1. Introduction

Chemistry exercises play an important role, including content and chemistry teaching methods in high school. Training skills to solve problems is indispensable in chemistry teaching activities. Within the scope of this paper, we will introduce some types of inorganic chemistry exercises that use graphs to infer solution methods. Thereby, training and enhancing skills to solve chemistry exercises in general and inorganic chemistry in particular is very important for students ^{[1, 2, 3]}.

2. Content

2.1. General Problem

In inorganic chemistry, a common problem is

(The symbol P↓ stands for “precipitate” in solution).

The precipitate P can be soluble in an excess reactant of A or B. At that time the same amount of precipitate can have two different values of A or B. To solve this problems, teacher can guide students to use the graph of the relationship between the number of moles of precipitate P ( ) and the number of moles of A or B ^{[4, 5]}.

2.2. Some Common Types
2.2.1. Type 1: Bubble Slowly the Gas of CO₂ or SO₂ through Solution of Ca(OH)₂ or Ba(OH)₂ → P↓ Soluble

In this case CO₂ will perform 2 tasks below.

Task 1: Increase gradually the mass of precipitate up to a maximum, according to the reaction

(1)

Task 2: Dissolve the precipitate, according to the reaction

(2)

The relationship between the number of moles of CO₂ and the number of moles of precipitate is represented as the graph in Figure 1.

2.2.2. Type 2: Bubble slowly the Gas of CO₂ or SO₂ Through the Mixture Solution of Ca(OH)₂/Ba(OH)₂ and NaOH/KOH → P↓ Soluble

In this case CO₂ will perform 3 tasks below.

Task 1: Form the maximum mass of precipitate, according to the reaction

(1)

Task 2: React between acidic oxide with alkali to form the acidic salt (not neutral salt because of excess CO₂), according to the reaction

(2)

Task 3: Dissolve the precipitate, according to the reaction

(3)

The relationship between the number of moles of CO₂ and the number of moles of precipitate is represented by the graph in Figure 2.

2.2.3. Type 3: Add Slowly Solution of NaOH to Solution of Al³⁺/Zn²⁺ P Soluble

In this case OH^- will perform 2 tasks below.

Task 1: Form the maximum mass of precipitate, according to the reaction

(1)

Task 2: Dissolve the precipitate, according to the reaction

(2)

The relationship between the number of moles of OH^- and the number of moles of precipitate is represented by the graph in Figure 3.

2.2.4. Type 4: Add Slowly Solution of NaOH to Mixture Solution of Al³⁺/Zn²⁺ and H⁺ P Soluble

In this case OH^- will perform 3 tasks below.

Task 1: Neutralize H⁺ ion in the solution, according to the reaction

(1)

Task 2: Form the maximum mass of precipitate, according to the reaction

(2)

Task 3: Dissolve the precipitate, according to the reaction

(3)

The relationship between the number of moles of OH^- and the number of moles of precipitate is represented by the graph in Figure 4.

2.2.5. Type 5: Add Slowly Solution of HCl to the Solution of [Al(OH)₄]^- / [Zn(OH)₄]^2- P Soluble

In this case H⁺ will perform 2 tasks below

Task 1: Form the maximum mass of precipitate, according to the reaction

(1)

Task 2: Dissolve the precipitate, according to the reaction

(2)

The relationship between the number of moles of H⁺ and the number of moles of precipitate is represented by the graph in Figure 5.

2.2.6. Type 6: Add Slowly Solution of HCl to the Mixture Solution of [Al(OH)₄]^- / [Zn(OH)₄]^2- and OH^- P Soluble

In this case H⁺ will perform 3 tasks below.

Task 1: Neutralize OH^- ion in the solution, according to the reaction

(1)

Task 2: React between H⁺ ion with complex ion to form the precipitate, according to the reaction

(2)

Task 3: Dissolve the precipitate, according to the reaction

(3)

The relationship between the number of moles of H⁺ ion and the number of moles of precipitate is represented by the graph in Figure 6.

