Problem 91 - Chemistry The Central Science In Si Units

Question

The "free-base" form of cocaine \(\left(\mathrm{C}_{17} \mathrm{H}_{21} \mathrm{NO}_{4}\right)\) and its protonated hydrochloride form \(\left(\mathrm{C}_{17} \mathrm{H}_{22} \mathrm{ClNO}_{4}\right)\) 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. (a) One of these forms of cocaine is relatively water-soluble: which form, the free base or the hydrochloride? (b) One of these forms of cocaine is relatively insoluble in water: which form, the free base or the hydrochloride? (c) The free-base form of cocaine has a solubility of \(1.00 \mathrm{~g}\) in \(6.70 \mathrm{~mL}\) ethanol \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\right) .\) Calculate the molarity of a saturated solution of the free-base form of cocaine in ethanol. (d) The hydrochloride form of cocaine has a solubility of \(1.00 \mathrm{~g}\) in \(0.400 \mathrm{~mL}\) water. Calculate the molarity of a saturated solution of the hydrochloride form of cocaine in water. (e) How many mL of a concentrated \(18.0 \mathrm{M} \mathrm{HCl}\) aqueous solution would it take to convert 1.00 kilograms (a "kilo") of the free-base form of cocaine into its hydrochloride form?

Step-by-Step Solution

Answer

(a) Hydrochloride; (b) Free-base; (c) 0.495 M; (d) 7.36 M; (e) 183 mL.

Step 1: Identify Water-Soluble Form

Compounds that are protonated (such as salts) tend to be more water-soluble because they carry a charge and can hydrogen bond with water. Since the hydrochloride form is a protonated salt, it is more soluble in water.

Step 2: Identify Water-Insoluble Form

The free-base form of cocaine lacks the charged state and thus is less soluble in water as compared to its salt form.

Step 3: Calculate Molar Mass of Free-Base Cocaine

Calculate the molar mass of the free-base cocaine, C\(_{17}\)H\(_{21}\)NO\(_4\):\ \(17 \times 12.01 + 21 \times 1.008 + 14.01 + 4 \times 16.00 = 303.37 \text{ g/mol}\).

Step 4: Calculate Molarity of Free-Base Cocaine in Ethanol

Convert solubility to molarity by dividing mass by molar mass, then divide by volume in liters:\ \(\text{Molarity} = \frac{1.00 \text{ g}}{303.37 \text{ g/mol}} \times \frac{1}{6.70 \times 10^{-3} \text{ L}} \approx 0.495 \text{ M}\).

Step 5: Calculate Molar Mass of Cocaine Hydrochloride

Calculate the molar mass of cocaine hydrochloride, C\(_{17}\)H\(_{22}\)ClNO\(_4\):\ \(17 \times 12.01 + 22 \times 1.008 + 14.01 + 35.45 + 4 \times 16.00 = 339.82 \text{ g/mol}\).

Step 6: Calculate Molarity of Cocaine Hydrochloride in Water

Convert solubility to molarity by dividing mass by molar mass, then divide by volume in liters:\ \(\text{Molarity} = \frac{1.00 \text{ g}}{339.82 \text{ g/mol}} \times \frac{1}{0.400 \times 10^{-3} \text{ L}} \approx 7.36 \text{ M}\).

Step 7: Determine Moles of Free-Base Cocaine

For the reaction, 1 mol of HCl converts 1 mol of free-base cocaine to its hydrochloride form. Calculate moles for 1 kg:\ \(\frac{1000 \text{ g}}{303.37 \text{ g/mol}} \approx 3.297 \text{ mol}\).

Step 8: Calculate Volume of HCl Needed

Using the number of moles, find the volume of 18.0 M HCl needed:\ \(\text{Volume} = \frac{3.297 \text{ mol}}{18.0 \text{ M}} \approx 0.183 \text{ L} = 183 \text{ mL}\).

Key Concepts

Molarity

Molarity is a key concept in chemistry that expresses the concentration of a solution. It is defined as the number of moles of a solute per liter of solution. This unit is often denoted as "M", which stands for molar. For example, if you have a solution with 1 mole of solute dissolved in 1 liter of solution, it would be a 1 M solution.
In the context of cocaine compounds, we calculated the molarity of both the free-base form of cocaine in ethanol and its hydrochloride form in water. This calculation helps us understand how concentrated the solutions are relative to each other.
To calculate molarity, you must know the mass of the solute and its molar mass. You also need to measure the volume of the solvent in liters. The general formula is: \[\text{Molarity} = \frac{\text{mass of solute (g)}}{\text{molar mass of solute (g/mol)}} \times \frac{1}{\text{volume of solvent (L)}}\]

• The molarity calculation for the free-base form of cocaine in ethanol is a crucial step to quantitatively analyze the solubility.
• For cocaine hydrochloride in water, molarity indicates a high concentration due to its higher water solubility.

Chemical Compounds

Chemical compounds are substances formed by the chemical combination of two or more elements. Each compound has a unique arrangement of atoms and specific chemical properties. They are often represented by chemical formulas, such as the free-base cocaine \(\mathrm{C}_{17}\mathrm{H}_{21}\mathrm{NO}_{4}\) and cocaine hydrochloride \(\mathrm{C}_{17}\mathrm{H}_{22}\mathrm{ClNO}_{4}\).
The composition of these compounds affects their properties, such as solubility, reactivity, and structure. In this exercise, understanding the distinction between the free-base form and the hydrochloride form of cocaine is crucial as they vary significantly in solubility with different solvents.

• Free-base forms are neutral and tend to be less soluble in polar solvents like water due to lack of charge.
• On the other hand, the presence of a charged group (like in cocaine hydrochloride) enhances solubility in water, a polar solvent.

Understanding the characteristics of chemical compounds allows chemists to anticipate the behavior and reactions of substances in different environments.

Water Solubility

Water solubility refers to the ability of a substance to dissolve in water, forming a homogeneous solution. It depends on the chemical nature of the solute and the solvent. In general, compounds that can ionize or are charged tend to be more soluble in water.
However, not all compounds dissolve easily. For instance, the free-base form of cocaine is not charged, making it insoluble in water. But when it becomes a salt, like cocaine hydrochloride, it dissolves readily in water.
Some principles that affect water solubility include:

• Polarity: Water is a polar solvent; hence, polar solutes or ionic compounds tend to dissolve well in water.
• Hydrogen bonding: Solutes that can form hydrogen bonds with water generally have higher solubility.

In our exercise, examining the solubility of cocaine forms highlights the practical importance of understanding solubility principles. By knowing which molecular features contribute to water solubility, chemists can manipulate compounds to achieve desired properties or formulations.