2) Let's say that again:

to find the limiting reagent, take the moles of each substance and divide it by its coefficient in the balanced equation. The substance that has the smallest answer is the limiting reagent.

You're going to need that technique, so remember it.

By the way, did you notice that I bolded the technique to find the limiting reagent? I did this so as to emphasize its importance to you when learning how to do limiting reagent problems.

3) Resuming with the problem solution:

Aluminum ---> 1.20 / 2 = 0.60
Iodine ---> 2.40 / 3 = 0.80

4) The lowest number indicates the limiting reagent. Aluminum will run out first in part (a) of the question. Why?

1.20/2 means there are 0.60 "groupings" of 2 and 2.40/3 means there are 0.80 "groupings" of 3. If they ran out at the same time, we'd need one "grouping" of each. Since there is less of the "grouping of 2," it will run out first.

If you're not sure what I just said, that's OK. The technique works, so remember it and use it.

5) The second part of the question "theoretical yield" depends on finding out the limiting reagent. Once we do that, it becomes a stoichiometric calculation.

Al and AlI₃ stand in a one-to-one molar relationship, so 1.20 mol of Al produces 1.20 mol of AlI₃. Notice that the amount of I₂ does not play a role, since it is in excess.

Solution for part (b):

1) Since we have grams, we must first convert to moles. The we solve just as we did in part (a) just above. For the mole calculation:

Aluminum ---> 1.20 g / 26.98 g mol¯¹ = 0.04477 mol
Iodine ---> 2.4 g / 253.8 g mol¯¹ = 0.009456 mol

2) To determine the limiting reagent:

Aluminum ---> 0.04477 / 2 = 0.02238
Iodine ---> 0.009456 / 3 = 0.003152

The lower number is iodine, so we have identified the limiting reagent.

3) Finally, we have to do a calculation and it will involve the iodine, NOT the aluminum.

I₂ and AlI₃ stand in a three-to-two molar relationship, so 0.009456 mol of I₂ produces 0.006304 mol of AlI₃. Again, notice that the amount of Al does not play a role, since it is in excess.

From here figure out the grams of AlI₃ and you have your answer.

Solution for part (c):

Since we have moles, we calculate directly and then convert to grams.

Al and I₂ stand in a two-to-three molar relationship, so 0.009456 mol of I₂ uses 0.006304 mol of Al.

Convert this aluminum amount to grams and subtract it from 1.20 g and that's the answer.

Just above was some discussion on a way to determine the limiting reagent in a chemistry problem. This particular thing (determine the limiting reagent) is a real stumbling block for students. Be aware!

Example #2: 15.00 g aluminum sulfide and 10.00 g water react until the limiting reagent is used up. Here is the balanced equation for the reaction:

Al₂S₃ + 6H₂O ---> 2Al(OH)₃ + 3H₂S

(a) Which is the limiting reagent?
(b) What is the maximum mass of H₂S which can be formed from these reagents?
(c) How much excess reagent remains after the reaction is complete?

Some comments first:

The key to this problem is the limiting reagent, part (a). Once you know that, part (b) becomes "How much H₂S can be made from the limiting reagent?" Part (c) becomes two connected questions: first, "How much Al₂S₃ is used up when reacting with the limiting reagent?" then second, "What is 15.00 minus the amount in the first part?"

Make sure you note that second part. The calculation o be performed gives you the answer to "How much reacted?" but the question is "How much remained?" Lots of students forget to do the second part (the 15 minus part) and so get graded down.

Note: I'm carrying a guard digit or two through the calculations. The final answers will appear with the proper number of significant figures.

Solution for limiting reagent, part (a):

1) Determine the moles of Al₂S₃ and H₂O

Aluminum sulfide ---> 15.00 g ÷ 150.158 g/mol = 0.099895 mol
Water ---> 10.00 g ÷ 18.015 g/mol = 0.555093 mol

2) Divide each mole amount by equation coefficient:

Aluminum sulfide ---> 0.099895 mol ÷ 1 mol = 0.099895
Water --> 0.555093 mol ÷ 6 mol = 0.0925155

3) The water is the lesser amount; it is the limiting reagent.

Solution for mass of H₂S formed, part (b)

Now that we know the limiting reagent is water, this problem becomes "How much H₂S is produced from 10.00 g of H₂O and excess aluminum sulfide?"

1) Determine moles of 10.00 g of H₂O

Water ---> 10.00 g ÷ 18.015 g/mol = 0.555093 mol

2) Use molar ratios to determine moles of H₂S produced from above amount of water.

(a) the H₂O/H₂S molar ratio is 6/3, a 2/1 ratio.
(b) water is associated with the two. This means the H₂S amount is one-half the water value = 0.2775465 mol.

3) Convert moles of H₂S to grams.

