4.E: The Mole Concept (Exercises)

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The following questions are related to the material covered in this chapter, however they may not be presented in the same order that they were in your chapter. For additional examples also check here (5.2 only) or here (5.75, 5.80, 5.105, 5.106 only)

4.1-4.5: Avogadro's Number, Molar Mass and the Mole

Conceptual Problems

Please be sure you are familiar with the topics discussed in Essential Skills 2 before proceeding to the Conceptual Problems.

Describe the relationship between an atomic mass unit and a gram.
Is it correct to say that ethanol has a formula mass of 46? Why or why not?
If 2 mol of sodium reacts completely with 1 mol of chlorine to produce sodium chloride, does this mean that 2 g of sodium reacts completely with 1 g of chlorine to give the same product? Explain your answer.
Construct a flowchart to show how you would calculate the number of moles of silicon in a 37.0 g sample of orthoclase (KAlSi₃O₈), a mineral used in the manufacture of porcelain.
Construct a flowchart to show how you would calculate the number of moles of nitrogen in a 22.4 g sample of nitroglycerin that contains 18.5% nitrogen by mass.

Numerical Problems

Please be sure you are familiar with the topics discussed in Essential Skills 2 before proceeding to the Numerical Problems.

1. Derive an expression that relates the number of molecules in a sample of a substance to its mass and molecular mass.

2. Calculate the molecular mass or formula mass of each compound.

KCl (potassium chloride)
NaCN (sodium cyanide)
H₂S (hydrogen sulfide)
NaN₃ (sodium azide)
H₂CO₃ (carbonic acid)
K₂O (potassium oxide)
Al(NO₃)₃ (aluminum nitrate)
Cu(ClO₄)₂ [copper(II) perchlorate]

3. Calculate the molecular mass or formula mass of each compound.

V₂O₄ (vanadium(IV) oxide)
CaSiO₃ (calcium silicate)
BiOCl (bismuth oxychloride)
CH₃COOH (acetic acid)
Ag₂SO₄ (silver sulfate)
Na₂CO₃ (sodium carbonate)
(CH₃)₂CHOH (isopropyl alcohol)

8. Calculate the number of moles in 5.00 × 10² g of each substance. How many molecules or formula units are present in each sample?

a. CaO (lime)

b. CaCO₃(chalk)

c. C₁₂H₂₂O₁₁ [sucrose (cane sugar)]

d. NaOCl (bleach)

e. CO₂ (dry ice)

9. Calculate the mass in grams of each sample.

a. 0.520 mol of N₂O₄

b. 1.63 mol of C₆H₄Br₂

c. 4.62 mol of (NH₄)₂SO₃

10. Give the number of molecules or formula units in each sample.

a. 1.30 × 10⁻² mol of SCl₂

b. 1.03 mol of N₂O₅

c. 0.265 mol of Ag₂Cr₂O₇

11. Give the number of moles in each sample.

a. 9.58 × 10²⁶ molecules of Cl₂

b. 3.62 × 10²⁷ formula units of KCl

c. 6.94 × 10²⁸ formula units of Fe(OH)₂

12. Solutions of iodine are used as antiseptics and disinfectants. How many iodine atoms correspond to 11.0 g of molecular iodine (I₂)?

13. What is the total number of atoms in each sample?

a. 0.431 mol of Li

b. 2.783 mol of methanol (CH₃OH)

c. 0.0361 mol of CoCO₃

d. 1.002 mol of SeBr₂O

14. What is the total number of atoms in each sample?

a. 0.980 mol of Na

b. 2.35 mol of O₂

c. 1.83 mol of Ag₂S

d. 1.23 mol of propane (C₃H₈)

15. What is the total number of atoms in each sample?

a. 2.48 g of HBr

b. 4.77 g of CS₂

c. 1.89 g of NaOH

d. 1.46 g of SrC₂O₄

16. Decide whether each statement is true or false and explain your reasoning.

There are more molecules in 0.5 mol of Cl₂than in 0.5 mol of H₂.
One mole of H₂ has 6.022 × 10²³ hydrogen atoms.
The molecular mass of H₂O is 18.0 amu.
The formula mass of benzene is 78 amu.

17. Complete the following table.

Substance	Mass (g)	Number of Moles	Number of Molecules or Formula Units	Number of Atoms or Ions
MgCl₂	37.62	a.	b.	c.
AgNO₃	d.	2.84	e.	f.
BH₄Cl	g.	h.	8.93 × 10²⁵	i.
K₂S	j	k.	l.	7.69 × 10²⁶
H₂SO₄	m.	1.29	n.	o.
C₆H₁₄	11.84	p.	q.	r.
HClO₃	s.	t.	2.45 × 10²⁶	u.

