179
Limiting Reactants
PRE-LAB ASSIGNMENTS:
To be assigned by your lab instructor.
STUDENT LEARNING OUTCOMES:
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Making calculations based upon the stoichiometry of a reaction
Performing an acid- base titration
Endpoint
Limiting reactant
Indicators
Equivalence point
EXPERIMENTAL GOALS:
The limiting reactant in an acid-base reaction will be identified experimentally, and the amount
of excess reactant remaining after the reaction will be determined by titration. These data will be
used to explore the limiting reagent concept.
INTRODUCTION:
When we are given a reaction between two or more reactants, one may be completely
consumed before the other(s). The reaction stops at this point, and no further product is made.
The reactant that we run out of first is known as the limiting reactant, because it limits the
amount of product(s) that can form. The amount of product(s) that are made based on the
limiting reactant is the theoretical yield. The other reactants are present in excess, because some
amount of those reactants will still be present when the reaction stops.
For example, suppose we were making standard 4-door cars, and we had the following
very incomplete list of “ingredients.” How many cars could we make?
4 engines
8 headlights
4 drivers’ seats
4 steering wheels
8 license plate holders
15 doors
4 rear-view mirrors
8 windshield wipers
11 wheels
From the 4 engines, 8 headlights (one on each side), 4 driver’s seats, 4 steering wheels, 8 license
plate holders (one in front and one in back), 4 rear-view mirrors, and 8 windshield wipers (one
on each side), we can make 4 cars. However, if we have 15 doors, and we need 4 per car, we can
only make 3 complete cars. The “yield” of cars is even further reduced when we consider the
wheels: if we have 11 wheels, and need 4 per car, we will only be able to make 2 complete cars.
Thus, in this example, the wheels are the limiting reactant, and the theoretical yield is 2 cars.
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Now, let’s consider a chemical example. Ammonia, NH3, is synthesized from nitrogen
gas, N2, and hydrogen gas, H2, in the Haber process by the following reaction:
N2(g) + 3H2(g)  2NH3(g)
Example 1: Suppose we mix 1.00 moles of N2 and 5.00 moles of H2. What is the
maximum amount of NH3 that can be produced? How much H2 will be left over?
In this example, figuring out the limiting reactant and theoretical yield is straightforward: according to the stoichiometry of the reaction, 1 mole of N2 requires 3
moles of H2. Since we have 5.00 moles of H2, only 3.00 moles of the H2 can react
with the 1.00 moles of N2, which will produce 2.00 moles of NH3, and there will
be 2.00 moles of H2 left over.
Example 2: Suppose we mix 2.15 moles of N2 and 6.15 moles of H2. What is the
theoretical yield of NH3? How much of the excess reactant will be left over?
In this case, we’re not dealing with whole numbers, so we need to do some math.
To figure out the limiting reactant, we will consider each reactant, and see how
much of the product is formed
Assuming the N2 reacts completely, how much NH3 can be made?
2 mol NH3
2.15 mol N 2 
 4.30 mol NH3
1 mol N 2
Assuming the H2 reacts completely, how much NH3 can be made?
2 mol NH3
6.15 mol H 2 
 4.10 mol NH3
3 mol H 2
Since the H2 produces the smallest amount of NH3, H2 is the limiting reactant, and
the theoretical yield of NH3 is 4.10 moles.
The N2 will be present in excess. To figure out how much is left over, first, we
need to figure out how much will react:
6.15 mol H 2 
1 mol N 2
 2.05 mol N 2
3 mol H 2
Since 2.05 moles of N2 react, and we have 2.15 moles of N2 available, the amount
left over will be:
2.15 mol N2 initially – 2.05 mol N2 reacted = 0.10 mol N2 left over
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Notice that in Example 2, even though there are more moles of H2 present than N2, the H2 is still
the limiting reactant. It’s not enough to look at just the number of moles of the reactants that are
present — we have to consider the stoichiometric ratio in which they react.
In this example, there was only one product, but the same logic applies to reactions with
more than one product: we figure out which reactant produces the smallest number of moles (or
grams) of one of the products, and that reactant is the limiting reactant. Since we are dealing
with balanced chemical reactions, the limiting reactant for one product is the limiting reactant for
all of the products.
Now, let’s look at an example involving grams of reactants and products, since that’s
what we would actually measure in the laboratory.
