11.1 Analyzing a Chemical Reaction
Interpreting the chemical equation
Stoichiometry is all about amounts! How much reactant is needed, and how much is used up? How much product can be formed? Stoichiometry allows us to answer these questions. To use stoichiometry we need to be able to correctly interpret a balanced chemical equation. A chemical equation tells us what substances are added together as reactants and what substances are produced as products. As you learned earlier we must always balance a chemical reaction because atoms can not be created or destroyed, just rearranged. To balance a chemical reaction we select the smallest coefficients that provide us with the same number of each type of atom on the reactants and products side of the equation. Using the reaction for water decomposing to its elements:
2H
2O (l) → Ο
2(g) + 2 H
2(g)
We can interpret the information from this equation in two ways.
Coefficients in a balanced equation tell us how much of each chemical
1) 2 molecules of H
2O(l) yields 1 molecule of O
2(g) and 2 molecules of H
2(g).
2) 2 moles of H
2O(l) yields 1 mole O
2(g) and 2 moles H
2(g)
Using the mole relationship of reactants and products from the balanced equation is the key to understanding stoichiometry
Why is the mole so important? Because it is impossible to weigh out an individual molecule or even 12 molecules! For this reason a chemist rarely carries out a reaction using individual molecules, instead the larger unit of the mole is chosen. The mole is the unit commonly used to determine the relative amounts of reactants and products. Since the mole represents a “quantity” of measure it is often referred to as the “chemists dozen”. Do you remember how chemists measure out a quantity in moles? They convert the amount of moles to grams, using the molar mass of the substance. The amount in grams can then be weighed out on a balance. This very easy to do and very useful.
TABLE 11.1. Information from a Balanced Equation
2CO(g) + O
2(g) → 2CO
2(g)
2 molecules of CO 1 molecule of O2 2 molecules of CO2
2 dozen CO molecules 1 dozen O2 molecules 2 dozen CO2 molecules 2 moles of CO molecules 1 mole of O2 molecules 2 moles of CO2 molecules 2(6.022 x1023)CO molecules 6.022 x 1023 O2 molecules 2(6.022 x 1023) CO2 molecules
stoichiometry - STOY-KEE-AHM-EH-TREE - is the study of the amounts of
substances involved in a chemical reaction. The amounts can be studied in moles or
in mass relationships.
Practice relating moles to molecules
Explaining the meaning of a chemical equation in words often helps us to understand what it represents. Here we are going to practice interpreting balanced chemical equations, and looking at what the coefficients give us for information.
Propane is a fuel commonly used for gas grills and sometimes for heating homes. The combustion of propane is shown below:
C
3H
8(g) + 5O
2(g) → 3CO
2(g) + 4H
2O(g)
Asked: Explain the meaning of the equation in terms of the number of moles and molecules.
Answer: 1 molecule of C
3H
8reacts with 5 molecules of O
2to yield 3 molecules of CO
2and 4 molecules of H
2O
Answer: 1 mole of C
3H
8reacts with 5 moles of O
2to yield 3 moles of CO
2and 4 moles of H
2O
Moles and Molecules are NOT conserved
It is important to notice that the total number of moles of reactants, 1 mole C
3H
8plus 5 moles of O
2, do not add up to the total number of moles of products, 3 moles CO
2plus 4 moles H
2O. Six does not equal seven! It is fine that the moles are not conserved.
Why is it OK that the total number of moles is not conserved on the reactant and products side?
Essentially because the atoms ARE conserved! The atoms were rearranged and they now
make up new compounds. The atoms are the building blocks of molecules and they are
still present in the same amount..
Mole to mole relationships
Comparing amounts of ingredients
The balanced equation gives us important information about how much of each reactant is required to form products. This is helpful because we need to know the relative amounts of chemicals in order to make the “chemical recipe”.
Here is an example:
This information tells us what the ingredients are, how much you need of each ingredient, and how much product will be formed using the required ingredients.
