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1 Mr. Dolgos Regents Chemistry PRACTICE PACKET Unit 9: Acids, Bases & Salts *STUDENT* *STUDENT* HC 2 H 3 O 2 (aq) + H 2 O(l) C 2 H 3 O 2 - (aq) + H 3 O + (aq)

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Page 1: Mr. Dolgos Regents Chemistry - Tilaro Science - Hometilaroscience.weebly.com/uploads/1/4/8/5/14853818/... ·  · 2015-05-18Mr. Dolgos Regents Chemistry PRACTICE PACKET Unit 9:

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Mr. Dolgos

Regents Chemistry

PRACTICE PACKET Unit 9: Acids, Bases & Salts

*STUDENT* *STUDENT*

HC2H3O2(aq) + H2O(l) ↔ C2H3O2-(aq) + H3O

+(aq)

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Acid/Base/Salt Characteristics: On the line on the left, write A if the statement is a property of an acidic solution. Write B if it is a property of a basic solution. Write X if it is a property of both acidic and basic solutions. ________ 1) Often feels smooth and slippery

________ 2) Has a sour taste

________ 3) Stings in open wounds

________ 4) Typically reacts vigorously with metals

________ 5) Has a bitter taste

________ 6) Turns litmus paper from blue to red

________ 7) Is an electrolyte

________ 8) Often looks like pure water

________ 9) Turns litmus paper from red to blue

________ 10) Typically does not react with metals 11. Compare acids and bases in terms of H+ and OH- concentration.

_________________________________________________________

_________________________________________________________

_________________________________________________________

12. Explain what it means to be an electrolyte and why acids, bases and salts are electrolytes.

_________________________________________________________

_________________________________________________________

_________________________________________________________

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Multiple Choice Questions:

1) Basic solutions are those that contain an excess of a) HS- b) H- c) HCO3

- d) OH- 2) Acidic solutions are those that contain an excess of

a) H2 molecules b) H2O molecules c) H+ ions d) OH- ions 3) A student accidentally spills an unknown chemical on her hand. She quickly washes it

off, and notices that her skin feels slippery. She has an electrical conductivity tester at her lab station and tests the conductivity of the solution. It is a good conductor of electricity. The then places a strip of litmus paper in a sample of the liquid and it turns blue. She can conclude that the liquid is a a) strong base b) weak base c) strong acid d) weak acid

4) As 1 gram of sodium hydroxide dissolves in 100 grams of water, the conductivity of

the water will a) remain the same b) decrease c) increase

Recognizing/Naming Acids, Bases, & Salts: Question: What is the general formula for each of the following?

ACID BASE Question: What combinations of elements or ions qualify as a salt?

SALT

Substance Acid, Base, or Salt? Name 1. NaOH

2. NH3

3. HCl

4. NaCl

5. HF

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6. K2SO4

7. AlPO4

8. Fe(OH)3

9. H2SO4

10. H2CO3

11. LiC2H3O2

12. H3PO4

13. Ca(NO3)2

14. KOH

15. MgCO3

16. NH4Br

17. HNO3

18. Ca(OH)2

19. MgCO3

20. NaNO3

21. HCl

22. KCl

23. Ba(OH)2

24. KOH

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25. H2S

26. Al(NO2)3

27. CaCl2

28. Na2SO4

29. Mg(OH)2

30. NH4OH

31. NH4Cl

32. HBr

33. FeBr3

34. HC2H3O2

35. CuCl2

36. HNO2

37. HClO

38. HClO2

39. HClO3

40. HClO4

41. H2SO3

42. Al(OH)3

43. LiOH

44. HI

45. H2Se

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46. H2CrO4

47. AgOH

48. Fe(OH)2

Bronsted-Lowry Problems: According to the Bronsted-Lowry theory, an acid is a proton (H+) donor and a base is a proton (H+) acceptor.

Example: HCl + OH- Cl- + H2O

In the following equations, draw brackets between conjugate acid-base pairs and label each species as a Bronsted-Lowry acid or base, and answer the question.

1) According to the Bronsted-Lowry theory, what does H3O+ act as in the following reaction?

CH3COO- + H3O+ CH3COOH + H2O

2) According to the Bronsted-Lowry theory, what does H2O act as in the following reaction?