(0.2775465 mol) (34.0809 g/mol) = 9.459 g

Solution for excess reagent remaining, part (c)

We will use the amount of water to calculate how much Al₂S₃ reacts, then subtract that amount from 15.00 g.

1) Determine moles of 10.00 g of H₂O

Water ---> 10.00 g ÷ 18.015 g/mol = 0.555093 mol

2) Use molar ratios to determine moles of Al₂S₃ that reacts with the above amount of water.

(a) the Al₂S₃/H₂O ratio is 1/6
(b) water is associated with the 6. This means the Al₂S₃ amount is one-sixth the water value = 0.09251447 mol

3) Convert moles of Al₂S₃ to grams.

(0.09251447 mol) (150.158 g/mol) = 13.891943 g

4) However, we are not done. We were asked for the amount remaining and the answer just above is the amount which was used up, so the final step is:

15.00 g − 13.891943 g = 1.108 g

Example #3: If there is 35.0 grams of C₆H₁₀ and 45.0 grams of O₂, how many grams of the excess reagent will remain after the reaction ceases?

2C₆H₁₀ + 17O₂ ---> 12CO₂ + 10H₂O

Solution:

1) Convert each substance to moles:

C₆H₁₀ ---> 35.0 g / 82.145 g/mol = 0.426 mol
O₂ ---> 45.0 g / 31.998 g/mol = 1.406 mol

2) Determine the limiting reagent:

C₆H₁₀ ---> 0.426 mol / 2 = 0.213
O₂ ---> 1.406 mol / 17 = 0.083

O₂ is the limiting reagent.

Comment: the units don't matter in this step. What we are looking for is the smallest number after carrying out the divisions. The value of 0.083 is the important thing. Not if it has a unit attached to it or not.

3) Determine how many moles of the excess reagent is used up when the limiting reagent is fully consumed:

the mole ratio we desire is 2/17 (C₆H₁₀ to O₂)

2		x
––––	=	–––––––
17		1.406 mol

x = 0.1654 mol of C₆H₁₀ consumed

4) Determine grams of C₆H₁₀ remaining:

0.426 mol − 0.1654 mol = 0.2606 mol of C₆H₁₀ remaining

(0.2606 mol) (82.145 g/mol) = 21.4 g remaining (to three sig figs)

Example #4: (a) What mass of Al₂O₃ can be produced from the reaction of 10.0 g of Al and 19.0 g of O₃? (b) How much of the excess reagent remains unreacted?

Solution to a:

1) Write balanced chemical equation:

2Al + O₃ ---> Al₂O₃

2) Convert grams to moles:

Al ---> 10.0 g / 26.982 g/mol = 0.37062 mol
O₃ ---> 19.0 g / 47.997 g/mol = 0.39586 mol

3) Determine limiting reagent:

Al ---> 0.37062 / 2 = 0.18531
O₃ ---> 0.39586 / 1 = 0.39586

Al is the limiting reagent

4) Determine moles of product formed:

Al to Al₂O₃ molar ratio is 2 to 1.

2		0.37062 mol
––––	=	––––––––––
1		x

x = 0.18531 mol

5) Determine grams of product:

(0.18531 mol) (101.961 g/mol) = 18.8944 g

To three sig figs, 18.9 g

Solution to b:

1) Determine moles of ozone that reacted:

Al to O₃ molar ratio is 2 to 1

2		0.37062 mol
––––	=	––––––––––
1		x

x = 0.18531 mol

2) Determine moles of ozone remaining:

0.39586 mol − 0.18531 mol = 0.21055 mol

3) Determine grams of ozone remaining:

(0.21055 mol) (47.997 g/mol) = 10.1 g (to three sig figs)

Example #5: Based on the balanced equation:

C₄H₈ + 6O₂ ---> 4CO₂ + 4H₂O

Calculate the number of excess reagent units remaining when 28 C₄H₈ molecules and 228 O₂ molecules react?

Solution:

Remember, numbers of molecules are just like moles, so treating the 28 and 228 as moles is perfectly acceptable. This is because I could divide the 28 and the 228 by Avogadro's Number to obtain the moles. Those mole amounts could be used in the calculation below and the final answer could then be multiplied by Avogadro's Number to obtain the answer of 60.

1) Determine the limiting reagent:

butane ---> 28 / 1 = 28
oxygen ---> 228 / 6 = 38

Butane is the limiting reagent.

2) Determine how much oxygen reacts with 28 C₄H₈ molecules:

the butane to oxygen molar ratio is 1:6

28 x 6 = 168 oxygen molecules react

3) Determine excess oxygen:

228 − 168 = 60

Here's aother way to consider this:

The 38 above means that there are 38 "groupings" of six oxygen molecules.