2.2.7. Type 7: Add Slowly Solution of NH₃ to the Solution of Cu²⁺/Cu¹⁺/Zn²⁺/Ag⁺ P Soluble

In this case NH₃ will perform 2 tasks below.

Task 1: Form the maximum mass of precipitate, according to the reaction

(1)

Task 2: Dissolve the precipitate, according to the reaction

(2)

The relationship between the number of moles of NH₃ and the number of moles of precipitate Cu(OH)₂ is represented by the graph in Figure 7.

2.3. Sample Problems

Based on the 7 types of common exercise above, we designed some following exercises to help students practising skills using graphs to solve the exercises of inorganic chemistry in high school.

Example 1: Bubble slowly the gas of CO₂ through mixture solution of Ca(OH)₂ and KOH. Observed the phenomena according to the following graph (data are calculated in units of moles).

The value of x is

A. 0.45B. 0.42

C. 0.48D. 0.60

Solution: Based on the above graph, we can see the order of tasks of CO₂ is

Task 1:

Task 2:

(do not form the neutral salt because of the excess carbon dioxide which dissolved the precipitate)

Task 3:

At the position at which = 3 = a + a + a a = 1 x = 0.6a = 0.6 Answer D.

Example 2: Add slowly an excess of NaOH solution to AlCl₃ solution. Experimental results are shown in the following graph (data are calculated in units of moles)

The value of x is

A. 0.412B. 0.456

C. 0.51  D. 0.546

Solution: From the graph, we find that

At the position at which

Answer B.

Example 3: Add slowly 0.2 M Ba(OH)₂ solution to a test tube containing V (L) of c (mol/l) Al₂(SO₄)₃ solution. Experimental results are shown in the following graph

When the mass of precipitate is a constant, the minimum volume of Ba(OH)₂ solution is required to be

A. 30 mLB. 60 mL

C. 45 mLD. 75 mL

Solution: From the graph, we find that OH^- ion performed 2 tasks below

Task 1: Increase gradually the mass of precipitate up to a maximum.

Task 2: Dissolve the precipitate.

In which parallel segment to the axis shown that BaSO₄ precipitate is insoluble in base.

We find that :

and

Answer B.

Example 4: Add slowly an excess of NaOH solution to the mixture of solution containing a mol HCl and b mol AlCl₃. Experimental results are shown in the following graph (data are calculated in units of moles)

The ratio of is

A. 4/3B. 2/3

C. 1/1D. 2/1

Solution: From the graph, we find that OH^- ion performed 3 tasks below.

Task 1: Neutralize the acid in that solution

Task 2: Increase gradually the mass of precipitate up to a maximum

Task 3 : Dissolve the precipitate

At the position at which

The ratio = Answer A.

Example 5: Add slowly an excess of HCl solution to the mixture of solution containing x mol Ba(OH)₂ and y mol Ba[Al(OH)₄]₂. Experimental results are shown in the following graph (data are calculated in units of moles).

The value of x and y are

A. 0.05 and 0.15B. 0.10 and 0.30

C. 0.10 and 0.15D. 0.05 and 0.30

Solution: From the graph, we find that H⁺ ion performed 3 tasks below.

Task 1: Neutralize the base in that solution

Task 2: Increase gradually the mass of precipitate up to a maximum

Task 3 : Dissolve the precipitate

At the position at which

Answer A.

Example 6: Add slowly an excess of HCl solution to the mixture of solution containing a mol KOH and b mol K₂[Zn(OH)₄]. Experimental results are shown in the following graph (data are calculated in units of moles).

The ratio of is

A. 1.5B. 1.0

C. 2.0D. 2.5

Solution: From the graph, we find that H⁺ ion performed 3 tasks below.

Task 1: Neutralize the base in that solution

Task 2: Increase gradually the mass of precipitate up to a maximum

Task 3: Dissolve the precipitate

At the position at which

= Answer C.