HCl + H2O H3O+ + Cl-

3) According to the Bronsted-Lowry theory, what does NH3 act as in the following reaction?

NH2

- + H2O NH3 + OH-

4) According to the Bronsted-Lowry theory, what does H3O+ act as in the following reaction?

H3O+ + OH- H2O + H2O

5) According to the Bronsted-Lowry theory, what does CN- act as in the following reaction?

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CN- + H2O HCN + OH-

6) According to the Bronsted-Lowry theory, what does CH3COOH act as in the following

reaction?

HClO4 + CH3COOH ClO4- + CH3COOH2

+

7) According to the Bronsted-Lowry theory, what does HCN act as in the following reaction?

HCN + H2O H3O+ + CN-

8) According to the Bronsted-Lowry theory, what does NH4+ act as in the following

reaction?

NH4+ + HSO4

- NH3 + H2SO4

9) According to the Bronsted-Lowry theory, what does Al(H2O)5(OH)+2 act as in the following reaction?

HCl + Al(H2O)5(OH)+2 Cl- + Al(H2O)6

+3

Challenge Problems: 10) HCl + NaOH NaCl + H2O 11) KOH + HNO3 KNO3 + H2O 12) H2CO3 + 2H2O CO2 + H3O+

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13) HCl + NH3 NH4+ + Cl-

14) H2O + NH3 NH4

+ + OH- 15) H2O + H2O H3O+ OH- 16) NH3 + NH3 NH4

+ + NH2-

17) H2SO4 + Ca(OH)2 CaSO4 + 2H2O 18) O3ClOH + H2O H3O+ + O3ClO- 19) H2O + HI H3O+ + I-

20) CH3COOH + H2O CH3COO - + H3O+ 21) NH4

+ + OH- NH3 + H2O 22) H2SO4 + OH- HSO4

- + H2O 23) HSO4

- + H2O SO4-2 + H3O+

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More Bronsted-Lowry Acids and Bases:

Directions: For questions 1-4 please circle the correct answer.

1. What are the two acids in the following reaction?

H2O + HI ↔ H3O+ + I-

a. H2O and HI b. HI and I- c. H2O and I- d. HI and H3O+

2. What are the two acids in the following reaction?

CH3COOH + H2O ↔ CH3COO- + H3O+

a. CH3COOH and H3O+ b. CH3COOH and CH3COO- c. CH3COO- and H2O d. CH3COO- and H3O+

3. What are the bases in the following reaction?

H3PO4 + H2O ↔ H2PO4

- + H3O+

a. H3PO4 and H2O b. H2O and H2PO4-

c. H3PO4 and H2PO4- d. H2PO4

- and H3O+

4. What are the bases in the following reaction?

H2O + H2SO4 ↔ H3O+ + HSO4-

a. H2O and H2SO4 b. H2O and HSO4

-

c. H2O and H3O+ d. H3O+ and HSO4-

Directions: For questions 5-13 please circle the acids and underline the bases in the following reactions. 5. CH3COO- + H3O+ ↔ CH3COOH + H2O 6. H3O + OH- ↔ H2O + H2O 7. HCl + H2O ↔ H3O+ + Cl- 8. NH2

- + H2O ↔ NH3 + OH-

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9. NH4

+ + HSO4- ↔ NH3 + H2SO4

10. HCN + H2O ↔ H3O+ + CN-

11. HClO4 + CH3COOH ↔ ClO4 + CH3COOH2

+ 12. SO4

2- + HNO3 ↔ HSO4- + NO3

-

13. CN- + H2O ↔ HCN + OH- 14. What is an amphoteric substance?

The Power of pH: For each question, the two pH values are being compared. How many times more acidic or basic does the pH of the solution become?

1) pH 5 pH 3 ________________________

2) pH 8 pH 4 ________________________

3) pH 10 pH 7 _______________________

4) pH 14 pH 7 _______________________

5) pH 4 pH 3 ________________________

6) pH 7 pH 3 ________________________

7) pH 5 pH 1 ________________________

8) pH 9 pH 3 ________________________

9) pH 8 pH 6 ________________________

10) pH 3 pH 6 ________________________

11) pH 1 pH 3 ________________________

12) pH 2 pH 7 ________________________

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Circle the answer the best completes the following sentences: 13) The pH scale was developed to express ([H+]/[OH-]) as a number between 0

and 14.