Only compare chemicals in moles
When we use the balanced equation to determine amounts of chemicals we are comparing amounts in moles. This method allows us to understand how elements combine. For example:
1 mole of CO(g) + 2 moles of H
2(g) yields 1 mole of CH
3OH(l) You can only compare the amounts of chemicals in moles!
This is because chemicals combine in simple molar proportions. When we work in the unit of the mole all substances relative amounts are equivalent.
Atoms have different masses so we can never compare amounts in grams, because grams are never equivalent for different molecules
We cannot compare in grams
For example, we can compare 12 apples to 12 oranges and we see the amounts are
equivalent, but we know the apple and the orange are different fruits and have different
masses. So we compare the amounts of each fruit and we can say twelve apples to is
equivalent to twelve oranges. Using the above chemical example, CO(g) and hydrogen
gas, H
2(g) are different chemicals, so their masses are different, but we can determine
what amounts combine using the mole, because the amounts in moles represent the same
quantity.
Mole to mole relationships
Lets consider the chemical reaction shown below:
The mole amounts given by the balanced equation are called stoichiometric equivalent amounts. The mole amounts of each substance are proportionate to one another in a balanced equation. This means they combine in the amounts given by the coefficients of the balanced equation.
As shown above: 1 mole CO(g) = 2 mole H
2(g) =1 mole CH
3OH(l),
Based on this equation the recipe calls for 1 mole of CO(g) and 2 moles of H
2(g) to make the product methanol, CH
3OH.
The only way to know how to mix chemicals together is to use the balanced chemical reaction
Equivalent amounts are also used in cooking
The concept of relative amounts are used in cooking also. For example, if you are baking cupcakes and the recipe calls for 1 package of mix, 1/4 cup of oil and 3 eggs to make one batch of cupcakes, then you could say that 1 package of mix is stoichiometrically equivalent to 1/4 cup of oil and 3 eggs. The fact that they are “equivalent” means for this particular recipe they are in a proportionate amounts. When you mix all the ingredients you get one batch. For some other recipe it is likely that the ratio of mix to oil and eggs is quite different.
Different chemical reactions require different amounts of chemicals Proportionate amounts in chemistry is an important concept, because we need to know how to mix our ingredients and how much will be formed when we do mix them.
stoichiometric equivalent - the mole amounts of each substance in a balanced
chemical equation are proportionate.
Determining mole relationships
Finding Mole Amounts
Glucose, C
6H
12O
6, is the primary sugar used by our bodies for energy. In yeast, glucose undergoes a process called fermentation. This process produces ethanol, the common form of alcohol. When making blackberry wine the sugar in the berries ferments according to the following chemical equation :
C
6H
12O
6(aq) → 2 C
2H
5OH(aq) + 2 CO
2(g)
This equation says that 1 mole of C
6H
12O
6yields 2
moles of C
2H
5OH plus 2 moles of CO
2. What if we have 3 moles of glucose? If 3 moles of C
6H
12O
6decomposes how many moles of products do we obtain?
Rebalance the chemical equation
One way to approach this is to multiply the entire equation by 3.
This gives us 3 moles of C
6H
12O
6yields 6 moles of C
2H
5OH plus 6 moles of CO
2. This tells us we get six moles of ethanol and carbon dioxide as products, which answers our question.
Non-integer amounts of moles
What if we have 7.5 moles of glucose, C
6H
12O
6,that decomposes? How many moles of products will be formed then? Here we can multiply the equation by 7.5 to obtain the answer.
This gives us 7.5 moles of C
6H
12O
6yields 15 moles of C
2H
5OH plus 15 moles of CO
2.
This process of rebalancing the chemical equation to obtain the number of moles always
works, but it can get tedious. If we want to know the amount of only one product there is
no need to calculate each of them. In the next section we will work with a more
convenient method that uses mole ratios. This method allows us to calculate the amount
of one substance relative to another. These ratios are used as conversion factors that help
us to determine the amounts of chemicals needed as ingredients, or produced as product.