18. Give the formula mass or the molecular mass of each substance.

\(PbClF\)
\(Cu_2P_2O_7\)
\(BiONO_3\)
\(Tl_2SeO_4\)

19. Give the formula mass or the molecular mass of each substance.

\(MoCl_5\)
\(B_2O_3\)
\(UO_2CO_3\)
\(NH_4UO_2AsO_4\)

Conceptual Answers

While both are units of mass, a gram is Avogadro’s number of atomic mass units so you would multiply the number of amu by 6.022x10^23 to find total number of grams
The correct way to state formula mass of ethanol is to show the units of mass which is amu.
No because moles and weight operate on different set of standards meaning that they’re not equal to each other. This means that moles of different compounds contain different weights. For example, 2 moles of Na = 2 x 22.989 g = 45.98g while 1 mole of Cl = 1 x 35.453 g = 35.453 g Cl. This makes the sodium react completely with chlorine. 2g of sodium would react with = (35.453/45.978) x 2 = 1.542 g Cl
Construct a flowchart to show how you would calculate the number of moles of silicon in a 37.0 g sample of orthoclase (KAlSi₃O₈), a mineral used in the manufacture of porcelain
1. .
Construct a flowchart to show how you would calculate the number of moles of nitrogen in a 22.4 g sample of nitroglycerin that contains 18.5% nitrogen by mass.
The information required to determine the mass of the solute would be the molarity of the solution because once that is achieved, volume of the solution and molar mass of the solute can be used to calculate the total mass. A derivatization that achieves this goes as: Molarity = moles of solute / volume of solution in liter -> Moles = molarity x volume in liter -> Mass= moles x molar mass.

Numerical Answers

1. Derive an expression that relates the number of molecules in a sample of a substance to its mass and molecular mass.

Derivative

2. Calculate the molecular mass or formula mass of each compound.

74.55 amu
49.01 amu
34.08 amu
65.01 amu
62.02 amu
94.20 amu
213.00 amu
262.45 amu

3. Calculate the molecular mass or formula mass of each compound.

165.88 amu
116.16 amu
260.43 amu
60.05 amu
311.80 amu
105.99 amu
60.10 amu

4. Calculate the molar mass of each compound.

a. 153.82 g/mol

b. 80.06 g/mol

c. 92.01 g/mol

d. 70.13 g/mol

e. 74.12 g/mol

5. Calculate the molar mass of each compound.

a. 92.45 g/mol

b. 135.04 g/mol

c. 44.01 g/mol

d. 40.06 g/mol

6. For each compound, write the condensed formula, name the compound, and give its molar mass.

a. C₅H₁₀O₂, Valeric Acid, 102.13 g/mol

b. H₃PO₃_,Phosphorous acid, 82 g/mol

7. For each compound, write the condensed formula, name the compound, and give its molar mass.

a. C₂H₅NH₂_,Ethylamine, 45.08 g/mol

b. HIO₃_,Iodic acid, 175.91 g/mol

8. Calculate the number of moles in 5.00 × 10² g of each substance. How many molecules or formula units are present in each sample?

a. 5.37 × 10²⁴ mol

b. 3.01 × 10²⁴ mol

c. 8.80 × 10²³ mol

d. 4.04 × 10²⁴ mol

e. 6.84 × 10²⁴ mol

9. Calculate the mass in grams of each sample.

a. 47.85 grams

b. 384.52 grams

c. 536.57 grams

10. Give the number of molecules or formula units in each sample.

a. 7.83x10²¹molecules

b. 6.20x10²³molecules

c. 1.60x10²³ molecules

11. Give the number of moles in each sample.

a. 1590.8 moles

b. 6011.3 moles

c. 115244.1 moles

12. Solutions of iodine are used as antiseptics and disinfectants. How many iodine atoms correspond to 11.0 g of molecular iodine (I₂)?