14) A pH of 1 is a (strong/weak) (acid/base).

15) A pH of 8 is a (strong/weak) (acid/base).

16) In an acid, the [H+] </> [OH-].

17) In a base, the [H+] </> [OH-]. 18) A decrease from 5 to 4 on the pH scale represents a tenfold

(increase/decrease) in the concentration of ([H+] / [OH-]).

19) Strong acids and bases will dissociate (completely/slightly).

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The pH Scale: A liquid may be an acid, base, or neutral. The degree of acidity or basicity can be measured by using the pH scale. The initials pH stand for the “power of Hydrogen” or for “Potential of Hydrogen.” The scale is divided into three areas: Acid (readings below 7), neutral (reading of 7), and basic (readings above 7). The strength of an acid or base depends on its ability to dissociate to form ions. When an acid or base completely ionizes or breaks down then we have a strong acid or base. For example, when 100 molecules of HCl dissolve in water, all 100 molecules dissociate to form H+ ions and Cl- ions:

HCl + H20 ↔ H+ (aq) + Cl- (aq)

A weak acid or base however only ionize or break down slightly. The fact that HCl dissociates so easily makes it a strong acid, and a good electrolyte. A weak acid on the other hand may only dissociate to form 1 H+ ion out of 100.

Each pH unit represents a tenfold difference of the H+ and OH- concentration. It is this mathematical feature that makes the pH scale so compact. For example a solution of pH 2 is not twice as acidic as a solution of pH 4, but a hundred times more acidic. The pH of 5 is ten times more acidic than a pH of 6. So when the pH of a solution changes slightly, it actually changes the concentrations of H+ and OH- substantially.

Measuring pH: To measure the pH of a solution we use pH indicators. A pH indicator is a paper strip or liquid solution that contains special chemicals or dyes that will change colors at different pH’s. An indicator is actually something called a Bronsted-Lowry conjugate acid-base pair in which the acid is a different color then the base. Common pH indicators can be found in Table M of your reference table.

Let’s take a look at table M. You will notice that it lists common acid-base indicators. For each indicator the name, an approximate pH range for color change and the color change is noted. Looking at bromthymol blue you will see that the color will change from yellow to blue at 6.0-7.6. Therefore, acids will maintain a yellow color, while bases will be blue. The diagram on the following page indicates the color change you will observe when using bromthymol blue at various pH’s.

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0 6.0 7.6 14

Approximate pH range for color change: 6.0-7.6 Color of acid form: yellow Color of base form: blue

1. Given the pH scale below shade acids red, bases blue, and any neutral values green.

1 2 3 4 5 6 7 8 9 10 11 12 13 14

2. Will an acidic solution have more [H+] or [OH-] in solution? _______________

3. Will a basic solution have more [H+] or [OH-] in solution? _________________

4. Will a neutral solution have more [H+] or [OH-] in solution? ________________

5. A pH change from 5 to 6 will result in a decrease in how much [H+]? _________

6. A pH change from 9 to 7 will result in an increase in how much [H+]? _________

7. What is a pH indicator? ____________________________________________________

pH & Indicators:

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Given the pH of the following common substances determine what color the indicator will turn when placed in each substance.

Substance pH Methyl

Orange Bromthymol Blue

Phenolphthalein Litmus Bromcresol green

Thymol blue

Stomach Acid

2

Cola Drink

3

Blood 7.5

Pure Water

7.0

Oven Cleaner

14

Tomatoes 4

Milk 6.5

Detergent 10

Coffee 5

Household Cleaners

11

For the following choose an appropriate indicator to note a transformation.

20) endpoint pH = 9 21) endpoint pH = 5

22) endpoint pH = 3

pH:

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pH is a scale that measures the hydronium ion (H+) concentration of a solution. A pH of less than 7 indicates an acidic solution. A solution with a pH of 7 is neutral. A solution with a pH of 7 to 14 is basic and contains a higher concentration of hydroxide ions than hydronium ions. Indicators are substances that change color in the presence of certain ions. Phenolphthalein is colorless in an acid and a neutral solution, but pink in a base. Litmus is red in an acid and blue in a base. This is outlined on Table M of the Reference Tables. For each of the following substances indicate the pH range expected: acid = pH < 7, neutral = pH = 7, or base = pH > 7. Also indicate the color the indicator will appear based on these values. Finally, state if the substance is an acid (A) or a base (B).