Example 3: Butane, C4H10, undergoes combustion with oxygen, O2, to form
carbon dioxide and water:
2C4H10(g) + 13O2(g)  8CO2(g) + 10H2O(g)
58.12 g/mol
32.00 g/mol
44.01 g/mol
18.02 g/mol
If 100. g of C4H10 and 250. g of O2 are mixed,
a. Which of the two reactants is the limiting reagent, and what is the theoretical yield of
CO2?
b. What is the theoretical yield of H2O?
c. How many grams of excess reagent are left over?
d. If the actual yield of CO2 had been 155 g, what would be the percent yield of the
reaction?
a. Since we’re asked how many grams of CO2 will be formed, we’ll convert grams of
each one of the reactants to grams of CO2:
100. g C 4 H10 
250. g O 2 
1 mol C 4 H10
8 mol CO 2
44.01 g CO 2


 303 g CO 2
58.12 g C 4 H10
2 mol C 4 H10
1 mol CO 2
1 mol O 2
8 mol CO 2
44.01 g CO 2


 212 g CO 2
32.00 g O 2
13 mol O 2
1 mol CO 2
Since O2 produces the smallest amount of CO2, O2 is the limiting reactant, and the
theoretical yield of CO2 is 212 g.
b. If O2 is the limiting reactant for the formation of CO2, it is also the limiting reactant
for the formation of H2O:
250. g O 2 
1 mol O 2
10 mol H 2 O 18.02 g H 2 O


 108 g H 2 O
32.00 g O 2
13 mol O 2
1 mol H 2 O
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c. To figure out how many grams of C4H10 are left over, we first need to figure out how
many grams will react with the O2:
250. g O 2 
2 mol C 4 H10
58.12 g C 4 H10
1 mol O 2


 70.0 g C 4 H10
32.00 g O 2
13 mol O 2
1 mol C 4 H10
Now, we take the difference between the amount we started with and the amount that
will react:
100. g C4H10 initially – 70.0 g C4H10 reacted = 30. g C4H10 left over1
d. The percent yield of CO2 is the actual yield divided by the theoretical yield:
percent yield 
155 g CO 2
 100  73.1%
212 g CO 2
In this experiment, we will explore the concept of limiting reactant as it relates to a
reaction between a strong acid and a strong base. You will be using acid-base indicators and
titrations to accomplish this. In acid-base titrations, an indicator dye is often used to determine
when the titration is complete. For most indicators, the endpoint occurs when the solution
changes color (e.g., clear solution  pink solution or vice versa).
Remember that titrations compare the moles of reactants on the basis of the reaction’s
stoichiometry, which is determined from the balanced chemical reaction. For example, if two
substances, A and B, react in a 2:1 stoichiometric ratio2, then one mole of B reacts with 2 moles
of A. If we know the moles of one substance (i.e, A), then this ratio permits us determine the
concentration of the other (B) at and only at the point where both reactants are limiting (neither
is in excess); this point is referred to as the equivalence point of the titration. The titration must
be stopped as close to the equivalence point as possible. This experimentally determined point is
referred to as the endpoint. If the volume of the titrant measured at the endpoint is below or
above the volume required to achieve an exact equivalence point, the results will be inaccurate.
Provided that a suitable indicator is used, there is very little difference between the end
point and the equivalence point. These organic dye compounds exhibit a change in color over a
narrow pH range. Table 1 lists the color changes which are observed for several indicators over
a particular pH range. (An acidic solution has a pH of less than 7, a basic solution has a pH of
greater than 7, and a neutral solution has a pH of 7.)
1
Is this the right number of significant figures? (Hint: Remember the rules for addition and subtraction.)
Remember that for chemical reactions, the stoichiometric ratio is simply the ratio of the stoichiometric coefficients
of the two substances in the balanced chemical reaction. In the above example, 2A + B  products, the
stoichiometric ratio of A to B is 2:1.
2
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Table 1. Color Changes for Various Indicators
Indicator
pH Range Color Change
Ethyl Red
4.0-5.8
Colorless to red
Cresol Red
7.0-8.8
Yellow to red
Bromothymol blue
6.0-7.6
Yellow to blue
Phenol red
6.4-8.0
Yellow to Red
Phenolphthalein
8.0-9.6
Colorless to pink
Thymolphthalein
9.5-10.6 Colorless to blue
In this lab you will use phenolphthalein to determine whether the excess reactant is the
acid or base. If excess acid is present, the resulting solution will be acidic (What color will the
solution be?). If the base is in excess, the solution will be basic after the reaction (again, what
color?). The number of moles of excess acid and base will be determined by titration using the
same indicator. When indicators are used in a titration, the point at which the indicator changes
color is the titration end point.
