Question

Acne Benzoyl peroxide \(\left(\mathrm{C}_{14} \mathrm{H}_{10} \mathrm{O}_{4}\right)\) is a substance used as an acne medicine. What is the mass in grams of \(3.50 \times 10^{-2} \mathrm{mol} \mathrm{C}_{14} \mathrm{H}_{10} \mathrm{O}_{4}\) ?

Short answer

The mass of \(3.50 \times 10^{-2} \mathrm{mol}\) of Acne Benzoyl Peroxide (C_{14}H_{10}O_{4}) is 8.48 grams.

Step-by-step solution

Calculate the molar mass of Acne Benzoyl Peroxide (C14H10O4)

First, we need to find the molar masses of the individual elements in the molecular formula C14H10O4. Using the periodic table, the molar mass of Carbon (C) is 12.01 g/mol, the molar mass of Hydrogen (H) is 1.01 g/mol, and the molar mass of Oxygen (O) is 16.00 g/mol. Now, we can calculate the molar mass of C14H10O4 by multiplying the molar masses of each element by their quantity, and then adding them together: Molar mass = (14 x 12.01 g/mol) + (10 x 1.01 g/mol) + (4 x 16.00 g/mol)

Calculate the molar mass of C14H10O4

Next, we need to substitute the values and calculate the molar mass of the compound: Molar mass = (14 x 12.01 g/mol) + (10 x 1.01 g/mol) + (4 x 16.00 g/mol) Molar mass = 168.14 g/mol + 10.10 g/mol + 64.00 g/mol Molar mass = 242.24 g/mol

Calculate the mass of 3.50 x 10^{-2} mol C14H10O4

Now that we have the molar mass of the compound, we can determine the mass of 3.50 x 10^{-2} moles of C14H10O4 by multiplying the given moles with the molar mass: Mass = (3.50 x 10^{-2} mol)(242.24 g/mol)

Calculate the final mass

Finally, we can calculate the mass of the given moles of C14H10O4: Mass = (3.50 x 10^{-2} mol)(242.24 g/mol) Mass = 8.48 g Hence, the mass of 3.50 x 10^{-2} moles of Acne Benzoyl Peroxide (C14H10O4) is 8.48 grams.

Key concepts

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in chemical reactions. It is akin to a recipe where you need precise amounts of each ingredient to make the perfect dish. Understand stoichiometry, and you unlock the ability to predict product formation and reactant consumption in reactions.

Imagine you are baking cookies and the recipe calls for 2 eggs per dozen cookies. What if you want to make 24 cookies? Stoichiometry would tell you that you need 4 eggs. Similarly, in chemistry, if you know the balanced chemical equation, you can determine how much of each reactant you need to produce a desired amount of product.

Key tools used in stoichiometry include the mole concept, molar mass, and Avogadro's number to relate masses, particles, and volumes. It helps students move from the molecular scale to the real-world scale with ease.

Molecular Formula

The molecular formula represents the actual number of atoms of each element in a molecule. Think of it as the detailed identity card of a compound. For example, the molecular formula for water is \(H_2O\), telling you there are 2 hydrogen atoms and 1 oxygen atom in each molecule of water.

To really understand a molecular formula, you also need to grasp isotopes and atomic weights. Isotopes are different forms of the same element with varying numbers of neutrons. Atomic weights are averages of these isotopes' weights based on their natural abundance. These details factor into the calculation of a substance's molar mass - a critical step in stoichiometry.

The molecular formula plays a fundamental role in stoichiometry as it allows chemists to write balanced equations, calculate molar masses, and eventually find out how much of each substance is involved in a chemical reaction.

Mole Concept

The mole concept is a central idea in chemistry that provides a bridge between the atomic world and our everyday measurements. A mole is not a furry critter in this context but a unit that signifies a specific number of particles—6.022 x \(10^{23}\) to be precise, known as Avogadro's number.

Why is this important? Well, atoms and molecules are incredibly small, and working with their individual numbers would be impractical. By using moles, chemists can ‘count’ particles in bulk, making the numbers handy and significant. One mole of any substance will have the same number of entities as one mole of any other substance.

Moles link the microscopic scale to the macroscopic world. When we say that we have 1 mole of carbon atoms, for instance, we mean that we have 6.022 x \(10^{23}\) carbon atoms, which also equals 12 grams of carbon—the molar mass of carbon. Understanding the mole concept is crucial for performing calculations in chemistry and is a foundational aspect of stoichiometry.