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Chapter 3: Problem 66

Prevacid is used to treat gastroesophageal reflux disease \((\mathrm{GERD})\) . The chemical formula of Prevacid is \(\mathrm{C}_{16} \mathrm{H}_{14} \mathrm{F}_{3} \mathrm{N}_{3} \mathrm{O}_{2} \mathrm{S}\) . a. What is the molar mass of Prevacid? b. What mass of fluorine is in 0.75 mol of Prevacid? c. What number of carbon atoms is in 0.75 mol of Prevacid? d. What is the mass of \(4.25 \times 10^{21}\) molecules of Prevacid?

Short Answer

Expert verified
a. The molar mass of Prevacid is approximately 369.372 g/mol. b. The mass of fluorine in 0.75 mol of Prevacid is 42.75 g. c. There are \(7.227 \times 10^{24}\) carbon atoms in 0.75 mol of Prevacid. d. The mass of \(4.25 \times 10^{21}\) molecules of Prevacid is approximately 1.054 g.

Step by step solution

01

Calculate the molar mass of Prevacid

To calculate the molar mass of Prevacid, we'll need to take the sum of the molar masses of all the atoms in the formula. Molar mass of Prevacid = (16 脳 molar mass of carbon) + (14 脳 molar mass of hydrogen) + (3 脳 molar mass of fluorine) + (3 脳 molar mass of nitrogen) + (2 脳 molar mass of oxygen) + molar mass of sulfur Here are the molar masses of each element: C = 12.01 g/mol, H = 1.008 g/mol, F = 19.00 g/mol, N = 14.01 g/mol, O = 16.00 g/mol, and S = 32.07 g/mol.
02

Calculate the total molar mass

Using the molar masses and the formula from Step 1, we can now find the molar mass of Prevacid. Molar mass of Prevacid = (16 脳 12.01) + (14 脳 1.008) + (3 脳 19.00) + (3 脳 14.01) + (2 脳 16.00) + 32.07 Molar mass of Prevacid = 192.16 + 14.112 + 57.00 + 42.03 + 32.00 + 32.07 = 369.372 g/mol (rounded to 3 decimal places) a. The molar mass of Prevacid is approximately 369.372 g/mol.
03

Calculate the mass of fluorine in 0.75 mol of Prevacid

Given that there are 3 fluorine atoms in one molecule of Prevacid and we have 0.75 mol of Prevacid, we can calculate the mass of fluorine: Mass of fluorine = Number of moles 脳 Molar mass of fluorine Mass of fluorine in 0.75 mol of Prevacid = 0.75 脳 3 脳 19.00 = 42.75 g b. The mass of fluorine in 0.75 mol of Prevacid is 42.75 g.
04

Calculate the number of carbon atoms in 0.75 mol of Prevacid

There are 16 carbon atoms in one molecule of Prevacid. We will use Avogadro's number (\(6.022 \times 10^{23}\)) to convert from moles to the number of carbon atoms: Number of carbon atoms = 0.75 mol 脳 16 carbon atoms/mol of Prevacid 脳 Avogadro's number Number of carbon atoms = 0.75 脳 16 脳 6.022 脳 10^{23} Number of carbon atoms = 7.227 脳 10^{24} c. There are \(7.227 \times 10^{24}\) carbon atoms in 0.75 mol of Prevacid.
05

Calculate the mass of \(4.25 \times 10^{21}\) molecules of Prevacid

Now we'll need to determine the mass of a specific number of molecules, in this case, \(4.25 \times 10^{21}\) molecules. To do this, we can use the molar mass of Prevacid and Avogadro's number to convert from molecules to mass: Mass of \(4.25 \times 10^{21}\) molecules = \(\dfrac{4.25 \times 10^{21}\mathrm{molecules}}{6.022\times10^{23} \mathrm{molecules/mol}}\) 脳 369.372 g/mol Mass of \(4.25 \times 10^{21}\) molecules = 2.854 脳 10^{-3} mol 脳 369.372 g/mol Mass of \(4.25 \times 10^{21}\) molecules = 1.054 g (rounded to 3 decimal places) d. The mass of \(4.25 \times 10^{21}\) molecules of Prevacid is approximately 1.054 g.

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Key Concepts

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

Chemistry Problem-Solving
Chemistry problem-solving is about breaking down complex problems into manageable steps. Let's take the example of finding the molar mass of Prevacid. First, identify all elements in the chemical formula and their quantities. Prevacid's chemical formula
contains several elements: carbon (C), hydrogen (H), fluorine (F), nitrogen (N), oxygen (O), and sulfur (S). Recognizing these can help us determine the molar mass by summing up the atomic masses of each element multiplied by its respective quantity in
the compound.
  • Step 1: List all elements and their atomic masses.
  • Step 2: Multiply the atomic mass of each element by the number of atoms as per
    the chemical formula.
  • Step 3: Sum these values to find the total molar mass.
Chemistry problem-solving often involves steps similar to these, providing a systematic approach to tackle such interesting challenges.
Avogadro's Number
Avogadro's number is a key concept in chemistry that represents the number of particles, such as atoms or molecules, in one mole of a substance. This number is a fundamental constant, approximately equal to \(6.022 \times 10^{23} \).
It's called Avogadro's number in honor of scientist Amedeo Avogadro, who contributed to molecular theory.
When solving problems, Avogadro's number is used for conversions between the amount (in moles) of a substance and the number of particles. For instance, to find the number of carbon atoms
in a certain amount of Prevacid, you would multiply the number of moles by Avogadro's number and the number of carbon atoms per molecule. This calculation is
essential for quantifying substances in chemical reactions and processes.
Chemical Formula Analysis
Chemical formula analysis involves understanding the composition of compounds and using their formulas to gather information about their molecular structure. For
Prevacid, the formula \( \mathrm{C}_{16} \mathrm{H}_{14} \mathrm{F}_{3} \mathrm{N}_{3} \mathrm{O}_{2} \mathrm{S} \) reveals much about its composition:
  • 16 carbon atoms
  • 14 hydrogen atoms
  • 3 fluorine atoms
  • 3 nitrogen atoms
  • 2 oxygen atoms
  • 1 sulfur atom
Through analysis, you can determine the molar mass by weighting each atom's contribution according to its atomic mass.
Understanding this helps solve various chemistry problems, like calculating how much of a specific element is present in a given amount of compound.
Stoichiometry
Stoichiometry is the branch of chemistry concerned with the quantitative relationships in chemical reactions. It involves using balanced chemical equations to
find the proportions of reactants and products. In solving problems like those with Prevacid, stoichiometry is crucial for determining how much of each component is present or needed.
For example, calculating how much fluorine is in 0.75 mole of Prevacid involves applying stoichiometric principles:
  • Identify the number of fluorine atoms per molecule.
  • Use the number of moles to find out the total fluorine mass.
Stoichiometry helps in predicting amounts and ensuring reactions go as predicted, making it essential for practical chemistry applications.

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