Problem 142 - Chemistry A Molecular Approach

Question

Morphine has the formula \(\mathrm{C}_{17} \mathrm{H}_{19} \mathrm{NO}_{3}\). It is a base and accepts one proton per molecule. It is isolated from opium. A 0.682 -g sample of opium is found to require \(8.92 \mathrm{~mL}\) of a \(0.0116 \mathrm{M}\) solution of sulfuric acid for neutralization. Assuming that morphine is the only acid or base present in opium, calculate the percent morphine in the sample of opium.

Step-by-Step Solution

Answer

The percent morphine in the sample of opium is calculated by neutralizing with sulfuric acid, finding moles of morphine, calculating its mass, and then determining the percentage based on the sample's mass.

Step 1: Calculate the moles of sulfuric acid used

Use the volume and molarity of the sulfuric acid to calculate the moles. The molarity tells us the number of moles of acid per liter of solution. The formula to calculate moles is: \( \text{Moles of Acid} = \text{Molarity} \times \text{Volume in Liters} \). Convert the volume of acid used from mL to L by dividing by 1000.

Step 2: Determine the moles of morphine

Since morphine is a monoprotic base (it accepts one proton per molecule), it reacts with an equal number of moles of acid. Therefore, the moles of sulfuric acid used will equal the moles of morphine that reacted.

Step 3: Calculate the molar mass of morphine

To find the molar mass of morphine (\(\mathrm{C}_{17} \mathrm{H}_{19} \mathrm{NO}_{3}\)), sum the molar masses of all the atoms in the formula: 17 carbon atoms, 19 hydrogen atoms, one nitrogen atom, and three oxygen atoms.

Step 4: Calculate the mass of morphine

Use the moles of morphine obtained in Step 2 and the molar mass from Step 3 to find the mass of morphine in grams: \(\text{Mass of Morphine} = \text{Moles of Morphine} \times \text{Molar Mass of Morphine}\).

Step 5: Calculate the percent morphine in the sample

To find the percent of morphine in the opium, divide the mass of morphine by the mass of the opium sample and multiply the result by 100%. Use the formula: \(\text{Percent Morphine} = \left(\frac{\text{Mass of Morphine}}{\text{Mass of Opium Sample}}\right) \times 100%\).

Key Concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. Think of it as the recipe book for chemists, which tells them how much of each reactant is needed to create a certain amount of product.

For example, in the calculation of percent morphine in opium, stoichiometry helps us understand the relationship between the amount of sulfuric acid used and the amount of morphine that can react with it. Since morphine is a monoprotic base, each molecule of morphine will react with one molecule of the acid. By using stoichiometry, you can precisely determine how many moles of morphine are present, based on the moles of sulfuric acid reacted.

Molar Mass

The molar mass of a substance is the mass of one mole of that substance. It's often measured in grams per mole (g/mol). This concept is essential for converting between the mass of a substance and the amount of substance in moles.

When calculating the percent composition of morphine in an opium sample, knowing the molar mass of morphine enables you to find the mass of morphine from the number of moles you've determined through stoichiometry. The molar mass is the sum of the masses of all atoms in the molecular formula of the compound and is used in the formula: \[\text{Molar Mass} = (\text{Number of Atoms of Element}) \times (\text{Atomic Mass of Element})\].

Neutralization Reactions

Neutralization reactions are chemical reactions between an acid and a base. When an acid and a base react, they produce water and an ionic compound known as a salt.

In the context of our problem, we have morphine, a base, reacting with sulfuric acid. The reaction allows us to determine the amount of morphine in the sample because it's a one-to-one reaction: one mole of acid reacts with one mole of base. This straightforward stoichiometric relationship is key in the process of calculating the percent composition of morphine in opium.

Acid-Base Titration

Acid-base titration is a technique used in chemistry to determine the concentration of an unknown acid or base solution. It involves adding a titrant (a solution of known concentration) to a solution of the substance whose concentration you want to find out, until the chemical reaction between the acid and base is complete—indicated by a change in color called the endpoint.

In the exercise about morphine content in opium, titration enables us to measure precisely how much sulfuric acid is necessary to neutralize the morphine. The volume of the titrant used during the titration, alongside its molarity, provides the data needed to calculate the moles of acid, which in turn, shows us the amount of morphine in the sample through stoichiometric calculations.