Problem 147 - Chemistry and Chemical Reactivity

Question

Pepto-Bismol, which can help provide relief for an upset stomach, contains \(300 .\) mg of bismuth subsalicylate, \(\mathrm{C}_{21} \mathrm{H}_{15} \mathrm{Bi}_{3} \mathrm{O}_{12}\), per tablet. If you take two tablets for your stomach distress, what amount (in moles) of the "active ingredient" are you taking? What mass of Bi are you consuming in two tablets?

Step-by-Step Solution

Answer

You are taking about 0.000572 moles and consuming approximately 0.359 g of bismuth.

Step 1: Determine the Total Mass of Bismuth Subsalicylate

First, calculate the total mass of bismuth subsalicylate when taking two tablets. Since each tablet contains 300 mg of the compound, two tablets would contain twice this amount. Thus, the mass is \(2 \times 300 \text{ mg} = 600 \text{ mg}\).

Step 2: Convert Milligrams to Grams

Convert the total mass from milligrams to grams for easier calculations in the following steps. Remember, there are 1000 milligrams in a gram. So, \(600 \text{ mg} = 0.600 \text{ g}\).

Step 3: Calculate Moles of Bismuth Subsalicylate

To find the amount in moles, use the molar mass of bismuth subsalicylate \(\mathrm{C}_{21} \mathrm{H}_{15} \mathrm{Bi}_{3} \mathrm{O}_{12}\). Calculate or look up the molar mass, which is approximately 1048.57 g/mol. Use the formula: \ \[\text{moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{0.600 \text{ g}}{1048.57 \text{ g/mol}} \approx 0.000572 \text{ mol}\].

Step 4: Calculate Mass of Bismuth in the Tablets

Now, calculate the mass of bismuth (Bi) consumed. First, we determine the molar mass of Bi in the compound. The molar mass of Bi is 208.98 g/mol, and there are 3 Bi atoms in each molecule of \(\mathrm{C}_{21} \mathrm{H}_{15} \mathrm{Bi}_{3} \mathrm{O}_{12}\), so Bi contributes \(3 \times 208.98 \text{ g/mol} = 626.94 \text{ g/mol}\) to the molar mass of the compound.

Step 5: Calculate Total Mass of Bismuth

Determine the total mass of bismuth in the tablets by using the moles calculated previously: \\[\text{mass of Bi} = \text{moles of Bi compound} \times \text{Bi molar contribution} = 0.000572 \text{ mol} \times 626.94 \text{ g/mol} \approx 0.359 \text{ g}\].

Key Concepts

Bismuth Subsalicylate

Bismuth subsalicylate is a compound that plays a crucial role in providing relief from an upset stomach. It is commonly found in medications like Pepto-Bismol. This compound has the chemical formula \(C_{21} H_{15} Bi_{3} O_{12} \), reflecting that it consists of carbon (C), hydrogen (H), bismuth (Bi), and oxygen (O). It is the bismuth component in this compound that is believed to have therapeutic effects on the stomach. When dealing with chemical calculations that involve this compound, it is vital to understand its molecular structure and the significance of each element involved.
Bismuth, being a heavy element, predominantly influences the molar mass of bismuth subsalicylate. Understanding these atomic parts allows for accurate calculations of how much of the active ingredient is being ingested when taking medications like Pepto-Bismol.

Molar Mass

Molar mass is a fundamental concept in chemistry that refers to the mass of one mole of a substance. It is expressed in grams per mole (g/mol). To find the molar mass of bismuth subsalicylate \( (C_{21} H_{15} Bi_{3} O_{12}) \), you sum up the atomic masses of all the atoms within the molecule:

• Carbon (C): 21 atoms \(\times \) 12.01 g/mol = 252.21 g/mol
• Hydrogen (H): 15 atoms \(\times \) 1.01 g/mol = 15.15 g/mol
• Bismuth (Bi): 3 atoms \(\times \) 208.98 g/mol = 626.94 g/mol
• Oxygen (O): 12 atoms \(\times \) 16.00 g/mol = 192.00 g/mol

Adding these values gives a total molar mass of roughly 1048.57 g/mol. This number is vital when calculating how many moles of a substance are present in a given mass. It serves as a conversion factor between the mass of a substance and the number of moles.

Stoichiometry

Stoichiometry involves the quantitative relationship between reactants and products in a chemical reaction. However, beyond reactions, it is used to determine the amounts of substances involved in compounds. When you know the mass of bismuth subsalicylate in a tablet (like 600 mg from two tablets), stoichiometry allows you to calculate the amount in moles using the formula:
\[\text{Moles} = \frac{\text{Mass in grams}}{\text{Molar Mass (g/mol)}}\]
In the exercise, by converting 600 mg to 0.600 g and using the molar mass of 1048.57 g/mol, we determine there are approximately 0.000572 moles of bismuth subsalicylate. This approach helps predict and quantify how much of each component in a compound contributes to the overall chemical process, ensuring precise and accurate scientific tasks.

Conversion from Milligrams to Grams

Understanding the conversion from milligrams to grams is crucial for accurate chemical calculations. Often in chemistry, measurements start in milligrams due to the small quantities of chemicals being used. Knowing how to convert milligrams to grams ensures readings are compatible with other data like molar mass. The conversion is simple:

• 1 gram = 1000 milligrams
• To convert milligrams to grams, divide the milligram value by 1000.

For example, the 600 mg of bismuth subsalicylate in the problem can be converted to grams by dividing 600 by 1000, equating to 0.600 g. Performing this conversion within calculations allows for the seamless transition into other units of measurement, which is particularly useful when dealing with bulk molecular masses in chemistry.