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.

Short answer

The mass of bismuth consumed when two bismuth tablets are digested is approximately 302.412 mg.

Step-by-step solution

Find the molar mass of bismuth subsalicylate (C₇H₅BiO₄)

To find the molar mass of bismuth subsalicylate (C₇H₅BiO₄), we must find the sum of the molar masses of its constituent elements. The molar mass of carbon (C): 12.01 g/mol The molar mass of hydrogen (H): 1.01 g/mol The molar mass of bismuth (Bi): 208.98 g/mol The molar mass of oxygen (O): 16.00 g/mol Now, we calculate the molar mass of C₇H₅BiO₄: Molar mass = 7(12.01) + 5(1.01) + 208.98 + 4(16.00) = 84.07 + 5.05 + 208.98 + 64.00 = 362.10 g/mol

Calculate the mass of bismuth in one tablet

First, let's find the mass fraction of bismuth in bismuth subsalicylate: Mass fraction of bismuth = (mass of Bi in the compound) / (molar mass of C₇H₅BiO₄) = (208.98 g/mol) / (362.10 g/mol) The mass fraction of bismuth is approximately 0.577. Now, we can find the mass of bismuth in one tablet by multiplying the mass of bismuth subsalicylate in one tablet by the mass fraction of bismuth: Mass of bismuth in one tablet = 262 mg × 0.577 = 151.206 mg (approximately)

Calculate the mass of bismuth in two tablets

Now, we can simply multiply the mass of bismuth in one tablet by the number of tablets (2) to find the total mass of bismuth consumed: Mass of bismuth in two tablets = 2 × 151.206 mg = 302.412 mg (approximately) The mass of bismuth consumed when two bismuth tablets are digested is approximately 302.412 mg.

Key concepts

Understanding Bismuth Subsalicylate

Bismuth subsalicylate is a chemical compound with the formula \( \mathrm{C}_{7} \mathrm{H}_{5} \mathrm{BiO}_{4} \). It is commonly used in medications to treat digestive issues like upset stomach, nausea, and diarrhea. This compound contains bismuth, a heavy metal known for stabilizing stomach linings and minimizing inflammation.
When discussing bismuth subsalicylate in chemistry, it is important to examine its composition. Each molecule contains:

• 7 carbon atoms
• 5 hydrogen atoms
• 1 bismuth atom
• 4 oxygen atoms

The unique attributes of each element contribute to the overall properties of bismuth subsalicylate. The bismuth center is crucial for its medicinal efficacy. Thorough understanding of these atoms helps when calculating the molar mass or determining composition within pharmaceuticals.

Calculating Mass Fraction

Mass fraction is a useful concept in chemistry to determine the proportion of a particular element in a compound. It is calculated by dividing the mass of the element by the total molar mass of the compound. This value reveals how much of the compound's mass comes from the specified element.
In the case of bismuth subsalicylate, we are interested in the mass fraction of bismuth. With a molar mass of 208.98 g/mol for bismuth, and a total molar mass of 362.10 g/mol for \( \mathrm{C}_{7} \mathrm{H}_{5} \mathrm{BiO}_{4} \), the calculation is: \[\text{Mass fraction of Bi} = \frac{208.98}{362.10} \approx 0.577\]The mass fraction means that approximately 57.7% of each molecule's mass in this compound is due to bismuth. Understanding mass fractions assists in determining how much of a particular element is present when given the mass of the compound, a common necessity in pharmaceuticals.

Stoichiometry in Bismuth Consumption

Stoichiometry involves using balanced chemical equations to calculate relative quantities of reactants and products. In terms of bismuth subsalicylate, stoichiometry allows us to determine how much bismuth is present in a given number of tablets.
Knowing the mass fraction (0.577) and the mass of bismuth subsalicylate per tablet (262 mg), the mass of bismuth in one tablet is easy to find:\[\text{Mass of Bi in one tablet} = 262 \times 0.577 = 151.206 \, \text{mg}\]To find the total bismuth consumed in two tablets, simply double this amount:\[\text{Total mass of Bi in two tablets} = 2 \times 151.206 = 302.412 \, \text{mg}\]This method illustrates stoichiometry’s practical applications. It helps to foresee the amount of substance consumed based on initial data, ensuring accuracy in both scientific calculations and pharmaceutical dosages.