38 − 28 = 10 oxygen "groupings" remain after the butane is used up

10 x 6 = 60

Example #6: Determine the maximum mass of TiCl₄ that can be obtained from 35.0 g of TiO₂, 45.0 g Cl₂ and 11.0 g of C. (See comment below problem.)

3TiO₂ + 4C + 6Cl₂ ---> 3TiCl₄ + 2CO₂ + 2CO

Solution:

1) Assume each reactant is the limiting reagent. Determine the moles of product produced by each assumption:

Note: the first factor in each case converts grams of each reactant to moles. The second factor uses a molar ratio from the chemical equation to convert from moles of the reactant to moles of product. There is no need to convert to grams because all three calculations yield moles of the same compound (the TiCl₄).

	1 mole Cl2		3 mole TiCl4
45.0 g Cl2 x	–––––––––––	x	–––––––––––	= 0.31732 mol TiCl4
	70.9064 g Cl2		6 mol Cl2

	1 mole C		3 mole TiCl4
11.0 g C x	–––––––––––	x	–––––––––––	= 0.68688 mol TiCl4
	12.01078 g C		4 mol C

	1 mole TiO2		3 mole TiCl4
35.0 g TiO2 x	–––––––––––	x	–––––––––––	= 0.438235 mol TiCl4
	79.8658 g TiO2		3 mol TiO2

Cl₂ makes the least amount of TiCl₄, so Cl₂ is the limiting reactant.

2) The mass of TiCl₄ produced is:

(0.31732 mol TiCl₄) (189.679 g TiCl₄/mol) = 60.2 g TiCl₄ (to three sig figs)

Note that the "divide moles by coefficient" was not used to determine the limiting reagent. Instead, a full calculation was done and the least amount of product identified the limiting reagent. Here is what the "divide moles by coefficient" set up looks like:

Cl₂ ---> 0.63464 / 6 = 0.10577 <--- there's our limiting reagent
C ---> 0.915844 / 4 = 0.228961
TiO₂ ---> 0.438235 / 3 = 0.14608

Example #7: Determine the starting mass of each reactant if 46.3 of K₃PO₄ is produced and 92.8 of H₃PO₄ remains unreacted.

3KOH(aq) + H₃PO₄(aq) ---> K₃PO₄(aq) + 3H₂O(ℓ)

Solution:

1) The fact that some phosphoric acid remains tells us it is the excess reagent. Let us determine the amount of KOH (the limiting reagent) required to produce the 46.3 g of K₃PO₄.

46.3 g / 212.264 g/mol = 0.2181246 mol of K₃PO₄

Three moles of KOH are required to produce one mole of K₃PO₄

(3) (0.2181246 mol) = 0.6543738 mol of KOH required

(0.6543738 mol) (56.1049 g/mol) = 36.7 g (to thee sig figs)

2) Determine the starting mass of H₃PO₄

0.2181246 mol of K₃PO₄ requires 0.2181246 mol of H₃PO₄ based on the 1:1 molar ratio from the balanced equation.

(0.2181246 mol) (97.9937 g/mol) = 21.4 g (to three sig figs)

21.4 + 92.8 = 114.2 g

Example #8: Determine the limiting reagent of this reaction:

Na₂B₄O₇ + H₂SO₄ + 5H₂O ---> 4H₃BO₃ + Na₂SO₄

There are 5.00 g of each reactant.

Solution:

1) Convert everything into moles, by dividing each 5.00 g by their respective molar masses:

Na₂B₄O₇ ---> 0.02485 mol
H₂SO₄ ---> 0.05097 mol
H₂O ---> 0.2775 mol

2) Note that there are three reactants. How is the limiting reagent determined when there are three reactants? Answer: determine the limiting reagent between the first two:

Na₂B₄O₇ ---> 0.02485 / 1 = 0.02485
H₂SO₄ ---> 0.05097 / 1 = 0.05097

Na₂B₄O₇ is the limiting reagent when compared to H₂SO₄

3) Now, compare the "winner" to the third reagent:

Na₂B₄O₇ ---> 0.02485 / 1 = 0.02485
H₂O ---> 0.2775 / 5 = 0.0555

Na₂B₄O₇ is the limiting reagent between itself and H₂O.

Na₂B₄O₇ is the overall limiting reagent in this problem.

Example #9: How much O₂ could be produced from 2.45 g of KO₂ and 4.44 g of CO₂?

4KO₂ + 2CO₂ ---> 2K₂CO₃ + 3O₂

Solution:

I will do a solution assuming KO₂ is the limiting reagent, then I will do a solution assuming CO₂ is the limiting reagent. The reactant that produces the lesser amount of oxygen is the limiting reagent and that lesser amount will be the answer to the question.

