Lesson 2: Quantitative Analysis of Compounds

Part b: Grams-Moles-Particles Relationship

Part a: Molar Mass of Compounds
Part b: Grams-Moles-Particles Relationship
Part c: Percent Composition
Part d: Empirical and Molecular Formulae

 

 

The Goals:

Lesson 2b will focus on the use of conversion factors to …

• Determine the number of moles that are equal to a given number of particles (molecules or formula units) of a compound.
• Determine the number of particles (molecules or formula units) that are equal to a given number of moles of a compound.
• Determine the number of moles that are equal to a given mass in grams of a compound.
• Determine the mass in grams that are equal to a given number of moles of a compound.
• Determine the number of particles (molecules or formula units) that are equal to a given mass in grams of a compound.
• Determine the mass in grams that are equal to a given number of particles (molecules or formula units) of a compound.

 
 

Relying on the Factor Label Method

Lesson 1d of this chapter pertained to the use of the factor label method to perform conversions from grams to moles to atoms for samples of elements. This part of Lesson 2 will involve a very similar logic, except that the conversions will be performed for compounds.
 
Compounds are different than elements. Compounds consist of two or more elements. For instance, water (H₂O) is a compound. Water consists of two elements – hydrogen and oxygen. Compounds are also different than elements in terms of the fundamental particles of which they are composed. Water is a molecular compound. A sample of a molecular compound like H₂O consists of molecules of H₂O. Molecules are the fundamental particles of molecular compounds. In contrast, sodium chloride (NaCl) is an example of an ionic compound. There are no molecules in an ionic compound. Ionic compounds consists of an organized collection of positive and negative ions that are gathered together in a highly structured network known as a crystal lattice. We refer to there being formula units of the ionic compound. One Na⁺ ion and one Cl^- ion make for one formula unit. When you encounter the word particles on this page, you can interpret this to mean molecules (for molecular compounds) or formula units (for ionic compounds).  
With some exceptions, atoms are the fundamental particles of elements. The element copper consists of copper atoms. The element sodium consists of sodium atoms. The most common exceptions to this include the seven elements that are found naturally as diatomic molecules (remember Professor H₂O₂N₂Cl₂Br₂I₂F₂) instead of the usual monatomic form.
 
The factor label method will be used to accomplish the goals of this unit. The factor label method relies on the use of conversion factors. Conversion factors are created from equivalence statements. The two most common equivalence statements are associated with Avogadro’s number and the molar mass concept. Avogadro’s number indicates the number of items (6.022x10²³) in one mole. The molar mass indicates the mass in grams of a substance per 1 mole (mol) of that substance. The molar mass value depends on the substance. For water, there are 18.0152 grams per 1 mole. The molar mass is determined from atomic mass values on the periodic table. Lesson 2a detailed the method of calculating the molar mass from a chemical formula.
 
 

Particles ⇔ Moles

The two conversion factors below are used to convert particles (molecules or formula units) to moles and moles to particles.
   
NOTE: Depending on the context of the problem, the particles may be replaced with either molecules (for molecular compounds) or formula units (for ionic compounds).
 
Conversion Factor #1 is used to convert from particles to moles. The denominator has units of particles. When this fraction is used as a multiplier, it will cancel the particles of the given quantity. The unit on the result is the uncancelled mol in the numerator. 
 
Conversion Factor #2 is used to convert from moles to particles. The denominator has units of mol (mole). When the fraction is used as a multiplier, it will cancel the moles of the given quantity. The unit on the result is the uncancelled particles of the numerator. 
 
Example #1  
Solution:  
 
Example #2 Solution:  
 
 

Moles ⇔ Grams

The two conversion factors below are used to convert from moles to grams and from grams to moles.
   
The value X in these factors depends on what the compound is. The compound name and/or formula will be stated in the problem. Use Lesson 2a to determine the molar mass of the compound. The molar mass of the compound is the X value.
 
Conversion Factor #3 is used to convert from mol (moles) to grams. The denominator has units of mol. When the fraction is used as a multiplier, it will cancel the mol of the given quantity. The unit on the result is the g (grams) of the numerator. 
 
Conversion Factor #4 is used to convert from grams to moles. The denominator has units of g (grams). When the fraction is used as a multiplier, it will cancel the g of the given quantity. The unit on the result is the mol (moles) from the numerator. 
 
 
Example #3  
Solution:  
 
Example #4  
Solution:    

Particles ⇔ Grams

So far, we have seen examples in which just a single conversion factor is used to convert the unit of the given quantity to the target unit. Now we will see instances in which two conversion factors are required.
 
