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Chapter 7: Problem 66

Write the empirical formula for each of the following: ( \(7.4)\) a. \(\mathrm{C}_{12} \mathrm{H}_{24} \mathrm{~N}_{2} \mathrm{O}_{4}\), carisoprodol, a skeletal muscle relaxant b. \(\mathrm{C}_{10} \mathrm{H}_{10} \mathrm{O}_{5}\), opianic acid, used to synthesize a drug to treat tuberculosis c. \(\mathrm{CrCl}_{3}\), chromium(III) chloride, used in chrome plating d. \(\mathrm{C}_{16} \mathrm{H}_{16} \mathrm{~N}_{2} \mathrm{O}_{2}\), lysergic acid, a controlled substance from ergot

Short Answer

Expert verified
a) \text{C}_6 \text{H}_{12} \text{N} \text{O}_2, b) \text{C}_2 \text{H}_2 \text{O}, c) \text{CrCl}_3, d) \text{C}_8 \text{H}_8 \text{N} \text{O}

Step by step solution

01

- Identify the subscripts in the molecular formula (Part a)

Look at the given molecular formula for carisoprodol: \( \text{C}_{12} \text{H}_{24} \text{N}_{2} \text{O}_{4} \). Identify the subscripts: C=12, H=24, N=2, O=4.
02

- Find the Greatest Common Divisor (GCD) (Part a)

Find the GCD of the subscripts 12, 24, 2, and 4. The GCD is 2.
03

- Divide each subscript by the GCD (Part a)

Divide each subscript by 2: \( \frac{12}{2} = 6 \), \( \frac{24}{2} = 12 \), \( \frac{2}{2} = 1 \), \( \frac{4}{2} = 2 \). Thus, the empirical formula is \( \text{C}_6 \text{H}_{12} \text{N}_1 \text{O}_2 \) or \( \text{C}_6 \text{H}_{12} \text{N} \text{O}_2 \).
04

- Identify the subscripts in the molecular formula (Part b)

Look at the given molecular formula for opianic acid: \( \text{C}_{10} \text{H}_{10} \text{O}_{5} \). Identify the subscripts: C=10, H=10, O=5.
05

- Find the GCD (Part b)

Find the GCD of the subscripts 10, 10, and 5. The GCD is 5.
06

- Divide each subscript by the GCD (Part b)

Divide each subscript by 5: \( \frac{10}{5} = 2 \), \( \frac{10}{5} = 2 \), \( \frac{5}{5} = 1 \). Thus, the empirical formula is \( \text{C}_2 \text{H}_2 \text{O}_1 \) or \( \text{C}_2 \text{H}_2 \text{O} \).
07

- Identify the subscripts in the molecular formula (Part c)

Look at the given molecular formula for chromium(III) chloride: \( \text{CrCl}_3 \). Identify the subscripts: Cr=1, Cl=3.
08

- Find the GCD (Part c)

Find the GCD of the subscripts 1 and 3. The GCD is 1.
09

- Divide each subscript by the GCD (Part c)

Divide each subscript by 1: \( \frac{1}{1} = 1 \), \( \frac{3}{1} = 3 \). Thus, the empirical formula is \( \text{CrCl}_3 \).
10

- Identify the subscripts in the molecular formula (Part d)

Look at the given molecular formula for lysergic acid: \( \text{C}_{16} \text{H}_{16} \text{N}_2 \text{O}_2 \). Identify the subscripts: C=16, H=16, N=2, O=2.
11

- Find the GCD (Part d)

Find the GCD of the subscripts 16, 16, 2, and 2. The GCD is 2.
12

- Divide each subscript by the GCD (Part d)

Divide each subscript by 2: \( \frac{16}{2} = 8 \), \( \frac{16}{2} = 8 \), \( \frac{2}{2} = 1 \), \( \frac{2}{2} = 1 \). Thus, the empirical formula is \( \text{C}_8 \text{H}_8 \text{N}_1 \text{O}_1 \) or \( \text{C}_8 \text{H}_8 \text{N} \text{O} \).

