Lesson 2: Chemical Reactions and Enthalpy Change

Part e: Thermal Stoichiometry

Part a: Enthalpy Change
Part b: Hess's Law
Part c: Heat of Formation
Part d: Bond Enthalpy and ∆H
Part e: Thermal Stoichiometry

 

Stoichiometry Revisited

We introduced the topic of Stoichiometry in Chapter 9 of our Chemistry Tutorial. Stoichiometry will be a sub-topic of nearly every Chapter for the remainder of our Tutorial. Why? Because stoichiometry pertains to the quantitative nature of chemical reactions and chemical reactions is central part of what Chemistry is all about.
 
Stoichiometry is the study of the quantitative relationship between the amounts of reactants and products involved in a chemical reaction. Stoichiometry focuses on the How much? questions of chemical reactions. Those How much? questions require a student to relate the amount of reactants to the amount of products. In Chapter 9, those amounts, or How much? quantities, included …

1. moles of a reactant
2. moles of a product
3. mass of a reactant (in grams)
4. mass of a product (in grams)

 
The task of solving a stoichiometry problem requires an understanding of what is related to what? and how are they related?
 
In Chapter 9, success at stoichiometry required that a student understand and be able to use mole ratios and molar mass. As a quick review, let’s consider the reaction for the synthesis of ammonia:
   
The coefficients 1, 3, and 2 in front of the formulae N₂, H₂, and NH₃ indicate how many moles of reactants and products are involved in the chemical reaction. They assist in answering all how much moles? type questions. Conversion factors can be made from these coefficients to convert between moles of reactants and moles of product or between moles of the two reactants.
   
The molar mass of a substance is the mass in grams of 1 mole of that substance. Molar mass values can be found using a periodic table and then used to convert between grams of a substance and moles of that same substance.
   
Coefficients (mole ratios), molar mass values, and the factor label method are the tools used to answer the how much? questions of stoichiometry. Their use was demonstrated through numerous examples in Chapter 9. If you find yourself a bit rusty on the topic, we encourage you to make a return visit to Chapter 9 and tool up. In Lesson 2e, we will apply those stoichiometry tools from Chapter 9 to situations that relate how much energy to how much reactant or product.  
 
 

Heat as a Stoichiometric Quantity

Earlier in this lesson, we mentioned that enthalpy is a stoichiometric quantity. For constant pressure conditions, the change in enthalpy for a reaction is equal to the amount of heat that is absorbed by or released from the system. This amount of heat is dependent upon the amount of reactants involved in the reaction. For the combustion of methane gas, approximately 890 kJ of heat is released by the reaction of 1 mole of CH₄. But if twice as much methane undergoes combustion, twice as much heat is produced. And if half as much methane is burned, half the heat is produced. This is why we refer to heat as a stoichiometric quantity.
 
Thermochemical equations are often used to express the relationship between the heat exchanged between the system and surroundings and the amount of reactants and products. For the combustion of methane, we would write …
   
When written like this, we can think of the 890 in front of the kJ in much the same way as we think of the implicit 1 in front of CH₄ and the 2 in front of O₂. These coefficients (numbers in front of the formulae) indicate how much (in moles) of each reactant and product are involved in the reaction. In the same way, the 890 indicates how much kJ of heat is involved in the reaction. These numbers can be used to create conversion factors that allow one to convert from the amount of reactant or product to the amount of heat (or vice versa).
   
 
 

Energy-Mole-Mass Relationships

Effectively solving thermal stoichiometry problems requires a solid understanding of the relationships between quantities - mass (in grams), amount (in moles), and energy (in kilojoules). The only quantity that the energy is directly related to is the moles of reactants and products. Energy can easily be related to the mass (in grams) or the volume (in mL or L) using additional information. As discussed above, mass and moles are related by the molar mass of the substance. For solids or liquids, the mass and volume are related by the density. And for gases, the moles and volume are related by the molar volume (22.4 L/mol at STP).
 
The graphic organizer below illustrates the many relationships between quantities for a thermal stoichiometry problem. In the example problems that follow, we will demonstrate how the graphic can be used.
   
 
 

Example 1

Consider the balanced chemical equation and enthalpy change value for the synthesis of sulfur trioxide from its elements:
   
How much energy will be required for the reaction of 7.20 moles of sulfur?
 
 

Solution:

Given: 7.20 mol S
Find: kJ of energy
 
Based on the coefficients and ∆H value, there are 790 kJ of energy required per 2 mole of sulfur. Using the graphic organizer presented above, it can be expected that the problem would require a single conversion factor. The conversion factor would be made from the ∆H value and the coefficients. The factor label solution is as follows:
   
 
 

Example 2

You have likely seen the demonstration of the burning of magnesium. The balanced chemical equation and associated enthalpy change are …
   
How much energy is released by the reaction of 1.12 g of magnesium?
 
 

Solution:

Given: 1.12 g Mg
Find: kJ of energy
 
We wish to determine the kJ of energy. This quantity is related by a single conversion factor to the moles of reactant. But it is the mass of reactant that is given. Mass is related to moles by the molar mass (24.305 g/mol). Using the graphic organizer presented above, it can be expected that the problem would require two conversion factors - one to convert from grams to moles and one to convert from moles to kJ.
   
