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The molecular formula of acetylsalicylic acid (aspirin), one of the most commonly used pain relievers, is \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\). a. Calculate the molar mass of aspirin. b. A typical aspirin tablet contains \(500 . \mathrm{mg} \mathrm{C}_{9} \mathrm{H}_{\mathrm{g}} \mathrm{O}_{4} .\) What amount (moles) of \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\) molecules and what number of molecules of acetylsalicylic acid are in a \(500 .-\mathrm{mg}\) tablet?

Short Answer

Expert verified
The molar mass of aspirin (acetylsalicylic acid) is approximately 180.154 g/mol. A 500-mg tablet contains approximately 0.00277 moles of aspirin, which is equivalent to \(1.67 \times 10^{21}\) molecules.

Step by step solution

01

Calculate the molar mass of aspirin.

To calculate the molar mass of aspirin, we sum up the molar masses of every atom in the molecule. Aspirin has the molecular formula \(C_9H_8O_4\). Thus, the molar mass can be calculated as follows: Molar mass = 9(Molar mass of C) + 8(Molar mass of H) + 4(Molar mass of O) Using the atomic masses from the periodic table: the molar mass of C = 12.01 g/mol, H = 1.008 g/mol, and O = 16.00 g/mol, we can plug these values into the equation: Molar mass = 9(12.01\(\ g/mol\)) + 8(1.008\(\ g/mol\)) + 4(16.00\(\ g/mol\)) Molar mass = 108.09\(\ g/mol\) + 8.064\(\ g/mol\) + 64.00\(\ g/mol\) Molar mass = 180.154\(\ g/mol\)
02

Convert mass of aspirin to moles.

Given that a typical aspirin tablet contains 500 mg of aspirin, we need to convert this mass into moles. To do this, we'll use the molar mass calculated in the previous step. First, convert 500 mg to grams: 500 mg = 0.5 g Then, we can use the molar mass to find the number of moles: Moles = mass (g) / molar mass (g/mol) Moles = \( \tfrac{0.5\ g}{180.154\ g/mol} \) Moles ≈ 0.00277 moles
03

Calculate the number of molecules of aspirin.

To find the number of molecules of aspirin, we'll use Avogadro's number, which is approximately \(6.022 \times 10^{23}\) particles/mol. Number of molecules = Moles × Avogadro's number Number of molecules = 0.00277 moles × \(6.022 \times 10^{23}\) molecules/mol Number of molecules ≈ \(1.67 \times 10^{21}\) molecules So, a 500-mg tablet contains approximately \(1.67 \times 10^{21}\) molecules of acetylsalicylic acid.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Acetylsalicylic Acid
Acetylsalicylic acid, also known as aspirin, is one of the most well-known medications used to relieve pain, reduce fever, and ease inflammation. Its popularity stems from both its effectiveness and its relatively simple chemical composition. Structurally, this compound belongs to the group of salicylates, and it was historically important for paving the way for modern medicinal chemistry. Its chemical name gives a hint to its origin and function, indicating an acetyl group bonded to a salicylic acid core. Understanding the molecular composition of acetylsalicylic acid not only aids in its practical applications but also provides insight into basic chemical principles such as bonding and molecular geometry. Recognizing
  • its structure (\( \mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4} \)),
  • its function within the body
is the first step toward understanding the chemistry behind many pharmaceuticals.
Chemical Formula
The chemical formula of a compound is a concise way of expressing information about the atoms that constitute a particular chemical compound. In the case of acetylsalicylic acid, the chemical formula is expressed as \( \mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4} \). This formula indicates that each molecule contains:
  • 9 carbon (C) atoms,
  • 8 hydrogen (H) atoms, and
  • 4 oxygen (O) atoms.
Chemical formulas not only help to visualize the composition of compounds but also serve as a fundamental tool for mole calculations and stoichiometry in chemical equations.
When chemists examine chemical reactions involving acetylsalicylic acid, the formula becomes essential for balancing chemical equations and determining reactants' and products' proportion.
Mole Calculations
Mole calculations are an essential part of chemistry, acting as a bridge between the microscopic world of atoms and molecules and the macroscopic world we observe. A mole defines a quantity, particularly \(6.022 \times 10^{23} \) entities, of molecular or atomic scale particles, such as atoms, molecules, ions, etc. Acetylsalicylic acid's molar mass, calculated from its chemical formula, \( \mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4} \), is approximately 180.154 g/mol.
To convert grams of acetylsalicylic acid to moles, divide the mass in grams by this molar mass. For instance, when we have 0.5 grams of aspirin, dividing by the molar mass gives \(0.00277\) moles.
  • Using moles makes it easier to perform calculations related to chemical reactions when considering mass or volume.
Understanding the concept of a mole allows us to perform calculations related to chemical reactions on a more practical, human scale, guiding us through processes like titrations or determining concentrations.
Avogadro's Number
Avogadro's Number is a fundamental constant that is central to the field of chemistry. Defined as approximately \(6.022 \times 10^{23} \) particles per mole, it offers a practical way to convert between the number of moles and the exact number of atoms, molecules, or other entities in a sample. This constant was named after the Italian scientist Amedeo Avogadro, whose work led to insights into the volume-amount relationships in gases.
To find the number of acetylsalicylic acid molecules in a given sample, such as a tablet containing 0.00277 moles of the compound, multiply the number of moles by Avogadro's Number: Number of molecules = Moles × \(6.022 \times 10^{23} \).
This calculation results in approximately \(1.67 \times 10^{21} \) molecules.
  • By providing a direct connection between the microscopic and macroscopic world, Avogadro's Number enhances our understanding of how reactions happen at a molecular level.
Using this number is crucial for professionals and students working on projects that measure or predict chemical quantities in real-world settings.

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Most popular questions from this chapter

A binary compound between an unknown element \(\mathrm{E}\) and hydrogen contains \(91.27 \% \mathrm{E}\) and \(8.73 \% \mathrm{H}\) by mass. If the formula of the compound is \(\mathrm{E}_{3} \mathrm{H}_{8}\), calculate the atomic mass of \(\mathrm{E}\).

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Which of the following statements about chemical equations is(are) true? a. When balancing a chemical equation, you can never change the coefficient in front of any chemical formula. b. The coefficients in a balanced chemical equation refer to the number of grams of reactants and products. c. In a chemical equation, the reactants are on the right and the products are on the left. d. When balancing a chemical equation, you can never change the subscripts of any chemical formula. e. In chemical reactions, matter is neither created nor destroyed so a chemical equation must have the same number of atoms on both sides of the equation.

Reference Section \(3.2\) to find the atomic masses of \({ }^{12} \mathrm{C}\) and \({ }^{13} \mathrm{C}\), the relative abundance of \({ }^{12} \mathrm{C}\) and \({ }^{13} \mathrm{C}\) in natural carbon, and the average mass (in u) of a carbon atom. If you had a sample of natural carbon containing exactly 10,000 atoms, determine the number of \({ }^{12} \mathrm{C}\) and \({ }^{1.3} \mathrm{C}\) atoms present. What would be the average mass (in u) and the total mass (in u) of the carbon atoms in this 10,000 -atom sample? If you had a sample of natural carbon containing \(6.0221 \times 10^{23}\) atoms, determine the number of \({ }^{12} \mathrm{C}\) and \({ }^{13} \mathrm{C}\) atoms present. What would be the average mass (in u) and the total mass (in u) of this \(6.0221 \times 10^{23}\) atom sample? Given that \(1 \mathrm{~g}=6.0221 \times 10^{23} \mathrm{u}\), what is the total mass of 1 mole of natural carbon in units of grams?

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