The mole ratio
Finding the mole ratio
The mole ratio comes from the coefficients in front of the reactants and products in the balanced chemical equation. Given the following reaction:
We can set up mole ratio’s that allow us to compare between reactants, or between reactants and products. Comparing the reactants we see that 1 mole CO is proportionate to 2 mole H
2and we can show this as a ratio:
mole ratio of reactants
In these ratios the quantities are the same but the comparison is reversed Suppose you want to know how much hydrogen gas, H
2you need to react with 4 moles of carbon monoxide, CO? To answer this question we can multiply by the mole ratio. We select the ratio that allows the proper units to cancel, and leaves the desired unit in the numerator (top).
If we want to know how much CO will react with 3.5 mole of H
2, we select the ratio with CO in the numerator (or top).
The important point is that the mole ratio is consistent. No matter what the starting amounts are these chemicals will always combine in the same ratio. We can use this ratio to determine how much of each chemical is consumed or produced.
mole ratio - A ratio comparison between substances in a balanced equation. The
ratio is obtained from the coefficients in the balanced equation. The ratio allows for
the conversion of one substance to another substance by using molar equivalent
Using the mole ratio
Comparing reactant to product
Not only can we compare reactants to reactants, we can compare reactants to products.
For instance using the same balanced equation: CO(g) + 2H
2(g) −> CH
3OH(l) , the ratio between CO(g) and CH
3OH(l) is one to one, but the ratio of H
2to CH
3OH(l) is two to one.
Comparing the reactant carbon monoxide, CO to the product methanol, CH
3OH we get:
Starting with product to find reactant
Another question might be: if the reaction produces 5 moles of methanol, CH
3OH, how many moles of H
2were consumed? Here we start with the amount of product and work backward to the reactant.
To select the correct mole ratio we look at the numerator and select the one with H
2in the top, because we are being asked how many moles of H
2.
Mole ratios are used as conversion factors that allow us to convert from one substance to another in a balanced chemical reaction . The important part is to select the ratio that allows the proper units to cancel.
Lets try this again to practice selecting the correct mole ratio.
A mixture of aluminum metal and chlorine gas reacts to form the compound aluminum chloride. How many moles of aluminum chloride (AlCl
3) will form when you react 5 moles of chlorine gas with excess aluminum metal?
2Al(s) + 3Cl
2(g) → 2AlCl
3(s) Asked: How many moles of AlCl
3are produced?
Given: 5 moles of Cl
2are reacting
Relationships: Mole ratio: 3 moles Cl
2= 2 moles AlCl
3Solve: Set up the mole ratios as proportions and select the one with AlCl
3on the top because that is what you are solving for.
Solve:
Answer: 3.3 moles of AlCl
3are produced.
5 moles Cl 2
2 moles AlCl 3 3 moles Cl
2 ---
× 3.3 moles AlCl
= 3
Practicing with mole ratios
Notice the molar coefficients in the balanced equation below :
Practice example
Using the steps outlined below, we will determine how many moles of oxygen, O
2(g) are required to react with 4 moles of methane, CH
4(g).
Our second example involves ammonia, which is the principal nitrogen fertilizer. It is prepared by the reaction between hydrogen and nitrogen.
Practice example
How many moles of ammonia, NH
3(g), can be prepared using 6.5 moles of H
2(g).
Assume that there is excess nitrogen.
Steps for Determining the Amount of Moles
Step 1 Step 2 Step 3
Determine which mole ratio between O
2and CH
4to use
Multiply by the appropriate
mole ratio Clearly state your answer
= 8 moles O 2
It requires 8 moles of O 2 to react with 4 moles of CH 4 1mole CH 4
2moles O 2
--- 2 moles O 2 1 mole CH 4 ---
= 4 moles CH 4
2 moles O 2 1mole CH
4 ---
×
Steps for Determining the Amount of Moles
Step 1 Step 2 Step 3
Determine which mole ratio between H
2and NH
3to use
Multiply by the appropriate
mole ratio Clearly state your answer
= 4.33 moles NH 3
4.33 moles of NH 3
is formed from 6.5 moles of H 2
2moles NH 3 3moles H 2
--- 3 moles H 2 2 moles NH 3 ---
=
6.5 moles H 2
2 moles NH 3 3moles H 2 ---
×
Gram to gram conversions
Our balances measure in grams
We have no scale that measures the mole! Students, chemists and people that work in the laboratory measure in grams, but substances combine in mole proportions. So in a very practical sense we must convert grams to moles so we can see how the chemicals will combine, we then convert back to grams, so that we can easily measure the amount. In the flow chart below, the mass of substance A represents the grams of reactant or product, that you are starting with, and substance D represents the amount of reactant used up or product formed.