The reaction that we will be using today is the reaction between HCl and NaOH:
HCl + NaOH  NaCl + H2O
There are some items of information that are necessary for understanding the calculations
in this lab:
 The stoichiometric ratio of reactants which can be obtained from the balanced equation.
 The moles of the unreacted excess reactant are determined using an acid-base titration.
PROCEDURE:
Safety Information
 HCl and HNO3 are strong acids and NaOH and KOH are strong bases. If you spill any of
these solutions on yourself, flush the area thoroughly with water, and inform your
instructor. If your skin comes in contact with NaOH or KOH solutions, you will feel
your skin become “slimy” as oils on your skin are converted to soap. Rinse your hands
with plenty of water if you notice this feeling.
 Clean up any spills of NaOH pellets immediately.
 Contact stockroom personnel to help clean up any large spills of acid or base solution.
 The addition of NaOH to water is an exothermic process; add the NaOH slowly, in small
portions to the solution.
A. Organizing Group Work
You will work in groups of eight. Each student will prepare one solution by adding different
masses of NaOH pellets to 30.00 mL HCl solution and then analyzing that solution. As a group,
you must make sure that the amounts NaOH used span the range of about 0.2 to 2.2 g NaOH,
with the points spaced out somewhat evenly across that range.
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B. Preparing the Solutions.
1. An NaOH pellet weighs approximately 0.2 grams. In a clean dry beaker, weigh out the mass
of NaOH assigned to you within ± 0.2 grams. This can be conveniently done by using the
Tare function on the balance.
a. Place a small, empty beaker on the balance, and press the “Tare” button; the reading
should go to 0.000, but may vary ± 0.002 g.
b. Using a spatula, add NaOH pellets until you get to the desired mass. (Do not handle
the pellets with your fingers, and clean up any spilled NaOH pellets.)
c. Record the exact mass of the NaOH.
d. Make sure that you replace the lid on the NaOH bottle, since NaOH is hygroscopic.
2. Clean a 250 mL Erlenmeyer flask, and rinse it three times with small portions of DI water.
Dry the outside of the flask; it is not necessary to dry the inside (the presence of a small
amount of DI water has no effect on the amount of acid or base present, and therefore no
effect on the titration or results.). From the buret labeled 1.0 M HCl, deliver 30.00 mL of
HCl solution into your beaker. Because it is important to use the same volume of HCl in
each run, use the following procedure:
a. Fill the buret to just above the 0.00 mark using the wash bottle labeled 1.0 M HCl.
b. Drain the buret into a waste container until the meniscus is as close to the 0.00 mark
as possible.
c. Place your Erlenmeyer flask under the buret; open the stopcock and drain the buret to
the 30.00 mL mark. Since some liquid may cling to the sides of the buret, wait about
one minute, and if the meniscus is above the 30.00 mL mark, open the stopcock and
again drain it to the 30.00 mark.
d. Record the exact concentration of the HCl.
3. Slowly add the NaOH pellets to your flask, swirling the flask gently as you do so. (The
dissolution of the NaOH and its reaction with the acid produce a lot of heat, which may cause
splattering if the pellets are added all at once.) Swirl the flask to completely dissolve the
NaOH. Make sure that you label your flasks in order to avoid confusion.
C. Setup for the Titrations.
1. Working as a group, obtain approximately 150 mL of 1.0 M HNO3 and 150 mL of 1.0 M
KOH in two separate beakers. Make sure that you record the actual concentration of the
HNO3 and KOH from the labels on the stock bottles.
2. Fill two burets with the HNO3 solution, and two with the KOH solution. Make sure to first
rinse the burets with two 3-5 mL portions of the solution you are filling them with. Label the
burets as KOH or HNO3 so that they can be identified later.
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D. Determining the Limiting Reagent and Performing the Titration.
Each member of your group must record the data for their titration during this portion of the lab.
Each student should titrate their solution according to the following procedure.
1. Add 3 drops of phenolphthalein to the solution being titrated. Based on the color of the
indicator in your solution, determine whether your solution is acidic or basic, whether HCl or
NaOH is the excess reagent, and whether you will use HNO3 or KOH to titrate your solution.
