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. \(\mathrm{A} 0.682 \mathrm{g}\) 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.

Short answer

The percent morphine in the opium sample is calculated to be approximately 46.85%.

Step-by-step solution

Calculate moles of H2SO4

To neutralize the base, H2SO4 provides 2 H+ ions per molecule. Calculate the amount (moles) of H2SO4 used in the reaction using the volume of H2SO4 solution and its molarity. Use the formula: \( \text{moles of H2SO4} = \text{Volume} (L) \times \text{Molarity} \).

Calculate moles of morphine

Since morphine accepts one proton per molecule, one mole of H2SO4 can neutralize two moles of morphine. Therefore, the number of moles of morphine neutralized is equal to twice the number of moles of H2SO4.

Calculate the mass of morphine

Use the molar mass of morphine (C17H19NO3) to convert the number of moles of morphine to grams. The molar mass of morphine is approximately 285.34 g/mol. Use the formula: \( \text{Mass of morphine} = \text{moles of morphine} \times \text{molar mass of morphine} \).

Calculate percent morphine in sample

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

Key concepts

Neutralization Reaction

A neutralization reaction is a chemical process where an acid and a base react to form water and a salt. This is commonly seen when dealing with acid-base titrations, where the goal is to determine the concentration of an unknown acid or base by reacting it with a base or acid of known concentration.

In the context of the exercise, morphine plays the role of the base and accepts a proton (H⁺) from sulfuric acid (H₂SO₄), thus undergoing a neutralization reaction. When sulfuric acid, which can donate two H⁺ ions per molecule, reacts with morphine, it creates water and a corresponding salt of morphine. By measuring the amount of sulfuric acid needed to neutralize morphine in opium, we can determine the amount of morphine present in the sample.

Molarity and Concentration

Molarity, symbolized as M, is a measure of concentration in chemistry. Specifically, it indicates the moles of solute per liter of solution. Concentration is crucial when preparing solutions for chemical reactions and for performing titrations as seen in the given exercise.

To calculate the molarity of a solution, the formula used is: \( \text{M} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \). In our case, the molarity of the sulfuric acid solution is given, and we use it along with the volume of acid required to neutralize the sample to calculate the moles of H₂SO₄ used in the reaction. This information is essential for quantifying the amount of morphine in the opium sample.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It allows chemists to predict the amounts of substances consumed and produced during a reaction.

Understanding the stoichiometry of the neutralization reaction between morphine and sulfuric acid enables us to establish the relationship that two moles of morphine will react with one mole of sulfuric acid. By calculating the moles of sulfuric acid used during the neutralization (as outlined in Step 1 of the solution), stoichiometry can then be employed to determine the moles of morphine in the sample. This step is fundamental in chemical calculations to accurately derive the mass of morphine from the moles.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is a critical property used to convert between the mass of a substance and the amount (in moles) of that substance.

For substances like morphine, with a known chemical formula (C₁₇H₁₉NO₃), the molar mass can be calculated by summing the atomic masses of all the atoms in the formula. For example, carbon (C) has an atomic mass of approximately 12.01 g/mol, hydrogen (H) 1.01 g/mol, nitrogen (N) 14.01 g/mol, and oxygen (O) 16.00 g/mol. In the exercise, knowing the molar mass of morphine is vital as it allows us to convert the moles of morphine, determined through stoichiometry, into the mass of morphine, leading us to calculate the percent composition of morphine in the opium sample.