You can’t get there from here!
This flow chart shows us that you CANNOT get from grams of substance A directly to grams of substance D!
You must go through the unit of the MOLE
Why is it important to know how much product is formed?
Chemists need to know how much product will be formed by a particular reaction for
many reasons. Sometimes the products formed are dangerous and not planing ahead
could be harmful to the people working and to the environment. For industrial
production, companies have to produce enough of a chemical to fill an order.
Gram to gram Calculations
To understand how the flow chart steps work we will consider the decomposition of calcium carbonate, CaCO
3(s), which is also known as limestone.
CaCO
3(s) → CaO(s) + CO
2(g)
Calcium carbonate is present in rocks found in many locations around the world. It is also found in nature as the primary component of egg shells and most sea shells. Calcium carbonate decomposes, or breaks apart when it is heated. How much carbon dioxide will be released when CaCO
3(s) is heated? Lets find out.
If 45.0 grams of calcium carbonate, CaCO
3decomposes, how many grams of carbon dioxide, CO
2(g) are produced? CaCO
3(s) → CaO(s) + CO
2(g)
Asked: How many grams of CO
2are produced?
Given: 45.0 g of CaCO
3reacting
Relationships: Molar mass of CaCO
3= 40.078 + 12.011+(15.999×3)
= 100.09 Mole ratio : 1 mole CaCO
3= 1mole CO
2Molar mass of CO
2= 12.011 + (15.999 × 2)= 44.01 Solve: Refer to flow chart and follow the steps (1-3).
Step 1)
Step 2)
Step 3)
g mole---
g mole---
45 g CaCO 3
1mole CaCO 3 100.09 g CaCO 3 ---
× 0.450 moles CaCO
= 3
0.450 moles CaCO 3
1 mole CO 2 1 mole CaCO 3 ---
× = 0.450 mole CO 2
0.450 mole CO 2
44.01 g CO 2 1 mole CO
2 ---
× 19.8 g CO
= 2
Gram to gram calculations
Astronauts use lithium hydroxide canisters to absorb exhaled carbon dioxide during their space missions. These canisters are critical in keeping carbon dioxide at safe levels for the astronauts to breath.
During the Apollo 13 space mission that began on April 11, 1970 there was an electrical explosion that caused a decrease in the oxygen supply. Astronauts had to move to a different cabin where the LiOH canisters were fresh and could support the crew members. LiOH canisters are changed roughly every twelve hours. In order to know when to replace them someone calculates the amount of CO
2they can absorb. Lets see how this is done.
Solid lithium hydroxide is used in space vehicles to remove exhaled carbon dioxide from the air inside the cabin. Lithium hydroxide reacts with the carbon dioxide to form solid lithium carbonate and water. How many grams of CO
2can be absorbed by 100.0g of LiOH(s)?
2LiOH(s) + CO
2(g) → Li
2CO
3(s) + H
2O(l) Asked: How many grams of CO
2will be absorbed?
Given: 100.0 g of LiOH reacting
Relationships: Molar mass of LiOH = 6.941 + 15.999+ 1.0079 = 23.95 Mole ratio : 2 moles LiOH = 1 mole CO
2Molar mass of CO
2= 12.011 + (15.999×2)= 44.01 Solve:
Answer: 91.98 grams of CO
2are absorbed
g mole---
g mole---