Solution PH range Methyl Orange

Thymol Blue

Litmus Brom- Cresol Green

Phenol- Phthalein

Bromo Thymol

blue

Acid or Base?

Vinegar

1.3

Soap

8.4

Cola

3.2

Ammonia

12

Rain

6.4

Milk of Magnesia

8.1

Milk

6.6

Saliva

6.5

Coffee

5.2

Gastric juices

1.5

Human blood

7.4

OJ

2.1

Kool-Aid

6.4

Drain cleaner

1.8

Bleach

6.2

Shampoo

6.3

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Neutralization Reactions: Remember that: Acid + Base Salt + Water Using the above general reaction, complete the following reactions with correct formulas. Then balance the entire double replacement reaction. Also name the salt that is produced in the space provided below the product side of the reaction. 1) HNO3(aq) + KOH(aq) 2) HCl(aq) + Ca(OH)2(aq) 3) H2SO4(aq) + NaOH(aq) 4) H3PO4(aq) + NaOH(aq) 5) NH4OH(aq) + HI(aq) 6) HClO(aq) + NaOH(aq) 7) Mg(OH)2 + CH3COOH 8) HNO3 + Al(OH)3

9) H3PO4 + LiOH

10) H2SO4 + Mg(OH)2 11) NH4OH + HCl

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Writing Balanced Reactions:

Directions: In the following reactions an acid is reacting with a base in neutralization reactions. Write out the reaction and balance the equation.

1. Hydrochloric acid reacts with potassium

hydroxide

2. A sample of hydrochloric acid neutralizes calcium hydroxide

3. Ammonia reacts with perchloric acid

4. Aluminum hydroxide is mixed with sulfuric acid

5. Hydrobromic acid neutralizes a sample of sodium hydroxide

6. A solution of HCl reacts with a solution of Ba(OH)2

7. KCN neutralizes HClO

8. HBr neutralizes calcium hydroxide

9. HCN reacts with NaOH

CHALLENGE: A volume of 10 mL of 0.75 M sodium hydroxide neutralizes a 30 mL sample of hypochlorous acid. Write a balanced equation for the reaction and calculate the concentration of the acid.

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ACID-BASE TITRATIONS: To determine the concentration of an acid (or base), we can react it with a base (or acid) of known concentration until it is completely neutralized. This point of exact neutralization, know as the endpoint or equivalence point, is noted by the change in color of the indicator. We use the following Titration formula from our Table T (Reference Tables):

MAVA = MBVB

Solve the following problems. SHOW ALL WORK! 1. A 25.0 mL sample of HCl was titrated to the endpoint with 15.0 mL of 2.0 M NaOH.

What is the molarity of the HCl? 2. A 10.0 mL sample of H2SO4 was exactly neutralized by 13.5 mL of 1.0 M KOH. What is

the molarity of the H2SO4?

3. How much 1.5 M NaOH is necessary to exactly neutralize 20.0 mL of 2.5 M H3PO4?

4. How much of 0.5 M HNO3 is necessary to titrate 25.0 mL of 0.05 M Ca(OH)2 solution to the endpoint?

5. What is the molarity of a NaOH solution if 15.0 mL is exactly neutralized by 7.5 mL of a 0.02 M HC2H3O2 solution?

Titration Practice:

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A titration was set up and used to determine the unknown molar concentration of a solution of NaOH. A 1.2 M HCl solution was used as the titration standard. The following data were collected.

Trial 1 Trial 2 Trial 3 Trial 4 Volume of 1.2 M HCl

10.0 mL

10.0 mL

10.0 mL

10.0 mL

Initial Reading of NaOH

0.0 mL

12.2 mL

23.2 mL

35.2 mL

Final Reading of NaOH

12.2 mL

23.2 mL

35.2 mL

47.7 mL

Volume of NaOH used (mL)

Molarity of NaOH (M)

1) Calculate the volume of NaOH used to neutralize the acid for each trial. Record in

data table above. Show one sample calculation below.

2) Using the MAVA = MBVB formula calculate the molarity of the base for each trial. Record in data table above. Show one sample calculation below.

3) Calculate the average molarity of the NaOH using your results from question 2.

Your answer must include the correct number of significant figures and the correct units.