These two-step problems of converting from particles to grams or from grams to particles can be thought of as a combining of the types of problems we have already solved. For instance, the conversion of the given quantity of particles to the mass in grams can be done by first converting from particles to moles and then from moles to grams. These two steps can be done together by stringing together the two conversion factors in consecutive fashion.
   
The process of converting from a given quantity of grams to the number of particles can be done in two steps as well. First convert from grams to moles and then from moles to particles.
   
Both Avogadro’s number (Conversion Factors #1 and #2) and molar mass (Conversion Factors #3 and #4) will be used to do these conversions.
  NOTE: Depending on the context of the problem, the particles may be replaced with either molecules (for molecular compounds) or formula units (for ionic compounds).
 
 
Example #5  
Solution:  
Example #6  
Solution:  
 
 

Determining the Number of Atoms of an Element in a Sample

Perhaps one of the more difficult conversions at this point in the Chemistry course is the determination of the number of atoms of an element in a given quantity of grams of a compound. So, what is meant by this? We have just seen in Example 6 that the number of particles (molecules or formula units) can be determined from a knowledge of the mass of a compound. Compounds consist of two or more elements. In example 6, copper(II) chloride was the compound and it consists of copper and chlorine in a 1:2 ratio. Every formula unit of CuCl₂ has one copper atom and two chlorine atoms in their ion form. So, there is one remaining step to such a problem. If the number of chlorine atoms must be determined, then it is a matter of multiplying the number of formula units of CuCl₂ by two.
 
The table illustrates the relationship between particles (molecules or formula units) and atoms, assuming that there was 1.00 mole of particles present in a sample.
 
 
Example #7  
Solution:  
 
 
 

Before You Leave

• Download our Study Card on Particles-Moles-Mass. Save it to a safe location and use it as a review tool. 
• Try our Concept Builder titled Particles-Moles-Mass. It begins with nice numbers and simple formulas and gradually increases in complexity. Give it a try.
• Our Calculator Pad section has three sets of Practice Problems on this topic. Your answers are evaluated and feedback is provided; you have infinite opportunities to correct your mistakes. The difficulty level increases for each consecutive set of problems. Try …
  • Problem Set PMG7 – Particles-Moles-Grams 2.
  • Problem Set PMG8 – Particles-Moles-Grams 3.
  • Problem Set PMG9 – Particles-Moles-Grams 4.
• The Check Your Understanding section below includes questions with answers and explanations. It provides a great chance to self-assess your understanding.

 
 
 

Check Your Understanding

Use the following questions to assess your understanding. Tap the Check Answer buttons when ready.
 
1. On an icy January morning, South’s custodian Hans Full pours 1350 grams of calcium chloride onto the sidewalks in front of the main entrance to the school.  Calculate the moles of calcium chloride that were used.


 
 
2. Clarence Pipes, the infamous local plumber, is called to a home to fix a clogged bathroom drain.  As he begins his duties, he pours a bottle of industrial strength drain cleaner down the drain.  The bottle contained 2.45 moles of sodium hydroxide. 

1. Calculate the number of formula units of sodium hydroxide that were poured into the drain. 
   
   Check Answer
   Answer: 1.48 x 10²⁴ formula units
   
   Solution:
   
   
    
   
    
2. Calculate the mass of sodium hydroxide. Reference our Polyatomic Ion list if necessary. 
   
   Check Answer
   Answer: 98.0 g NaOH
   
   Solution:
   
   
    
   
    

 
 
3. In an effort to keep the shoes in a shoe box dry, a shoe company places 2.58 grams of silicon dioxide into the box.  (The silicon dioxide is the hygroscopic chemical that is present in the small mesh bag sometimes found in shoe boxes.)  Calculate the number of molecules of silicon dioxide that are used.
 

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4. Tilda Earth is preparing her garden for the upcoming spring growth.  As a fertilizer, she works 459 grams of ammonium nitrate into the soil.  Determine the moles of ammonium nitrate that were added to the soil. Reference our Polyatomic Ion list if necessary.
 
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5. Overcome by a cold, Colin Sick stays home from work.  During the course of the day he consumes 1.29 grams of pseudoephedrine, the active ingredient in Sudafed.  Pseudoephedrine has the chemical formula C₁₀H₁₅NO. Calculate the molecules of C₁₀H₁₅NO ingested by Colin.
 
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6. The active ingredient in Milk of Magnesia is magnesium hydroxide.  The magnesium hydroxide acts as an antacid and a saline laxative.  After a trip to Taco Bell, Indiana Jestun (Indy to his friends) drops 4.79 x 10²² formula units of magnesium hydroxide into his stomach.  Determine the mass of magnesium hydroxide. Reference our Polyatomic Ion list if necessary.

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