Problem 84 - Chemistry The Molecular Science

Question

Acetaminophen, an analgesic, has the molecular formula \(\mathrm{C}_{8} \mathrm{H}_{9} \mathrm{O}_{2} \mathrm{~N}\) (a) Calculate the molar mass of acetaminophen. (b) Calculate the amount of acetaminophen in \(5.32 \mathrm{~g}\) acetaminophen. (c) Calculate the mass of acetaminophen in \(0.166 \mathrm{~mol}\) acetaminophen.

Step-by-Step Solution

Answer

(a) 151.17 g/mol; (b) 0.0352 mol; (c) 25.09 g.

Step 1: Determine Atomic Masses

Identify the atomic masses of the elements in acetaminophen: Carbon (C) is 12.01 g/mol, Hydrogen (H) is 1.01 g/mol, Oxygen (O) is 16.00 g/mol, and Nitrogen (N) is 14.01 g/mol.

Step 2: Calculate Molar Mass

Add the atomic masses of the elements in the molecular formula \[ \text{C}_8\text{H}_9\text{O}_2\text{N} \] to find the molar mass:\[ 8(12.01) + 9(1.01) + 2(16.00) + 14.01 = 151.17 \, \text{g/mol}\] Thus, the molar mass of acetaminophen is 151.17 g/mol.

Step 3: Calculate Amount in Moles

To find the amount in moles for a given mass, use the formula: \[\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}\]For 5.32 g of acetaminophen:\[\text{moles} = \frac{5.32}{151.17} = 0.0352 \, \text{mol}\]So, 5.32 g of acetaminophen is approximately 0.0352 mol.

Step 4: Calculate Mass from Moles

To find the mass from a given number of moles, use the formula:\[\text{mass (g)} = \text{moles} \times \text{molar mass (g/mol)}\]For 0.166 mol of acetaminophen:\[\text{mass} = 0.166 \times 151.17 = 25.09 \, \text{g}\]So, 0.166 mol of acetaminophen corresponds to 25.09 g.

Key Concepts

Acetaminophen

Acetaminophen, commonly known for its use as a pain reliever and fever reducer, is a familiar household medication. Its molecular formula is \( \text{C}_8\text{H}_9\text{O}_2\text{N} \). This formula indicates that each molecule of acetaminophen consists of 8 carbon atoms, 9 hydrogen atoms, 2 oxygen atoms, and 1 nitrogen atom. Understanding the composition of acetaminophen helps us in determining its molar mass, which is essential for various calculations in chemistry.

By recognizing the arrangement and number of each type of atom, scientists can study how acetaminophen interacts at molecular levels. This knowledge doesn't only assist in creating effective medicines but also ensures safety and efficacy in their usage.

Atomic Mass

Atomic mass is a fundamental concept in chemistry that refers to the mass of an atom, typically measured in grams per mole (g/mol). Each element has its own defined atomic mass. For instance:

• Carbon (C) has an atomic mass of 12.01 g/mol
• Hydrogen (H) is 1.01 g/mol
• Oxygen (O) is 16.00 g/mol
• Nitrogen (N) is 14.01 g/mol

These values are crucial when you need to calculate the molar mass of a compound, like acetaminophen, because they represent the weight of a single atom of each element as referenced to carbon-12, according to the periodic table.

To calculate the molar mass, you sum the products of the atomic masses by the number of corresponding atoms in the compound's molecular formula. This gives you a means to convert between the mass of a substance and the amount of substance, expressed in moles.

Moles and Mass Relationship

In chemistry, it's vital to comprehend the relationship between moles and mass to solve problems effectively. Moles represent an amount of substance, and the molar mass provides the conversion factor between the mass of a substance and the number of moles.

The formula for calculating moles from mass is:

\[\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}\]

Conversely, to find the mass from a given number of moles, you use the equation:

\[\text{mass (g)} = \text{moles} \times \text{molar mass (g/mol)}\]

This reciprocal relationship allows chemists to determine how much of any given substance is present, which is indispensable when dealing with reactions and understanding their stoichiometry. For instance, knowing that 5.32 g of acetaminophen equates to approximately 0.0352 moles can help determine ratios for reactants and products in a chemical reaction.