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4) According to Reference Table M, what indicator would be most appropriate in determining the end point of this titration? Explain the reasoning behind your choice.

5) Explain why it is better to use the average data from multiple trials rather than

the data from a single trial to calculate the results of the titration.

6) If 3.00 liters of 2M HCl neutralizes 1.00 liter of NaOH, what is the molarity of the NaOH?

7) If 40mL of 2.50M HCl neutralizes 500mL of KOH, what is the molarity of the

KOH?

8) If 2.00 liters of 4.00M KOH neutralizes a HNO3 solution whose concentration is

8.00M, how many liters of HNO3 were neutralized? 9) How many mL of 1.00M HCl are needed to neutralize 400mL of 0.200M NaOH?

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10) How many milliliters of 4.00 M NaOH are required to exactly neutralize 50.0 milliliters of a 2.00 M solution of HNO3?

11) ** If 21.0mL of 0.100M H2SO4 neutralizes 42.0mL of NaOH, what is the molarity of

the NaOH?

12) ** How many mL of 0.500M HNO3 are needed to neutralize 250mL of 2.50M

Ca(OH)2?

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Titration Calculation Chart: MA VA MB VB

1

1.00M

25mL

4.00M

2

2.00M

25mL

50mL

3

3.00M

50mL

100mL

4

1L

3.00M

2L

5

1.50M

3.00M

500mL

6

6.00M

2.00M

75mL

7

200mL

4.00M

150mL

8

5.00M

100mL

2.50M

9

3.5M

7.00M

200mL

10

2.50M

250mL

5.00M

*Assume all acids and bases are MONOPROTIC

More Titration Calculations:

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1) How many milliliters of 0.2M KOH are

needed to neutralize 20mL of 0.1M HCl?

2) How many moles of HCl are in 20mL of a

0.1M solution? 3) If 6mL of 1M HCl is exactly neutralized

by 3mL of KOH, what is the molarity of the KOH?

4) A 30 mL sample of HCl is completely

neutralized by 10mL of a 1.5M NaOH solution. What is the molarity of the HCl solution?

5) What is the total number of moles of

hydrogen ion that will be neutralized by 2.0 moles of hydroxide ion?

6) What is the molarity of a 250mL HCl solution that contains 0.25 moles of HCl?

7) Equal volumes of 0.5M HCl and 0.5M NaOH

are mixed. The total volume of the mixture is 2L. What is the pH of the solution?

8) How many moles of HCl can be neutralized

by 0.1 liters of a 0.5M NaOH? 9) How many milliliters of 5M NaOH are

needed to neutralize 40mL of 2M H2SO4? 10) How many liters of 0.2M HCl are needed to

neutralize 20 liters of 0.1M Ca(OH)2?

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Neutralization Reactions & Titrations:

1) When 34.2 mL of a 1.02 M sodium hydroxide solution is added from a burette to 25.00 mL of a phosphoric acid solution that contains phenolphthalein, the solution changes from colorless to red.

A.) Write the balanced equation for the titration reaction.

B.) Calculate the molarity of the phosphoric acid.

2) 34.57 mL of an acetic acid solution are needed to neutralize 25.19 mL of 0.1025 M sodium hydroxide.

A.) Write the balanced equation for the titration reaction.

B.) Calculate the molarity of the acetic acid solution.

3) 0.300M nitric acid is titrated with 24 mL of 0.250M potassium hydroxide.

A.) Write the balanced equation for the titration reaction.

B.) Calculate the volume of the nitric acid.

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4) 0.250M sodium hydroxide is used to neutralize 116 mL of 0.0625M sulfuric acid.

A.) Write the balanced equation for the titration reaction.

B.) Calculate the volume of the sodium hydroxide.

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Show all work for the following word problems:

1) How many milliliters of 2.5 M HCl are required to exactly neutralize 1.5 L of 5.0 M NaOH? Use Table T.

2) A 2.0-mL sample of NaOH solution is exactly neutralized by 4.0 mL of 3.0 M HCl solution. What is the concentration of the NaOH solution?

3) A 30. mL volume of HCl is titrated with 23 mL of 0.20 M NaOH. What is the molarity of HCl in this solution?

4) A 26 mL volume of NH3 is titrated with 23 mL of 0.20 M HCl. What is the molarity of NH3 in this solution?