The factor label solution is as follows:
   
 
 

Example 3

Most outdoor gas grills rely on propane combustion to cook food:
   
Noah Formula is doing the outdoor cooking for his family’s fourth of July celebration. He estimates that it will take 75 kJ of heat per burger to cook it to medium. He has 12 hamburgers to cook. What volume of propane gas (in liters at STP) does he need to cook all 12 hamburgers?
 
 

Solution:

Given: 12 hamburgers,
75 kJ/hamburger
Find: volume of C₃H₈ at STP
 
We wish to determine the volume of propane gas. We can plot out the solution using the graphic organizer presented above. From the given information - 12 hamburgers and 75 kJ energy per hamburger - we can determine the total amount of energy. We will use 75 kJ/1 burger as a conversion factor to do this. The kJ of energy is related to the moles of C₃H₈ by the coefficients and ∆H value. And the moles of C₃H₈ is related to the volume of C₃H₈ by the molar volume. This means we will be using three conversion factors in our solution. The factor label solution is as follows:
   
 
 

Practice, Practice, Practice

Like many mathematical skills in Chemistry, practice is essential for developing a mastery of the skill. We have provided several suggestions in the Before You Leave section. Be sure to take advantage of at least one of the opportunities to master the skill of solving thermal stoichiometry problems.
 
 
 
 

Before You Leave

• Download our Study Card on Thermal Stoichiometry. Save it to a safe location and use it as a review tool.
• Our Thermal Stoichiometry Concept Builder provides a great means of building confidence. It breaks the topic down into levels, allowing you and your understanding to progress from an apprentice level to a wizard level
• You’ll find plenty of practice problems on our Thermal Chemistry page. Of our Calculator Pad section There’s three different sets of problems, with each set being progressively more difficult than the previous: Thermal Stoichiometry 1 || Thermal Stoichiometry 2 || Thermal Stoichiometry 3
• The Check Your Understanding section below include 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. Consider the thermochemical equation for methanol combustion:
   
The reaction of ...
... 1.0 mole of CH₃OH will release ____________ kJ of energy. 


... 3.0 mole of CH₃OH will release ____________ kJ of energy. 


... _________ mole of CH₃OH will release 445 kJ of energy. 


... 16.0 grams of CH₃OH will release ____________ kJ of energy. 


... 64.0 grams of CH₃OH will release ____________ kJ of energy. 


 
 
2. Consider the thermochemical equation for propane combustion:
   
Fill in the table showing the mass-mole-energy relationships for this reaction.  



 
3. The thermochemical equation for the decomposition of water is
   

1. How much energy is required for the reaction of 1.0 moles of water? 
   
   Check Answer
   Answer: 286 kJ
   
   1.0 mol H₂O • (572 kJ/2 mol H₂O)
   
    
   
    
2. How much energy is required for the reaction of 4.0 moles of water? 
   
   Check Answer
   Answer: 1144 kJ
   
   4.0 mol H₂O • (572 kJ/2 mol H₂O)
    
   
    
3. How much energy is required for the reaction of 16.2 moles of water? 
   
   Check Answer
   Answer: 4630 kJ (rounded from 4633.2 kJ)
   
   16.2 mol H₂O • (572 kJ/2 mol H₂O)
   
    
   
    
4. How much energy is required for the reaction of 36.0 g of water? 
   
   Check Answer
   Answer: 572 kJ
   
   36.0 g H₂O • (1 mol H₂O/18.0 g H₂O) • (572 kJ/2 mol H₂O)
   
    
   
    
5. How much energy is required for the reaction of 180.0 g of water? 
   
   Check Answer
   Answer: 2860 kJ
   
   180.0 g H₂O • (1 mol H₂O/18.0 g H₂O) • (572 kJ/2 mol H₂O)
   
    
   
    
6. How much energy is required for the reaction of 77.5 g of water? 
   
   Check Answer
   Answer: 1230 kJ (rounded from 1231.388 ... kJ)
   
   77.5  g H₂O • (1 mol H₂O/18.0 g H₂O) • (572 kJ/2 mol H₂O)
   
    
   
    

 
 
4. The thermochemical equation for the combustion of butane (C₄H₁₀) in a butane lighter is …

2 C₄H₁₀(g)   +   13 O₂(g)   → 8 CO₂(g)   +   10 H₂O(l)   +   5760 kJ

There is 1.25 grams of butane remaining in a lighter. How much energy will it produce if all of it could be burned?
 

 
 
5. Gas stoves use methane gas. The balanced chemical equation and associated enthalpy change for the energy-producing reaction is

CH_4(g)   +   2 O_2(g)   →   CO_2(g)   +   2 H₂O_(g)      ∆H = -890 kJ

It is estimated that an average-sized Thanksgiving turkey will require 1150 kJ of energy to cook fully. What volume of methane gas at STP must be supplied to provide this energy requirement?

​
 
 
6. Anita Gitdere is planning a 292-mile trip in her Ford Focus. She predicts that she will average 32.3 miles/gallon. The energy demands will be met by the reaction of octane (C₈H₁₈) gasoline in the internal combustion engine. The thermochemical reaction is …

2 C₈H₁₈(l)  +  25 O₂(g)  →  16 CO₂(g)  +  18 H₂O(l)  +  10150 kJ

Determine the amount of energy used during Anita’s trip. (The density of octane gasoline is 0.703 g/mL and 1.00 gallon = 3.785 L.)

​