Problem 136 - Chemistry An Atoms First Approach

Question

Some bismuth tablets, a medication used to treat upset stomachs, contain \(262 \mathrm{mg}\) of bismuth subsalicylate, \(\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{BiO}_{4},\) per tablet. Assuming two tablets are digested, calculate the mass of bismuth consumed.

Step-by-Step Solution

Answer

The mass of bismuth consumed after digesting two bismuth tablets is \(302 \thinspace mg\).

Step 1: Calculate moles of bismuth subsalicylate in one tablet

We need to find the molar mass of bismuth subsalicylate. Using the periodic table, we find that: Bi : \(208.98\thinspace g∙mol^{-1}\) C : \(12.01\thinspace g∙mol^{-1}\) H : \(1.01\thinspace g∙mol^{-1}\) O : \(16.00\thinspace g∙mol^{-1}\) Now, we can calculate the molar mass of bismuth subsalicylate (\(\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{BiO}_{4}\)): \[ M_{C_{7}H_{5}BiO_{4}} = 7 \times M_C + 5 \times M_H + M_{Bi} + 4 \times M_O \] \[ M_{C_{7}H_{5}BiO_{4}} = 7 \times 12.01 \thinspace g∙mol^{-1} + 5 \times 1.01 \thinspace g∙mol^{-1} + 208.98 \thinspace g∙mol^{-1} + 4 \times 16.00 \thinspace g∙mol^{-1} \] \[ M_{C_{7}H_{5}BiO_{4}} = 362.23\thinspace g∙mol^{-1} \] Now, we can find the number of moles of bismuth subsalicylate in one tablet: \[ \text{moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{262\thinspace mg}{362.23\thinspace g∙mol^{-1}} = \frac{0.262\thinspace g}{362.23\thinspace g∙mol^{-1}} \] \[ \text{moles} = 7.23\times10^{-4} \thinspace mol \]

Step 2: Find moles of bismuth in one tablet

Since the mole ratio of bismuth (Bi) to bismuth subsalicylate (\(\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{BiO}_{4}\)) is 1:1, the number of moles of bismuth in one tablet will be the same as the number of moles of bismuth subsalicylate in one tablet. Moles of bismuth in one tablet = 7.23 × 10^{-4} mol

Step 3: Convert moles of bismuth to mass

To convert the moles of bismuth to mass (in mg), we will use the molar mass of bismuth: Mass of bismuth in one tablet = moles × molar mass \[ \text{Mass}_{\text{Bi}} = 7.23\times10^{-4} \thinspace mol \times 208.98 \thinspace g∙mol^{-1} \] Mass of bismuth in one tablet = 0.151 g = 151 mg

Step 4: Calculate the total mass of bismuth consumed

Since two tablets are consumed, we need to multiply the mass of bismuth in one tablet by 2: Total mass of bismuth consumed = 2 × Mass of bismuth in one tablet Total mass of bismuth consumed = 2 × 151 mg = 302 mg The mass of bismuth consumed after digesting two bismuth tablets is 302 mg.

Key Concepts

bismuth subsalicylate

Bismuth subsalicylate is a well-known compound often used in medications to treat issues like upset stomachs, heartburn, and nausea. Chemically, it is represented as \(\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{BiO}_{4}\). Understanding its structure is crucial when calculating its molar mass. Each molecule contains seven carbon (C) atoms, five hydrogen (H) atoms, one bismuth (Bi) atom, and four oxygen (O) atoms. This compound's complexity requires precise calculations to ensure accurate medical dosages.

When you read about medication dosages in tablets, it's often measured in milligrams, such as the 262 mg of bismuth subsalicylate per tablet mentioned in the exercise. Calculating the molar mass of bismuth subsalicylate helps pharmacologists determine how much of the active element bismuth is available in each dose, ensuring the safety and efficacy of the medication.

stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It helps us calculate the amounts of substances required or produced.

In the context of our exercise, stoichiometry enables us to determine how much bismuth is present in a bismuth subsalicylate tablet. By using the molar mass we calculated—362.23 g/mol for bismuth subsalicylate—we can convert the given tablet mass from milligrams to moles, allowing us to find the number of moles present.

Once we have the moles of the compound, stoichiometry is again useful in determining the amount of bismuth. Because the mole ratio of bismuth to bismuth subsalicylate is 1:1, the number of moles of bismuth is the same as the number of moles of the compound itself. This ratio simplifies our calculations and forms an integral part of stoichiometry.

tablet dosage calculation

Tablet dosage calculation involves determining the amount of a drug or active ingredient in a certain number of tablets. This ensures a patient receives the correct dosage for optimal treatment results.

In this exercise, we calculate how much bismuth is consumed when two bismuth subsalicylate tablets are ingested. After determining the mass of bismuth in a single tablet to be 151 mg, we simply double it to find the total mass consumed with two tablets. This step—multiplying by the number of tablets—is crucial in dosage calculations.

Such calculations are vital in medicine to adjust dosages appropriately, depending on the number of tablets prescribed. They ensure that the medicine administered remains within safe and effective boundaries, tailored to the needs and health conditions of patients.