Problem 115 - Chemistry The Molecular Science

Question

Pepto-Bismol, which helps provide relief for an upset stomach, contains \(300 \mathrm{mg}\) bismuth subsalicylate, \(\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{BiO}_{4},\) per tablet. (a) You take two tablets for your stomach distress. Calculate the amount of the "active ingredient" you are taking. (b) What mass of Bi did the two tablets contain?

Step-by-Step Solution

Answer

600 mg of bismuth subsalicylate taken; 347 mg of bismuth was present.

Step 1: Tablets Consumption Calculation

You take two tablets. Each tablet contains \(300\, \text{mg}\) of bismuth subsalicylate. Therefore, the calculation for the total amount taken is:\[2\, \text{tablets} \times 300\, \text{mg/tablet} = 600\, \text{mg}\]This step determines the total mass of bismuth subsalicylate consumed.

Step 2: Determine Molar Mass of Bismuth Subsalicylate

The formula for bismuth subsalicylate is \(\text{C}_7\text{H}_5\text{BiO}_4\). We calculate the molar mass as follows:- Carbon (C): 12.01 g/mol. Multiply by 7: \(84.07\, \text{g/mol}\)- Hydrogen (H): 1.01 g/mol. Multiply by 5: \(5.05\, \text{g/mol}\)- Bismuth (Bi): 208.98 g/mol- Oxygen (O): 16.00 g/mol. Multiply by 4: \(64.00\, \text{g/mol}\)Adding these amounts gives the total molar mass:\[\text{Molar mass} = 84.07 + 5.05 + 208.98 + 64.00 = 362.10\, \text{g/mol}\]

Step 3: Calculate Moles of Bismuth Subsalicylate

First, convert the 600 mg (0.600 g) of bismuth subsalicylate to moles:\[\text{Moles of } \text{C}_7\text{H}_5\text{BiO}_4 = \frac{0.600\, \text{g}}{362.10\, \text{g/mol}} \approx 0.00166\, \text{mol}\]

Step 4: Determine Mass of Bi in Two Tablets

Each mole of \(\text{C}_7\text{H}_5\text{BiO}_4\) contains exactly one mole of Bi. Thus, the moles of Bi is also 0.00166 mol. Calculate the mass of Bi:\[\text{Mass of Bi} = 0.00166\, \text{mol} \times 208.98\, \text{g/mol} \approx 0.347\, \text{g} \approx 347\, \text{mg}\]

Step 5: Interpret the Findings

You ingested 600 mg of bismuth subsalicylate with the two tablets (part a). The tablets contain approximately 347 mg of bismuth itself (part b).

Key Concepts

Bismuth Subsalicylate

Bismuth subsalicylate is an active ingredient commonly found in over-the-counter medications like Pepto-Bismol. It is a compound that provides relief for digestive discomfort, particularly in cases of upset stomachs, heartburn, or indigestion.
When we talk about this compound in terms of its chemical formula, it is represented as \(\mathrm{C}_7\mathrm{H}_5\mathrm{BiO}_4\). This formula indicates that each molecule of bismuth subsalicylate is composed of carbon, hydrogen, bismuth, and oxygen atoms.
Owing to its chemical composition, bismuth subsalicylate acts to provide a soothing effect in the gastrointestinal tract.

• It works by coating the lining of the stomach, creating a protective barrier.
• It also inhibits the growth of bacteria such as Helicobacter pylori which can cause infections and ulcers.

Understanding the chemical structure of bismuth subsalicylate helps us appreciate its effectiveness in treating stomach and digestive disorders.

Chemical Composition

The chemical composition of any compound is essential in understanding its properties and how it functions. In the case of bismuth subsalicylate, its formula is \(\mathrm{C}_7\mathrm{H}_5\mathrm{BiO}_4\), which tells us the constituent atoms and their quantities.
The components are:

• Carbon (C): There are 7 carbon atoms, each contributing a mass of 12.01 g/mol, totalling to 84.07 g/mol.
• Hydrogen (H): With 5 hydrogen atoms at 1.01 g/mol each, adding up to 5.05 g/mol.
• Bismuth (Bi): Bismuth is the largest contributor in weight due to its atomic weight of 208.98 g/mol.
• Oxygen (O): Comprising 4 oxygen atoms, each with a mass of 16.00 g/mol, totalling 64.00 g/mol.

When these numbers are added together, they give us the molar mass of bismuth subsalicylate, which is approximately 362.10 g/mol.
This precise breakdown allows for a better understanding of how each element attributes to the function and therapeutic properties of the compound.

Stoichiometry

Stoichiometry is a critical concept in chemistry that deals with the relative quantities of reactants and products in chemical reactions. It helps us understand the relationships and conversions between different substances.
When considering bismuth subsalicylate, stoichiometry plays a vital role in calculating the amount of active ingredient consumed and specifically how much of this is bismuth.
For example, if you take two tablets containing 300 mg of bismuth subsalicylate each, you have consumed a total mass of 600 mg. By converting this to grams (0.600 g) and using stoichiometry, you can calculate the number of moles of bismuth subsalicylate, which is \[\frac{0.600\, \text{g}}{362.10\, \text{g/mol}} \approx 0.00166\, \text{mol}\].
As each molecule of \(\mathrm{C}_7\mathrm{H}_5\mathrm{BiO}_4\) contains one bismuth atom, the moles of bismuth in the tablets equals \(0.00166\, \text{mol}\). Using this, you can find the mass of bismuth alone by multiplying the number of moles by the molar mass of bismuth \( (208.98 \text{ g/mol}) \), which results in approximately 347 mg of bismuth.
Understanding these stoichiometric relationships is essential for calculating and predicting outcomes in chemical processes, ensuring accurate and safe dosage in pharmaceutical applications.