If you are uncertain of this choice, check with your instructor before titrating. Record your
conclusions in section D of the Lab Report. If you fail to add the phenolphthalein, it will be
difficult to perform this experiment!
2. Bring your flask to the buret required for your titration. Before starting each titration, the
buret used should be filled to near the 0.0 mark. Remove any bubbles from the stopcock by
draining a small amount of solution into a waste container. Record the position of the
meniscus as the initial volume.
3. Titrate your solution to the appropriate endpoint (from clear to pink if titrating with KOH,
and from pink to clear if titrating with HNO3). In each case, a permanent transition should
occur with the addition of no more than one drop of solution.
4. Record the final volume on the buret.
E. Analysis of Individual Titration Results
Complete this section of your lab report, showing any required calculations. You can consult
with your partner or other group members, but you should do your own calculations and give
your own observations and answers.
F. Analysis of Group Data
Complete the group analysis section of your lab report.
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LAB REPORT
Limiting Reactants
Name ________________________________
Date _________
Partner ________________________________
Section _________
Report Grade ______
A. Organizing Group Work
Name
≈ mass NaOH
Name
≈ mass NaOH
____________________
__________
____________________
__________
____________________
__________
____________________
__________
____________________
__________
____________________
__________
____________________
__________
____________________
__________
DATA ANALYSIS PERFORMED BY EACH STUDENT ON THEIR SOLUTION
B. Preparing the Solutions; C. Setup for the Titrations.
Actual Mass of NaOH used
____________
Moles of NaOH used
____________
Volume of HCl
____________
Concentration of HCl
____________
Concentration of HNO3
____________
Concentration of KOH
____________
D. Determining the Limiting Reagent and Performing the Titration.
Color of indicator added to solution
____________
Is the solution acidic or basic?
____________
Which reagent is in excess?
____________
This reagent will be titrated with
HNO3
or
KOH
(circle one)
(If you are uncertain of this choice, check with your instructor before titrating.)
If your excess reagent is NaOH, go to section E1.
If your excess reagent is HCl, go to section E2.
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E1. Analysis of Individual Titration Results (NaOH in excess)
In this procedure, you will be titrating unreacted NaOH.
Concentration of HNO3 Titrant
____________
Initial Volume of HNO3
____________
Final Volume of HNO3
____________
Volume of HNO3
____________
Use the titration data recorded above to complete the following section.
1. Calculate the total number of moles of NaOH that were added to your reaction mixture.
2. Use the volume and concentration of the HNO3 used during the titration to determine how
many moles of the NaOH were left over after the reaction between the HCl and the NaOH.
3. How many moles of the NaOH were consumed during the reaction between HCl and NaOH?
4. From the moles of NaOH that were consumed (calculated in step 3), determine the number of
moles and grams of NaCl that were produced during the reaction between HCl and NaOH.
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E2. Analysis of Individual Titration Results (HCl in excess)
In this procedure, you will be titrating unreacted HCl.
Concentration of KOH Titrant
____________
Initial Volume of KOH
____________
Final Volume of KOH
____________
Volume of KOH
____________
Use the titration data recorded above to complete the following section.
1. Calculate the total number of moles of HCl that were added to your reaction mixture.
2. Use the volume and concentration of the KOH used during the titration to determine how
many moles of the HCl were left over after the reaction between the HCl and the NaOH.
3. How many moles of the HCl were consumed during the reaction between HCl and NaOH?
4. From the moles of HCl that were consumed (calculated in step 3), determine the number of
moles and grams of NaCl that were produced during the reaction between HCl and NaOH.
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F. Analysis of Group Data
1. Group Data Table:
Name
Target g
NaOH
Actual g
NaOH
Moles
NaOH
Volume
HCl
solution
Moles
HCl
Indicator
color
Limiting
Reactant
Titrant
Volume
Moles
NaCl
formed
Moles
excess
NaOH
Moles
excess
HCl
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2. On the graph paper provided, plot the moles of NaOH used on the x-axis versus the following
quantities on the y-axis:
moles of NaCl formed
moles of excess NaOH
moles of excess HCl
3. Explain the observed trends in your graph in light of the concept of the limiting reagent.
4. Briefly sketch how your graph would have looked if this experiment would have been carried
out using a fixed amount of NaOH and varying the amount of HCl.
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Name ________________________________