2.61 x10²² molecules

13. What is the total number of atoms in each sample?

a. 2.60x10²³ atoms

b. 1.01x10²⁵ atoms

c. 1.09x10²³ atoms

d. 2.41x10²⁴ atoms

14. What is the total number of atoms in each sample?

a. 5.9x10²³ atoms

b. 2.8x10²⁴ atoms

c. 3.31x10²⁴ atoms

d. 8.15x10²⁴ atoms

15. What is the total number of atoms in each sample?

a. 3.69x10²² atoms

b. 1.13x10²³ atoms

c. 8.54x10²² atoms

d. 3.50x10²³ atoms

16.

a. False, the number of molecules in 0.5 mol Cl2 are the same amount of molecules in H2

b. False, the number of molecules in H2 is 2 x (6.022 x10^23) H atoms

c. True, 2 H (1.01 amu) + 1 O (16.01) = 18.0 amu

d. True, C6H6 -> 12(6) + 1(6) = 78 amu

17. Complete the following table

a. 0.39

b. 2.36x10^23

c. 7.08x10^23

d. 482.8

e. 1.71x10^24

f. 8.55x10^24

g. 7932.7

h. 148.3

i. 5.36x10^26

j. 46938.5

k. 425.7

l. 1276.98

m. 126.5

n. 7.77x10^23

o. 5.44x10^24

p. 0.14

q. 8.27x10^22

r. 1.65x10^24

s. 34358

t. 406.8

u. 1.23x10^2

18. Give the formula mass or the molecular mass of each substance.

261.67 amu
301.04 amu
286.98 amu
551.73 amu

19. Give the formula mass or the molecular mass of each substance.

273.21 amu
69.62 amu
330.04 amu
426.99 amu

4.6-4.9: Percent Composition, Empirical Formula, and Molecular Formula

Conceptual Problems

What is the relationship between an empirical formula and a molecular formula
Construct a flowchart showing how you would determine the empirical formula of a compound from its percent composition.

Numerical Problems

1. What is the mass percentage of water in each hydrate?

a. H₃AsO₄·5H₂O

b. NH₄NiCl₃·6H₂O

c. Al(NO₃)₃·9H₂O

2. What is the mass percentage of water in each hydrate?

a. CaSO₄·2H₂O

b. Fe(NO₃)₃·9H₂O

c. (NH₄)₃ZrOH(CO₃)₃·2H₂O

3. Which of the following has the greatest mass percentage of oxygen—KMnO₄, K₂Cr₂O₇, or Fe₂O₃?

4. Which of the following has the greatest mass percentage of oxygen—ThOCl₂, MgCO₃, or NO₂Cl?

5. Calculate the percent composition of the element shown in bold in each compound.

a. SbBr₃

b. As₂I₄

c. AlPO₄

d. C₆H₁₀O

6. Calculate the percent composition of the element shown in bold in each compound.

a. HBrO₃

b CsReO₄

c. C₃H₈O

d. FeSO₄

7. A sample of a chromium compound has a molar mass of 151.99 g/mol. Elemental analysis of the compound shows that it contains 68.43% chromium and 31.57% oxygen. What is the identity of the compound?

8. The percentages of iron and oxygen in the three most common binary compounds of iron and oxygen are given in the following table. Write the empirical formulas of these three compounds.

Compound	% Iron	% Oxygen
1	69.9	30.1
2	77.7	22.3
3	72.4	27.6

9. What is the mass percentage of water in each hydrate?

a. LiCl·H₂O

b. MgSO₄·7H₂O

c. Sr(NO₃)₂·4H₂O

10. What is the mass percentage of water in each hydrate?

a. CaHPO₄·2H₂O

b. FeCl₂·4H₂O

c. Mg(NO₃)₂·4H₂O

11. Two hydrates were weighed, heated to drive off the waters of hydration, and then cooled. The residues were then reweighed. Based on the following results, what are the formulas of the hydrates?

Compound	Initial Mass (g)	Mass after Cooling (g)
NiSO₄·xH₂O	2.08	1.22
CoCl₂·xH₂O	1.62	0.88

12. Which contains the greatest mass percentage of sulfur—FeS₂, Na₂S₂O₄, or Na₂S?

13. Given equal masses of each, which contains the greatest mass percentage of sulfur—NaHSO₄ or K₂SO₄?

14. Calculate the mass percentage of oxygen in each polyatomic ion.

a. bicarbonate

b. chromate

c. acetate

d. sulfite

15. Calculate the mass percentage of oxygen in each polyatomic ion.

a. oxalate

b. nitrite

c. dihydrogen phosphate

d. thiocyanate

16. The empirical formula of garnet, a gemstone, is Fe₃Al₂Si₃O₁₂. An analysis of a sample of garnet gave a value of 13.8% for the mass percentage of silicon. Is this consistent with the empirical formula?

17. A compound has the empirical formula C₂H₄O, and its formula mass is 88 g. What is its molecular formula?

18. Mirex is an insecticide that contains 22.01% carbon and 77.99% chlorine. It has a molecular mass of 545.59 g. What is its empirical formula? What is its molecular formula?