5) A 40. mL volume of H2SO4 is titrated with 38 mL of 0.24 M NaOH. What is the molarity of H2SO4 in this solution? (Be careful with this one!)

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Reactions with Acids and Bases:

1) Using Table J in your Reference Tables, list two metals that will react with H2 (or an

acid) _________________

2) Using Table J in your Reference Tables, list two metals that will NOT react with H2

(or an acid) _________________

3) What type of reaction (of the four we have learned) is involved when an acid reacts

with a metal? _________________________________________

4) Write the general formula (using ABC etc.) for this type of reaction

5) Predict the products of the following reaction:

Mg + HNO3 ________ + _________

5) Will copper react with an acid? ______ Explain your answer in terms of activity.

________________________________________________________________

6) Predict the products of the following neutralization reaction:

RbOH + HBr ___________ + ____________

7) Set up a reaction below that would occur between HNO3 and LiOH. Predict the products using your general reaction for neutralization reactions.

8) Predict the products of the following reaction. Remember to create your formulas

using the criss cross rule! BALANCE the reaction also.

H2SO4 + Ca(OH)2 ____________ + _____________

Name salt that was produced _________________________________

9) According to your reference tables, which metal would react spontaneously with hydrochloric acid?

a. Gold b. Silver c. Copper d. Zinc

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WORKSHEET ON THE REACTIVITY SERIES 1) Use table J and your knowledge of chemistry to answer the following questions in

complete sentences.

a) Why does gold occur native (uncombined) whereas zinc does not?

………………………………………………………………………………………………

………………………………………………………………………………………………

b) Why was silver used to make coins in the past?

………………………………………………………………………………………………

………………………………………………………………………………………………

c) Why is copper used to make electrical cables and wires?

………………………………………………………………………………………………

………………………………………………………………………………………………

d) Why do we know so little about the lifestyles of the people of the Iron Age?

………………………………………………………………………………………………

……………………………………………………………………………………………… 2) Rank the following metals in order of reactivity (most reactive = 1, least reactive = 4)

_____ zinc _____ sodium _____ magnesium _____ copper

a) Which metals will react when added to dilute hydrochloric acid? Describe the reaction.

………………………………………………………………………………………………

………………………………………………………………………………………………

b) Which of the four metals would be suitable for making saucepans? Explain why the others are not.

………………………………………………………………………………………………

………………………………………………………………………………………………

c) Which of the four metals forms a protective coating when it oxidizes?

………………………………………………………………………………………………

3) Describe what you would see if you dropped a piece of magnesium ribbon into some

copper sulphate solution in a test tube. Write a word equation for the reaction.

………………………………………………………………………………………………

……………………………………………………………………………………………...

………………………………………………………………………………………………

………………………………………………………………………………………………

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4) Complete the following word equations.

a) zinc + lead nitrate solution ………………………………………………………….

b) iron + zinc sulphate solution ………………………………………………………..

c) lead + copper nitrate solution ………………………………………………………..

d) magnesium + zinc chloride solution ………………………………………………...

e) copper + sodium chloride solution ………………………………………………….

f) zinc + iron sulphate solution ………………………………………………………..

g) gold + silver nitrate solution ………………………………………………………...

h) magnesium + calcium nitrate solution ………………………………………………

5) Three metals X, Y and Z have the following reactions:-

Y will displace X from a solution of its salt.

Z will displace both X and Y from solutions of their salts.

Place the three metals in order of reactivity, starting with the least reactive.

………………………………………………………………………………………………

6) Here is a list of metals in order of decreasing reactivity. Q and R are mystery metals.

K > Q > Ca > Mg > Al > Zn > R > Fe > Cu

a) Will Q react with cold water? …………

b) Will R react with cold water? …………

c) Will R react with dilute hydrochloric acid? ...……….

d) Will R displace copper from copper sulphate solution? ...……….

e) Write word equations for any reactions in parts a) to d)

………………………………………………………………………………………………….

………………………………………………………………………………………………….

………………………………………………………………………………………………….

………………………………………………………………………………………………….

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a) ______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

b) ______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

c) ______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

d) ______________________________________________________________________________

______________________________________________________________________________

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a) ______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

b) ______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

c) ______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

d) ______________________________________________________________________________

______________________________________________________________________________