Question

Chlorisondamine chloride \(\left(\mathrm{C}_{14} \mathrm{H}_{20} \mathrm{Cl}_{6} \mathrm{N}_{2}\right)\) is a drug used in the treatment of hypertension. A \(1.28-\mathrm{g}\) sample of a medication containing the drug was treated to destroy the organic material and to release all the chlorine as chloride ion. When the filtered solution containing chloride ion was treated with an excess of silver nitrate, 0.104 g silver chloride was recovered. Calculate the mass percent of chlorisondamine chloride in the medication, assuming the drug is the only source of chloride.

Short answer

The mass percent of chlorisondamine chloride in the medication can be calculated using the following steps: 1. Calculate the moles of silver chloride (Moles of AgCl = \( \frac{0.104}{143.35} \) mol). 2. Determine the moles of chloride ions (Moles of Cl⁻ = Moles of AgCl). 3. Calculate the mass of chlorine present (Mass of chlorine present = Moles of Cl⁻ x 35.45 g/mol). 4. Find the mass of chlorisondamine chloride containing this mass of chlorine (mass_of_chlorisondamine = \( \frac{mass\_of\_chlorine \times 535.69 \, g/mol}{212.7 \, g/mol} \)). 5. Calculate the mass percent of chlorisondamine chloride in the medication (Mass percent of chlorisondamine chloride = \( \frac{mass\_of\_chlorisondamine}{1.28 \, g} \times 100 \)). After plugging in the values obtained in the previous steps, you'll get the mass percent of chlorisondamine chloride in the medication.

Step-by-step solution

Calculate the moles of silver chloride present.

Given that the mass of silver chloride recovered is 0.104 g, we need to first determine the number of moles present. The molar mass of silver chloride (AgCl) is 107.9 g/mol (Ag) + 35.45 g/mol (Cl) = 143.35 g/mol. So, the moles of silver chloride can be calculated as: Moles of AgCl = mass of AgCl / molar mass of AgCl = \( \frac{0.104}{143.35} \) mol

Calculate the moles of chloride ions present.

Since chloride ions come only from the chlorisondamine chloride and each silver chloride molecule contains one chloride ion, the number of moles of silver chloride is equal to the number of moles of chloride ions present. Moles of Cl⁻ = Moles of AgCl

Calculate the mass of chlorine present.

Now, we need to find the mass of chlorine present. The molar mass of chlorine (Cl) is 35.45 g/mol, so the mass can be calculated as: Mass of chlorine present = Moles of Cl⁻ x molar mass of Cl = Moles of AgCl x 35.45 g/mol

Calculate the mass of chlorisondamine chloride containing this mass of chlorine.

For chlorisondamine chloride, we need to find the mass of the molecule that contains the mass of chlorine found in step 3. The molar mass of chlorisondamine chloride is given by: \(14(12.01)+20(1.01)+6(35.45)+2(14.01) = 535.69 \, g/mol \). There are 6 chlorine atoms in chlorisondamine chloride, which contributes to a total mass of \(6 \times 35.45 = 212.7 \,g/mol \) from chlorine. To find the mass of chlorisondamine chloride that contains the mass of chlorine found in step 3, we can set up a proportion: \( \frac{mass\_of\_chlorine}{mass\_of\_chlorisondamine} = \frac{212.7 \, g/mol}{535.69 \, g/mol} \) Solving for mass_of_chlorisondamine, we get: mass_of_chlorisondamine = \( \frac{mass\_of\_chlorine \times 535.69 \, g/mol}{212.7 \, g/mol} \)

Calculate the mass percent of chlorisondamine chloride in the medication.

Finally, to calculate the mass percent of chlorisondamine chloride in the medication, we will divide the mass of chlorisondamine chloride obtained in step 4 by the total mass of the medication sample (1.28 g), and then multiply by 100 to get the percentage: Mass percent of chlorisondamine chloride = \( \frac{mass\_of\_chlorisondamine}{1.28 \, g} \times 100 \) Now, we can plug in the values obtained in previous steps to calculate the mass percent of chlorisondamine chloride in the medication.

Key concepts

Stoichiometry

Stoichiometry is the section of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. In the context of the exercise provided, stoichiometry is essential to determine the correct proportions of reactants and products involved in the reaction to calculate the percent composition of chlorisondamine chloride in a sample.

For a student trying to understand stoichiometry, it's important to first grasp the concept of a 'mole,' which is a count of the number of molecules or atoms, analogous to a dozen representing 12 items. One mole contains Avogadro's number of entities (approximately 6.022 x 10^23). Stoichiometry relies on mole ratios derived from the balanced chemical equations to convert between masses and moles and to compare quantities of different substances.

When using stoichiometry in problems like these, it's crucial to write down the balanced chemical equation and to use the mole ratio to convert between substances. However, in this case, we don't have a chemical reaction but a decomposition and subsequent precipitation, where stoichiometry helps us to connect the moles of silver chloride to the moles of chloride ions and ultimately to the mass of chlorisondamine chloride.

Molar Mass Calculation

Molar mass calculation is fundamental in stoichiometry as it allows the conversion of mass in grams to amount in moles, which is a necessary step in most stoichiometric problems. The molar mass of a substance is the weight in grams of one mole of that substance. To calculate the molar mass, one adds up the atomic masses of every atom in the molecule, which can be found on the periodic table.

In the given exercise, to calculate the molar mass of silver chloride, simply sum the atomic masses of silver (Ag) and chlorine (Cl). The molar mass is then used to convert the given mass of silver chloride into moles, which is a critical step in finding out how much chlorisondamine chloride was in the original sample.

To improve understanding, visualize the molar mass as an exchange rate between grams and moles. Just like converting currency, if you know how much one unit is in another system, you can convert between them freely. This concept is pivotal when solving percentage composition problems, as you need to calculate the quantity of a specific element or compound in a sample, translating between the mass of different components and the total mass.

Limiting Reagent

The concept of the limiting reagent is key in chemical reactions and is deeply connected with stoichiometry. It refers to the reactant that is completely consumed first and thus determines when the reaction stops, and it limits the amount of product that can be formed from the reactants. In the context of percent composition analysis and stoichiometry, identifying the limiting reagent can be critical to accurately calculate the theoretical yields.

In the case of the exercise given, the student must recognize that silver nitrate was added in excess, meaning that it is not the limiting reagent. The amount of chlorisondamine chloride in the original sample is said to be the only source of chloride ions, therefore it is the limiting reagent.

To develop a deeper understanding of this concept, consider a simple analogy: If you are making sandwiches and you have 10 slices of bread but only 3 slices of ham, the ham is the limiting 'reagent' because it will run out first, limiting the total number of sandwiches to 3. Similarly, in the exercise, the drug determines the amount of chloride ions, and thus, the formation of silver chloride. Understanding which reagent limits the reaction helps to calculate the maximum amount of product that can be formed from the given reactants, which in turn is essential for determining percent composition.