Example 7: Add slowly an excess of NaOH solution to the mixture of solution containing a mol HCl and b mol ZnCl₂. Experimental results are shown in the following graph (data are calculated in units of moles)

The total value of (a + b) is

A. 1.4B. 1.6

C. 1.2D. 1.3

Solution: From the graph, we find that OH^- ion performed 3 tasks below.

Task 1: Neutralize the acid in that solution

Task 2: Increase gradually the mass of precipitate up to a maximum

Task 3: Dissolve the precipitate

At the position at which

Answer C.

Example 8: Add slowly an excess of NaOH solution to AlCl₃ solution, experimental results are shown in the following graph (data are calculated in units of moles)

The ratio of is

A. 7/8B. 6/7

C. 5/4D. 4/5

Solution: From the graph, we find that OH^- ion performed 2 tasks below.

Task 1: Increase gradually the mass of precipitate up to a maximum

Task 2: Dissolve the precipitate

From the graph, we find that

Answer B.

Example 9: Bubble slowly the gas of CO₂ through mixture solution of Ca(OH)₂ and NaOH. Experimental results are shown in the following graph (data are calculated in units of moles)

The value of x is

A. 0.64B. 0.58

C. 0.68D. 0.62

Solution: From the graph, we find that CO₂ performed 3 tasks below.

Task 1: Increase gradually the mass of precipitate up to a maximum

Task 2: Keep the constant mass of precipitate

Task 3: Dissolve the precipitate

We have: Answer A.

2.4. Test Yourself

1. Bubble slowly the gas of CO₂ through solution of Ba(OH)₂. Observed the phenomena happening according to the following graph (data are calculated in units of moles)

The value of x is

A. 1.8B. 2.0

C. 2.2D. 2.4

Answer B

2. Bubble slowly V (L) at s.t.p. of the gas of CO₂ through the mixture of Ba(OH)₂ and KOH solution. Experimental results are shown in the following graph (data are calculated in units of moles). Hint: 1 mole of gas at s.t.p. occupies 22.4 dm³.

In order to obtain the maximum precipitate, the value of V is

A. 4.480 V 8.960B. 2.240 V 6.720

C. 3.654 V 6.585D. 4.200 V 8.904

Answer D

3. Add slowly an excess of NaOH solution to AlCl₃ solution. Experimental results are shown in the following graph (data are calculated in units of moles)

The value of x is

A. 0.412B. 0.456

C. 0.515D. 0.546

Answer B

4. Add slowly an excess of NaOH solution to the mixture of solution containing a mol HCl and b mol AlCl₃. Experimental results are shown in the following graph (data are calculated in units of moles)

The ratio of  is

A. 4/3B. 2/3

C. 1/1D. 2/1

Answer A

5. Add slowly an excess of HCl solution to the mixture of solution containing x mol Ba(OH)₂ and y mol Ba[Al(OH)₄]₂. Experimental results are shown in the following graph (data are calculated in units of moles)

The value of x and y are

A. 0.05 và 0.15B. 0.10 và 0.30

C. 0.10 và 0.15D. 0.05 và 0.30

Answer A

6. Add slowly 0.2 M Ba(OH)₂ solution to a test tube containing V (L) of c (mol/l) ZnSO₄ solution. Experimental results are shown in the following graph

In order to constant precipitate, the volume of Ba(OH)₂ solution is the minimum needed

A. 50 mLB. 60 mL

C. 45 mLD. 75 mL

Answer D

7. Add slowly an excess of NaOH solution to X solution containing x mol H₂SO₄ and y mol Al₂(SO₄)₃. Experimental results are shown in the following graph (data are calculated in units of moles)

If add slowly a solution containing 0.7 mol Ba(OH)₂ to solution X until the reaction occurs completely, we obtain m grams of precipitate. Value of m is closest to which of the following value?

A. 170B. 150

C. 180D. 120

Answer A

8. Add slowly an excess of X solution to Y solution to form Z precipitate. Experimental results are shown in the following graph (data are calculated in units of moles)

Which result of the following experiment is shown as the above graph?