27. Calculate the formula mass or the molecular mass of each compound.

a. MoCl₅

b. B₂O₃

c. bromobenzene

d. cyclohexene

e. phosphoric acid

f. ethylamine

Conceptual Answers

1) What is the relationship between an empirical formula and a molecular formula

An empirical formula refers to the simplest ratio of elements that is obtained from a chemical formula while a molecular formula is calculated to show the actual formula of a molecular compound.

2) Construct a flowchart showing how you would determine the empirical formula of a compound from its percent composition.

Numerical Answers

a. What is the formula mass of each species?

a. 53.49146 amu

b. 49.0072 amu

c. 58.3197 amu

d. 310.177 amu

e. 73.891 amu

f. 81.07 amu

b. What is the molecular or formula mass of each compound?

a.158.034 amu

b. 142.04 amu

c. 27.0253 amu

d. 97.181 amu

e. 124.1 amu

f. 65.99 amu

1. To two decimal places, the percentages are:

a. 5.97%

b. 37.12%

c. 43.22%

2. Percentage of Oxygen in each hydrates are:

a. 20.93%

b. 40.13%

c. 9.52%

3. % oxygen: KMnO₄, 40.50%; K₂Cr₂O₇, 38.07%; Fe₂O₃, 30.06%

4. % oxygen: ThOCl2, 5.02%; MgCO3, 56.93%; NO2Cl, 39.28%

5. To two decimal places, the percentages are:

a. 66.32% Br

b. 22.79% As

c. 25.40% P

d. 73.43% C

a. 61.98% Br

b. 34.69% Cs

c. 59.96% C

d. 21.11% S

7. Cr₂O₃.

8. Empirical Formulas

Fe₂O₃
Fe₄O₄
Fe₆O₈

9. To two decimal places, the percentages are:

a. 29.82%

b. 51.16%

c. 25.40%

10. What is the mass percentage of water in each hydrate?

a. 20.94%

b. 36.25%

c. 32.70%

11. NiSO₄ · 6H₂O and CoCl₂ · 6H₂O

12. FeS₂

13. NaHSO₄

14. Calculate the mass percentage of oxygen in each polyatomic ion.

a. 78.66%

b. 55.17%

c. 54.19%

d. 59.95%

15.

a. 72.71%

b. 69.55%

c. 65.99%

d. 0%

No, the calculated mass percentage of silicon in garnet is 16.93%

17. C₄H₈O₂

18.

Empirical Formula: C₁₀Cl₁₂

Molecular Formula: C₁₀Cl₁₂

19. How many moles of CO₂ and H₂O will be produced by combustion analysis of 0.010 mol of styrene?

Moles of CO2: 0.08 mol CO₂

Moles of H2O: 0.04 mol H₂O

20. How many moles of CO₂, H₂O, and N₂ will be produced by combustion analysis of 0.0080 mol of aniline?

Mole of CO2: 0.048 mol CO₂

Mole of H2O: 0.028 mol H₂O

Mole of N2: 0.004 mol N₂

21. How many moles of CO₂, H₂O, and N₂ will be produced by combustion analysis of 0.0074 mol of aspartame?

Mole of CO2: 0.104 mol CO₂

Mole of H2O: 0.666 mol H₂O

Mole of N2: 0.0074 mol N₂

22. How many moles of CO₂, H₂O, N₂, and SO₂ will be produced by combustion analysis of 0.0060 mol of penicillin G?

Mole of CO2: 0.096 mol CO₂

Mole of H2O: 0.054 mol H₂O

Mole of N2: 0.060 mol N₂

Mole of SO2: 0.060 mol SO₂

23.

a. 27.6 mg C and 1.98 mg H

b. 5.2 mg O

c. 15%

d. C₇H₆O

e. C₇H₆O

24. Salicylic acid is used to make aspirin. It contains only carbon, oxygen, and hydrogen. Combustion of a 43.5 mg sample of this compound produced 97.1 mg of CO₂ and 17.0 mg of H₂O.

a. What is the mass of oxygen in the sample?

70.4mg

b. What is the mass percentage of oxygen in the sample?

61.70%

c. What is the empirical formula of salicylic acid?

C₇H₆O₃

d. The molar mass of salicylic acid is 138.12 g/mol. What is its molecular formula?

C₇H₆O₃

25. hydrocyanic acid, HCN

26. Calculate the formula mass or the molecular mass of each compound.

a. 130.1849 amu

b. 60.1 amu

c. 158.034 amu

d. 323.4 amu

e. 82.07 amu

f. 106.17 amu

27. To two decimal places, the values are:

a. 273.23 amu

b. 69.62 amu

c. 157.01 amu

d. 82.14 amu

e. 98.00 amu

f. 45.08 amu

28. Cyclobutene

29. Urea