Question

Which weighs more, \(5.00 \mathrm{~g}\) or \(0.0225 \mathrm{~mol}\) of acetaminophen \(\left(\mathrm{C}_{8} \mathrm{H}_{9} \mathrm{NO}_{2}\right) ?\)

Short answer

5.00 g of acetaminophen weighs more than 0.0225 mol.

Step-by-step solution

Calculate the Molar Mass of Acetaminophen

To find the molar mass of acetaminophen ( C_{8} H_{9} NO_{2}), we add the molar masses of all atoms in the molecule. The atomic masses are approximately 12.01 g/mol for Carbon (C), 1.008 g/mol for Hydrogen (H), 14.01 g/mol for Nitrogen (N), and 16.00 g/mol for Oxygen (O). The calculation is as follows: \ - Carbon: 8 atoms \( \times 12.01 = 96.08 \) g/mol - Hydrogen: 9 atoms \( \times 1.008 = 9.072 \) g/mol - Nitrogen: 1 atom \( \times 14.01 = 14.01 \) g/mol - Oxygen: 2 atoms \( \times 16.00 = 32.00 \) g/mol Thus, the molar mass of acetaminophen is the sum: \( 96.08 + 9.072 + 14.01 + 32.00 = 151.162 \) g/mol.

Calculate the Mass of 0.0225 mol of Acetaminophen

To find the mass of 0.0225 mol of acetaminophen, we use the molar mass calculated in Step 1. \ We use the formula: \ \[ \text{Mass (g)} = \text{Number of moles} \times \text{Molar mass (g/mol)} \] Substituting the given values, we have: - Number of moles = 0.0225 mol - Molar mass = 151.162 g/mol Hence, the mass is: \ \( 0.0225 \times 151.162 = 3.401145 \) g.

Compare the Masses

Now, we compare the given mass of acetaminophen (5.00 g) with the mass of 0.0225 mol we calculated in Step 2, which is 3.401145 g. Since 5.00 g is greater than 3.401145 g, the 5.00 g of acetaminophen weighs more than 0.0225 mol of acetaminophen.

Key concepts

Molar Mass Calculation

When working with chemical substances, understanding the concept of molar mass is essential. The molar mass is the weight of one mole of a substance. It is expressed in grams per mole (g/mol). To calculate the molar mass of a compound, you need the atomic masses from the periodic table.

Here's a step-by-step guide on how to calculate the molar mass of acetaminophen (C₈H₉NO₂):

• Identify the number of each type of atom in a molecule of acetaminophen.
• Use the periodic table to find the atomic mass of each element:
• Carbon (C) has an atomic mass of approximately 12.01 g/mol.
• Hydrogen (H) has an atomic mass of approximately 1.008 g/mol.
• Nitrogen (N) has an atomic mass of approximately 14.01 g/mol.
• Oxygen (O) has an atomic mass of approximately 16.00 g/mol.
• Multiply the atomic mass by the number of each type of atom in the compound.
• Add the masses to get the molar mass:
• 8 Carbon atoms: 8 × 12.01 = 96.08 g/mol
• 9 Hydrogen atoms: 9 × 1.008 = 9.072 g/mol
• 1 Nitrogen atom: 1 × 14.01 = 14.01 g/mol
• 2 Oxygen atoms: 2 × 16.00 = 32.00 g/mol

Adding these values gives a total molar mass of 151.162 g/mol for acetaminophen. This molar mass is used in further conversions and comparisons in chemistry.

Moles to Grams Conversion

Converting moles into grams is a fundamental technique used in chemistry calculations. Understanding this conversion allows you to measure and compare substances accurately in experiments and reactions.

This process involves using the molar mass of the substance as a conversion factor. Here's how you can convert moles of acetaminophen into grams:

• Use the formula: \[ \text{Mass (g)} = \text{Number of moles} \times \text{Molar mass (g/mol)} \]
• For acetaminophen, the number of moles is given as 0.0225 mol.
• You earlier calculated the molar mass to be 151.162 g/mol.
• Plug these numbers into the formula:
• Mass = 0.0225 mol × 151.162 g/mol = 3.401145 g

This calculation converts 0.0225 moles of acetaminophen into its corresponding mass in grams. This method is essential for determining how much of a substance is needed or the mass of a substance present in a chemical sample.

Comparative Analysis in Chemistry

In chemistry, comparing physical quantities such as mass is crucial to understand substance behavior and proportion in reactions. Here is how you can perform a comparative analysis between two different quantities of the same substance:

1. **Identify the Quantities:**
- In this context, we compare two quantities: a given mass of a substance (5.00 g) and a calculated mass from a known amount of moles (3.401145 g).

2. **Quantitative Comparison:**
- Use the calculated values to analyze the differences.
- The mass from the moles in our calculation (3.401145 g) is less than the given mass (5.00 g).

3. **Conclusion:**
- In this exercise, through comparative analysis, it is determined that 5.00 g of acetaminophen is indeed heavier than 0.0225 moles of the same substance.
- Such comparisons help in determining the more substantial amount or predicting the yield in reactions if quantities reach precise thresholds.

Understanding these analyses assists in making informed decisions regarding substance amounts in lab settings or theoretical scenarios.