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Key Concepts

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

chemical formula
A chemical formula is a way to represent a substance using symbols for its constituent elements. It provides information about the types and quantities of atoms in a molecule. For instance, the chemical formula of water is \(\text{H}_2\text{O}\), indicating two hydrogen atoms and one oxygen atom for each molecule of water.
There are different types of chemical formulas:
  • Empirical formulas: Show the simplest whole-number ratio of elements in a compound. For example, the empirical formula of hydrogen peroxide (\(\text{H}_2\text{O}_2\)) is \(\text{HO}\).
  • Molecular formulas: Provide the actual number of each type of atom in a molecule. Hydrogen peroxide, for instance, has a molecular formula of \(\text{H}_2\text{O}_2\).
  • Structural formulas: Show how atoms in a molecule are bonded together, giving a clearer picture of a molecule鈥檚 structure.
The chemical formula is fundamental in chemistry for accurately conveying what a chemical substance consists of.
greatest common divisor
The greatest common divisor (GCD) is the largest number that can divide two or more integers without leaving a remainder. It is essential in chemistry, particularly when simplifying the ratios of elements in chemical formulas to find empirical formulas.
  • To find the GCD of two numbers, use methods like the Euclidean algorithm or prime factorization.
  • For example, to simplify the formula \(\text{C}_{12}\text{H}_{24}\text{N}_2\text{O}_4\) for carisoprodol, the subscripts are 12, 24, 2, and 4.
  • The GCD of 12, 24, 2, and 4 is 2. Dividing each subscript by 2, we get the empirical formula: \(\text{C}_6\text{H}_{12}\text{N}\text{O}_2\).
The process of finding the GCD can simplify chemical formulas and make calculations more manageable.
molecular formula
A molecular formula reveals the exact number of each type of atom present in a molecule. Unlike the empirical formula, which shows the simplest ratio, the molecular formula represents the actual quantity and can be the same as or a multiple of the empirical formula.
Understanding molecular formulas helps in:
  • Determining the molar mass by summing the atomic masses of all atoms in the formula.
  • Identifying isomers, which are compounds with the same molecular formula but different structures.
For example, glucose has the molecular formula \(\text{C}_6\text{H}_{12}\text{O}_6\), but its empirical formula is \(\text{CH}_2\text{O}\) as it reflects the simplest ratio of elements.
The molecular formula provides a detailed picture of a compound's composition, vital for chemical synthesis and reactions.
chemical compounds
Chemical compounds are substances formed by the chemical combination of two or more different elements. They are characterized by a fixed ratio of elements and can be broken down into simpler substances by chemical reactions.
Characteristics and types of chemical compounds include:
  • Ionic compounds: Formed by the electrostatic attraction between cations and anions. Example: \(\text{NaCl}\) (table salt).
  • Covalent compounds: Formed by sharing electrons between atoms. Example: \(\text{H}_2\text{O}\) (water).
  • Metallic compounds: Formed by a sea of shared electrons among metal atoms. Example: \(\text{Fe}\) (iron).
Compounds have unique properties distinct from the elements that compose them. For example, water is liquid at room temperature, unlike hydrogen and oxygen gases. Understanding chemical compounds enables us to manipulate and use materials for various applications, from medicine to manufacturing.

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Most popular questions from this chapter

The carbohydrate fructose found in honey and fruits has an empirical formula of \(\mathrm{CH}_{2} \mathrm{O}\). If the experimental molar mass of fructose is \(180 \mathrm{~g}\), what is its molecular formula?

Iron(III) chromate, a yellow powder used as a pigment in paints, contains \(24.3 \% \mathrm{Fe}, 33.9 \% \mathrm{Cr}\), and \(41.8 \% \mathrm{O}\). If it has an experimental molar mass of \(460 \mathrm{~g}\), what are its empirical and molecular formulas? \((7.4,7.5)\)

Calculate the mass percent of \(\mathrm{S}\) in each of the following: a. \(\mathrm{Na}_{2} \mathrm{SO}_{4}\), sodium sulfate b. \(\mathrm{Al}_{2} \mathrm{~S}_{3}\), aluminum sulfide c. \(\mathrm{SO}_{3}\), sulfur trioxide d. \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{SO}\), dimethylsulfoxide, topical anti-inflammatory e. \(\mathrm{C}_{10} \mathrm{H}_{10} \mathrm{~N}_{4} \mathrm{O}_{2} \mathrm{~S}\), sulfadiazine, antibacterial

Calculate the number of atoms of \(\mathrm{N}\) in each of the following: a. \(0.755 \mathrm{~mol}\) of \(\mathrm{N}_{2}\) b. \(0.82 \mathrm{~g}\) of \(\mathrm{NaNO}_{3}\) c. \(40.0 \mathrm{~g}\) of \(\mathrm{N}_{2} \mathrm{O}\) d. \(6.24 \times 10^{23}\) molecules of \(\mathrm{NH}_{3}\) e. \(1.4 \times 10^{22}\) molecules of \(\mathrm{N}_{2} \mathrm{O}_{4}\)

Propane gas, \(\mathrm{C}_{3} \mathrm{H}_{8}\), is used as a fuel for many barbecues. a. How many grams are in \(1.50 \mathrm{~mol}\) of propane? b. How many moles are in \(34.0 \mathrm{~g}\) of propane? c. How many grams of carbon are in \(34.0 \mathrm{~g}\) of propane? d. How many atoms of hydrogen are in \(0.254 \mathrm{~g}\) of propane?
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