Question

The active ingredient in Pepto-Bismol \(^{\circledast}\) (an overthe-counter remedy for an upset stomach) is bismuth subsalicylate, \(\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{BiO}_{4}\). Analysis of a \(1.7500-\mathrm{g}\) sample of Pepto-Bismol yields \(346 \mathrm{mg}\) of bismuth. What percent by mass is bismuth subsalicylate in the sample? (Assume that there are no other bismuth- containing compounds in Pepto-Bismol.)

Short answer

Question: Calculate the percent by mass of bismuth subsalicylate in a 1.7500 g sample containing 346 mg of bismuth. Answer: The percent by mass of bismuth subsalicylate in the sample is 34.2%.

Step-by-step solution

Convert the mass of bismuth to moles

To convert the mass of bismuth to moles, we use the molar mass of bismuth, which is 208.98 g/mol. We are given that the mass of bismuth in the sample is 346 mg, which is equal to 0.346 g. So we have, Moles of bismuth = (0.346 g) / (208.98 g/mol) = 0.001654 moles.

Find the molar mass of bismuth subsalicylate

To find the molar mass of bismuth subsalicylate, \(\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{BiO}_{4}\), we need to sum the molar masses of its constituent elements. Here's the breakdown: - 7 Carbon (C) atoms have a molar mass of (7 * 12.01) g/mol - 5 Hydrogen (H) atoms have a molar mass of (5 * 1.01) g/mol - 1 Bismuth (Bi) atom has a molar mass of 208.98 g/mol - 4 Oxygen (O) atoms have a molar mass of (4 * 16.00) g/mol Adding these values, we get: Molar mass of bismuth subsalicylate = (7 * 12.01 + 5 * 1.01 + 208.98 + 4 * 16.00) g/mol = 362.2 g/mol.

Calculate the mass of bismuth subsalicylate

Now that we have the number of moles of bismuth and the molar mass of bismuth subsalicylate, we can use this information to calculate the mass of bismuth subsalicylate in the sample. We know that the ratio of bismuth to bismuth subsalicylate is 1:1 (since there is only one bismuth atom in each mole of bismuth subsalicylate). Therefore, the moles of bismuth subsalicylate present in the sample is also 0.001654 moles. Now, using the molar mass of bismuth subsalicylate, we can calculate its mass: Mass of bismuth subsalicylate = (moles of bismuth subsalicylate) * (molar mass of bismuth subsalicylate) = (0.001654 moles) * (362.2 g/mol) = 0.599 g

Calculate the percent by mass of bismuth subsalicylate in the sample

Finally, we can calculate the percent by mass of bismuth subsalicylate in the sample using the following formula: Percent by mass = (mass of bismuth subsalicylate) / (mass of the sample) * 100 = (0.599 g) / (1.7500 g) * 100 = 34.2% The percent by mass of bismuth subsalicylate in the sample is 34.2%.

Key concepts

Molar Mass

Understanding the concept of molar mass is crucial for performing stoichiometric calculations in chemistry. Molar mass is defined as the mass of one mole of a substance, which is numerically equal to the substance's molecular or formula weight expressed in grams.

It serves as a bridge between the mass of a substance and the amount of entities (such as atoms or molecules) in that mass. The molar mass of a compound is determined by summing up the molar masses of the individual elements that make up the compound, multiplied by the number of atoms of each element present in a single molecule of the compound.

For example, in the case of bismuth subsalicylate, \( \mathrm{C}_{7} \mathrm{H}_{5} \mathrm{BiO}_{4} \), we calculate the molar mass by multiplying the atomic masses of carbon, hydrogen, bismuth, and oxygen by their respective quantities in the molecular formula and adding them together. This gives us the total molar mass of the compound, which is essential for the next steps of stoichiometric calculations.

Stoichiometry

Stoichiometry is the section of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It is based on the law of conservation of mass, which states that in a chemical reaction, matter is neither created nor destroyed.

Stoichiometry involves using the balanced chemical equation as a roadmap to understand the ratios of the reactants and products. For example, if we know the amount of one reactant in a reaction, stoichiometry helps us calculate the amount of another reactant required or the amount of a product that will be produced.

When it comes to substances in a sample, as in the case of the Pepto-Bismol problem, stoichiometry allows us to determine the percentage by mass of a component in a compound, assuming we know the compound's chemical formula and the sample's total mass.

Chemical Composition

The chemical composition of a substance refers to the identities and proportions of the elements that make up that substance. Each compound has a unique chemical composition represented by a chemical formula.

The chemical formula not only gives the types of atoms in a compound but also their ratios. This information is fundamental to calculating the percent by mass of an element in a compound, which is the ratio of the mass of a specific element to the total mass of the compound expressed as a percentage. This concept is particularly significant when determining purity or concentration, such as deducing the amount of active ingredient in a pharmaceutical product like Pepto-Bismol.

By knowing the chemical composition and the sample's total mass, as well as the specific mass of an element such as bismuth, it becomes possible to evaluate the quality or potency of the compound in various practical and industrial applications.