A. Add slowly an excess of HCl solution to Na[Al(OH)₄] solution

B. Add slowly an excess of NaOH solution to AlCl₃ solution

C. Add slowly an excess of NaOH solution to ZnCl₂ solution

D. Bubble slowly the gas of CO₂ through solution of Ca(OH)₂

Answer A

9. When add slowly a substance X to a substance Y to form a precipitate Z. Experimental results are shown in the following graph (data are calculated in units of moles)

Which result of the following experiment is shown as the graph above?

A. Add slowly an excess of HCl solution to Na[Al(OH)₄] solution

B. Add slowly an excess of NaOH solution to AlCl₃ solution

C. Add slowly an excess of HCl solution to Na₂[Zn(OH)₄] solution

D. Bubble slowly the gas of CO₂ through solution of Ca(OH)₂

Answer B

10. Add slowly a substance X to a substance Y to form a precipitate Z. Experimental results are shown in the following graph (data are calculated in units of moles)

Which result of the following experiment is shown as the above graph?

A. Add slowly an excess of KOH solution to ZnCl₂ solution

B. Bubble slowly the gas of CO₂ through solution of Ca(OH)₂

C. Bubble slowly the gas of NH₃ through solution of AlCl₃

D. Bubble slowly the gas of NH₃ through solution of ZnCl₂

Answer C

11. Add slowly an excess of X solution to Y solution to form Z precipitate. Experimental results are shown in the following graph (data are calculated in units of moles)

Which result of the following experiment is shown as the graph above?

A. Add slowly an excess of Ba(OH)₂ solution to AlCl₃ solution

B. Add slowly an excess of Ba(OH)₂ solution to Al₂(SO₄)₃ solution

C. Add slowly an excess of Ba(OH)₂ solution to mixture solution of HCl and AlCl₃

D. Add slowly an excess of NaOH solution to Al₂(SO₄)₃ solution

Answer B

12. Dissolve AlCl₃ in water to form a solution X. Add slowly an excess of NaOH solution to X solution. Experimental results are shown in the following graph.

Based on the above graph, the maximum mass of the precipitate obtained in above experiment is

A. 12.48 gramsB. 14.04 grams

C. 16.77 gramsD. 23.40 grams

Answer C

13. A solution X contains a mol of ZnSO₄, a solution Y contains b mol of AlCl₃ and a solution Z contains c mol of KOH. Perform 2 following experiments:

Experiment 1: Add slowly to the end of an excess of the solution Z to the solution X.

Experiment 2: Add slowly to the end of an excess of the solution Z to the solution Y.

The precipitate of two experiments changed according to the following graph

If each experiment used x mol KOH, the total mass (grams) precipitate obtained in two experiments will be closest to which of the following value?

A. 8.0B. 8.5

C. 9.0D. 9.5

Answer B

14. Bubble slowly the gas of CO₂ through 11 % (by mass) Ca(OH)₂ solution. The reaction occurs completely to form a solution X. Experimental results are shown in the following graph (data are calculated in units of moles)

Defining concentration of solution X in terms of mass percent?

A. 16.20 %B.14.59 %

C. 15.28 %D. 16.87 %

Answer C

15. Dissolve a mixture X containing a mol K and b mol Ca in 200 mL 0.1 M Ca(OH)₂ solution to form the solution Y and V (L) the gas of H₂ (at s.t.p.). Bubble slowly an excess of CO₂ gas through Y solution. Experimental results are shown in the following graph (data are calculated in units of moles). Hint: 1 mol of gas at s.t.p. occupies 22.4 dm³.

The value of V is

A. 14.56B. 19.04

C. 22.40D. 26.88

Answer A

3. Conclusions

The paper proposed identification signs of 7 types of inorganic chemistry exercises can use the graphic method to solve easily. Based on the experimental results are shown in the graph, easily infer the relationship between the number of moles of precipitate and the number of moles of reactants. Thereby, teacher will practice skills to solve chemical exercises for students based on the experimental results are illustrated by the graph. They are exciting forms of exercise for students in high school.

Acknowledgements

We thank the anonymous reviewers of this paper for many very helpful suggestions.

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