1) Solution using KO₂:

2.45 g / 71.096 g/mol = 0.03446045 mol

4		0.03446045 mol
–––	=	––––––––––––––
3		x

x = 0.02584534 mol

(0.02584534 mol) (31.998 g/mol) = 0.827 g of O₂

2) Solution using CO₂:

4.44 g / 44.009 g/mol = 0.10088845 mol

2		0.10088845 mol
–––	=	––––––––––––––
3		x

x = 0.151332 mol

(0.151332 mol) (31.998 g/mol) = 4.84 g of O₂

3) 0.827 g is the answer.

Note that I could have calculated the mole amounts, used the "divide moles by coefficient" to determine the limiting reagent, and then done just one complete calculation.

Example #10: (a) What mass of hydrogen peroxide should result when 1.45 g of barium peroxide is treated with 25.5 mL of hydrochloric acid solution containing 0.0277 g of HCl per mL? (b) How much of the excess reactant is left?

BaO₂(s) + 2HCl(aq) ---> H₂O₂(aq) + BaCl₂(aq)

Solution:

Calculate the amount of product using each reactant. The reactant that produces the lesser of the two amounts will tell you the limiting reactant. This solution will use dimensional analysis (also called the unit-factor, or unit-label, method) for the proposed solution.

1) First, determine the mass of HCl that reacts:

(0.0277 g/mL) (25.5 mL) = 0.70635 g

2) The barium peroxide solution:

(1.45 g BaO2)	(1 mol BaO2 / 169.3 g BaO2)	(1 mol H2O2 / 1 mol BaO2)	(34.0 g H2O2 / 1 mol H2O2)	= 0.291 g H2O2
	↑ convert grams to moles ↑	↑ molar ratio ↑ from equation	↑ convert moles to grams ↑

3) The hydrochloric acid solution:

(0.70635 g) (1 mol HCl / 36.46 g HCl) (1 mol H₂O₂ / 2 mol HCl) (34.0 g H₂O₂ / 1 mol H₂O₂) = 0.332 g H₂O₂

4) Since 0.291 g is less than 0.332 g, the BaO₂ is the limiting reactant.

5) The other method to determine the limiting reagent is to divide the moles of each reactant by their respective coefficient in the balanced equation:

BaO₂ ---> 1.45 g / 169.3 g/mol = 0.008565 mol
HCl ---> 0.70635 g / 36.46 g/mol = 0.01937 mol

0.008565 / 1 = 0.008565
0.01937 / 2 = 0.009685

BaO₂ (the 0.008565) is the lesser amount, so it is the limiting reagent.

6) To solve part (b), we observe that 0.008565 mol of BaO₂ was used. Using a 1:2 molar ratio, we can determine the amount of HCl that was used:

1		0.008565 mol
–––	=	–––––––––––
2		x

x = 0.01713 mol of HCl used up in the reaction

7) Next, we subtract the amount used up from the total amount that was present:

0.01937 mol − 0.01713 mol = 0.00224 mol of HCl remains after reaction stops

8) Convert moles to grams:

(0.00224 mol) (36.46 g/mol) = 0.0817 g (to three sig figs)

Bonus Example: Consider the following reaction at 1.10 atm and 19.0 °C:

2NaCl(s) + 2NH₃(g) + CO₂(g) + H₂O(ℓ) ---> 2NH₄Cl(aq) + Na₂CO₃(s)

0.218 mol of sodium chloride, 2.55 L of ammonia, 2.00 L of carbon dioxide, and an unlimited amount of water react to form aqueous ammonium chloride and solid sodium bicarbonate. How many moles of ammonium chloride are formed in the reaction?

Comment: this question was asked and answered on a now-defunct "answers" website and the one answer given (besides mine) totally missed the point of the question. The answerer focused on the non-realistic nature of the above chemical equation. However, the point of the question is to determine the limiting reagent and the non-realistic nature of the chemical equation is completely beside the point.

Solution:

1) Use PV = nRT to determine moles of ammonia and carbon dioxide:

ammonia:

(1.10 atm) (2.55 L) = (n) (0.08206 L atm / mol K) (292 K)

n = 0.11706 mol

carbon dioxide:

(1.10 atm) (2.00 L) = (n) (0.08206 L atm / mol K) (292 K)

n = 0.091814 mol

2) Determine the limiting reagent:

0.218 / 2 = 0.109
0.11706 / 2 = 0.05853
0.091814 / 1 = 0.091814

Ammonia is the limiting reagent.

3) Now, the problem becomes this: 0.11706 moles of ammonia produces how many moles of ammonium chloride?

The molar ratio between ammonia and ammonium chloride is 1:1.

0.11706 moles of ammonia produces 0.117 moles of ammonium chloride (rounded off to three significant figures).

And we are done.