Question

Some bismuth tablets, a medication used to treat upset stomachs, contain \(262 \mathrm{mg}\) of bismuth subsalicylate, \(\mathrm{C}_{7} \mathrm{H}_{3} \mathrm{BiO}_{4}\), per tablet. Assuming two tablets are digested, calculate the mass of bismuth consumed.

Short answer

The mass of bismuth consumed from digesting two tablets is 0.303 grams.

Step-by-step solution

Find the mass of bismuth subsalicylate in two tablets

Each tablet contains 262 mg of bismuth subsalicylate. If two tablets are digested, the total amount consumed is: (2 tablets) x (262 mg/tablet) = 524 mg

Calculate the molar mass of bismuth subsalicylate

Using the periodic table, find the molar mass of each element in the compound and then add them all up: Bismuth (Bi): 208.98 g/mol Carbon (C): 12.01 g/mol Hydrogen (H): 1.01 g/mol Oxygen (O): 16.00 g/mol Molar mass of Bismuth subsalicylate (C7H3BiO4): (7 * 12.01) + (3 * 1.01) + (1 * 208.98) + (4 * 16.00) = 362.07 g/mol

Convert the mass of bismuth subsalicylate to moles

Now, we want to find the number of moles of bismuth subsalicylate contained in the mass consumed. To do that, divide the mass of bismuth subsalicylate consumed by the molar mass: moles of bismuth subsalicylate = (524 mg * 1 g/1000 mg) / 362.07 g/mol = 0.00145 mol

Determine the mole ratio of bismuth to bismuth subsalicylate

The formula for bismuth subsalicylate is C7H3BiO4, which contains 1 mole of bismuth (Bi) for every 1 mole of bismuth subsalicylate (C7H3BiO4). Therefore, the mole ratio is 1:1.

Calculate the moles of bismuth consumed

Using the mole ratio found in Step 4, we can calculate the moles of bismuth consumed: moles of bismuth = moles of bismuth subsalicylate * (1 mol Bi / 1 mol C7H3BiO4) = 0.00145 mol * 1 = 0.00145 mol

Convert the moles of bismuth to mass

Finally, we can find the mass of bismuth consumed by multiplying the moles of bismuth by its molar mass (208.98 g/mol): mass of bismuth = moles of bismuth * molar mass of bismuth = 0.00145 mol * 208.98 g/mol = 0.303 g Thus, the mass of bismuth consumed from digesting two tablets is 0.303 grams.

Key concepts

Molar Mass Calculation

Understanding how to calculate molar mass is an essential skill in chemistry, particularly when dealing with stoichiometry problems like in our example with bismuth tablets. Molar mass is defined as the mass of one mole of a particular substance and is expressed in grams per mole (g/mol).

To calculate the molar mass of a compound, you add up the masses of all the atoms present in a molecule of that compound. Each element's mass is found on the periodic table and is given in atomic mass units (amu). However, for molar mass calculations, we use the molar mass of each element which is approximately equal to the atomic mass but expressed in g/mol.

Steps to Calculate Molar Mass:

• Write down the chemical formula of the compound.
• Determine the number of atoms of each element in the compound.
• Find the atomic mass of each element on the periodic table.
• Multiply the atomic mass of each element by the number of atoms of that element in the compound.
• Add up the total mass for all the elements to get the molar mass of the compound.

For example, in the case of bismuth subsalicylate ((C7H3BiO4)), the molar mass is calculated by adding the mass contributions from each atom based on its atomic mass and the number of times it appears in the molecule. It's crucial to ensure accuracy in the calculation as it directly influences subsequent stoichiometry calculations.

Mole Concept

The mole concept is another fundamental principle in chemistry that facilitates the understanding of quantities at the atomic and molecular scale. A mole represents 6.022 x 10^23 particles, which can refer to atoms, ions, molecules, or electrons. This constant is known as Avogadro's number.

In the context of stoichiometry, the mole is a bridge between the small world of atoms and the tangible world of grams. It allows us to count particles by weighing them. When chemists say 'one mole of a substance,' they are referring to a quantity that includes Avogadro's number of particles, whatever those particles may be.

To convert from mass to moles, one divides the mass of the compound by its molar mass (the conversion factor). This step is crucial in stoichiometry as it helps in finding out how many particles are involved in a reaction, as shown in our exercise with bismuth subsalicylate.

Understanding the mole concept also means being comfortable with conversions between grams and moles. Real-world problems often provide mass in various units, and knowing how to manipulate these units can make or break your ability to correctly solve an exercise.

Chemical Formula

The chemical formula of a substance, such as bismuth subsalicylate's (C7H3BiO4), provides valuable information. It tells not only the types of atoms present but also their ratios. These ratios are crucial for calculating molar mass and for understanding the composition of molecules for reaction equations.

In stoichiometry, chemical formulas are used to determine the mole ratios of reactants and products in a chemical reaction. For instance, the formula of bismuth subsalicylate implies a 1:1 mole ratio between bismuth atoms and the compound as a whole. This is a direct consequence of the 'subscripts' in the formula (the small numbers following symbols in a formula) which indicate the number of atoms of each element in one molecule of the compound.

Chemical Formula and Stoichiometry:

• Subscripts in a formula indicate the proportion of atoms in the compound.
• The ratios derived from the chemical formula are used to determine the stoichiometry of the reaction.
• These ratios can also be interpreted as mole ratios, essential in reactions.

This interpretation of the chemical formula enables us to balance chemical equations, predict product formation, and understand the quantitative aspects of chemical reactions, serving as the backbone of many calculations in chemistry.