving in that volume.

Stoichiometry is the study of the quantitative relationships between the amounts of reactants and products in a chemical reaction.
It allows us to predict how much product we can obtain from given reactants and how much reactants are needed to form a desired amount of product.

In this exercise, after calculating the mass of pure cocaine from the hydrochloride salt, we needed to determine how much water was required to dissolve it. This problem required a stoichiometric conversion based on the known solubility of pure cocaine (1.70 g/L).

First, we calculated the volume of water needed to dissolve 111.6 grams of pure cocaine using the solubility value. Then, we subtracted the initial volume used to get the additional water volume needed.
This step-by-step approach is fundamental in stoichiometric calculations, allowing for precise measurements and conversions.
Understanding stoichiometry is essential for mastering various chemistry problems and performing accurate laboratory calculations.