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Naproxen, found in Aleve, is used to treat the pain and inflammation caused by arthritis. Naproxen has a formula of \(\mathrm{C}_{14} \mathrm{H}_{14} \mathrm{O}_{3}\). a. How many moles of \(\mathrm{C}\) are present in 2.30 moles of naproxen? b. How many moles of \(\mathrm{H}\) are present in 0.444 mole of naproxen? c. How many moles of \(\mathrm{O}\) are present in \(0.0765 \mathrm{~mole}\) of naproxen?

Short Answer

Expert verified
a) 32.2 moles of C. b) 6.216 moles of H. c) 0.2295 moles of O.

Step by step solution

01

Understand the molecular formula

The molecular formula of Naproxen is \( \mathrm{C}_{14} \mathrm{H}_{14} \mathrm{O}_{3} \). This means that each molecule of Naproxen contains 14 carbon (C) atoms, 14 hydrogen (H) atoms, and 3 oxygen (O) atoms.
02

Calculating moles of \(\mathrm{C}\) in Naproxen for Question (a)

Given that there are 14 carbon atoms in one molecule of Naproxen, use the formula: \(\text{Moles of C} = \text{Moles of Naproxen} \times \text{Number of C atoms per molecule}\). Thus, \(2.30 \text{ moles of Naproxen} \times 14 = 32.2 \text{ moles of C}\)
03

Calculating moles of \(\mathrm{H}\) in Naproxen for Question (b)

Given that there are 14 hydrogen atoms in one molecule of Naproxen, use the formula: \(\text{Moles of H} = \text{Moles of Naproxen} \times \text{Number of H atoms per molecule}\). Therefore, \(0.444 \text{ moles of Naproxen} \times 14 = 6.216 \text{ moles of H}\)
04

Calculating moles of \(\mathrm{O}\) in Naproxen for Question (c)

Given that there are 3 oxygen atoms in one molecule of Naproxen, use the formula: \(\text{Moles of O} = \text{Moles of Naproxen} \times \text{Number of O atoms per molecule}\). Thus, \(0.0765 \text{ moles of Naproxen} \times 3 = 0.2295 \text{ moles of O}\)

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Key Concepts

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

Understanding Molecular Formulas
The molecular formula represents the number and types of atoms in a molecule. For instance, the molecular formula for Naproxen is \(\text{C}_{14}\text{H}_{14}\text{O}_{3}\). This means one molecule of Naproxen consists of:
  • 14 Carbon (C) atoms
  • 14 Hydrogen (H) atoms
  • 3 Oxygen (O) atoms

Understanding the molecular formula is crucial because it helps identify how many moles of each atom are present in a given amount of substance. This forms the basis for calculating moles of individual elements in a compound.
Calculating Moles of Atoms
To calculate moles of atoms within a compound, you need the molecular formula and the number of moles of the compound. For example:
  • Given \(\text{C}_{14}\text{H}_{14}\text{O}_{3}\), each molecule contains 14 Carbon atoms, 14 Hydrogen atoms, and 3 Oxygen atoms.
  • The formula to calculate moles of a specific atom is:
    \(\text{Moles of element} = \text{Moles of compound} \times \text{Number of that element in one molecule}\)
  • For question (a), to find moles of \(\text{C}\) in 2.30 moles of Naproxen:
    \(\text{Moles of C} = 2.30 \times 14 = 32.2 \text{ moles of C}\)
  • For question (b), to find moles of \(\text{H}\) in 0.444 moles of Naproxen:
    \(\text{Moles of H} = 0.444 \times 14 = 6.216 \text{ moles of H}\)
  • For question (c), to find moles of \(\text{O}\) in 0.0765 moles of Naproxen:
    \(\text{Moles of O} = 0.0765 \times 3 = 0.2295 \text{ moles of O}\)
This approach allows us to determine the exact amount of each atom in a specific quantity of a compound.
Stoichiometry in Chemistry
Stoichiometry involves calculations of the quantities of reactants and products in chemical reactions. It relies on the conservation of mass and energy, ensuring the total mass and number of atoms remain constant during the reaction. Here's why stoichiometry is essential:
  • It allows the calculation of how much of each reactant is needed to form a product.
  • It can predict the amount of product formed in a reaction.
  • Accurate stoichiometric calculations ensure that reactions are efficient and reduce waste.

When using stoichiometry, understanding the molecular formula and moles of atoms aids in precise measurements. For example, knowing that Naproxen has \(\text{C}_{14}\text{H}_{14}\text{O}_{3}\) helps in determining the proportional amounts of reactants needed in a reaction producing Naproxen. Accurate stoichiometric calculations pave the way for successful chemical synthesis and industrial applications. By mastering these calculations, you can effectively balance chemical equations and optimize reactions.

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Most popular questions from this chapter

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