# 2: Atoms, Molecules, and Ions

## Protons, Neutrons, and Electrons

Exercise $$\PageIndex{1.a}$$

How are electrons and protons similar? How are they different?

Both are subatomic particles. Protons are positively charged, and reside in an atom’s nucleus. Whereas, electrons are negatively charged and reside outside an atom’s nucleus.

Exercise $$\PageIndex{1.b}$$

How are protons and neutrons similar? How are they different?

Both are subatomic particles that reside in an atom’s nucleus. Both have approximately the same mass. Protons are positively charged, whereas neutrons are uncharged.

## Dalton's Theory

Exercise $$\PageIndex{2.a}$$

The existence of isotopes violates one of the original ideas of Dalton’s atomic theory. Which one?

Dalton originally thought that all atoms of a particular element had identical properties, including mass. Thus, the concept of isotopes, in which an element has different masses, was a violation of the original idea. To account for the existence of isotopes, the second postulate of his atomic theory was modified to state that atoms of the same element must have identical chemical properties.

(See 2.1.2.2)

## Atomic Number, Mass Number, and Atomic Mass Units

Exercise $$\PageIndex{3.a}$$

Write the symbol for each of the following ions:

1. the ion with a 1+ charge, atomic number 55, and mass number 133
2. the ion with 54 electrons, 53 protons, and 74 neutrons
3. the ion with atomic number 15, mass number 31, and a 3− charge
4. the ion with 24 electrons, 30 neutrons, and a 3+ charge

(see

133Cs+

127I

31P3+

57Co3+

Exercise $$\PageIndex{3.b}$$

Average atomic masses listed by IUPAC are based on a study of experimental results. Bromine has two isotopes 79Br and 81Br, whose masses (78.9183 and 80.9163 amu) and abundances (50.69% and 49.31%) were determined in earlier experiments. Calculate the average atomic mass of bromine based on these experiments.

 Isotope Mass Percent Abundance Fraction 79Br 78.9183amu 50.69% 0.5069 81Br 80.9163 amu 49.31% 0.4931

${X_A}{(m_A)} +{X_B}{(m_B)} = {m_{ave}}$

${X_{79Br}}{(m_{79Br})} +{X_{81Br}}{(m_{81Br})} = {m_{ave}}$

${0.5069}{(78.9183amu)} +{0.4931}{(80.9163 amu)} = {m_{ave}}$

${m_{ave}}=79.904 amu$

Exercise $$\PageIndex{3.c}$$

Average atomic masses listed by IUPAC are based on a study of experimental results. The average atomic mass of Copper is 63.546 amu. Copper has two isotopes 63Cu and 65Cu. The mass of 63Cu was determined in an earlier experiment and found to be 62.930 amu. The abundance of 63Cu was found to be 69.17%. Calculate the mass and abundance of 65Cu.

 Isotope Mass Percent Abundance Fraction 63Cu 62.930 amu 69.17% 0.6917 65Cu $$m_B\nonumber$$ $$%_B\nonumber$$ $$X_B\nonumber$$

$X_A + X_B=1$

$X_B=1-X_A$

$X_B=1-0.6917=0.3083=30.83%$

${X_A}{(m_A)} +{X_B}{(m_B)} = {m_{ave}}$

$m_B=\frac{m_{ave}-X_A(m_A)}{X_B}$

$m_B=\frac{63.546amu-0.6917(62.930 amu)}{0.3083}$

$m_B= 64.928amu$

Exercise $$\PageIndex{3.d}$$

Average atomic masses listed by IUPAC are based on a study of experimental results. The average atomic mass of Gallium is 69.723 amu. Gallium has two isotopes 69Ga and 71Ga, whose masses (68.9257 and 70.9249 amu) were determined in earlier experiments. What is the natural abundance of each isotope?

 Isotope Mass Fraction 69Ga 68.9257 amu $$X_A\nonumber$$ 71Ga 70.9249 amu $$X_B\nonumber$$

${X_A}{(m_A)} +{X_B}{(m_B)} = {m_{ave}}$

$X_A + X_B=1$

$X_B=1-X_A$

${X_A}{(m_A)} +{1-X_A}{(m_B)} = {m_{ave}}$

${X_A}=\frac{m_{ave}-m_B}{m_A-m_B}$

${X_A}=\frac{69.723 amu-70.9249amu}{68.9257amu-70.9249amu}$

${X_A}=0.6012$

$X_B=1-X_A$

$X_B=1-0.6012=0.3988$

The natural abundance of 69Ga is 60.12% and of 71Ga is 39.88%

Exercise $$\PageIndex{3.e}$$

In an alternate universe on the planet Htrae, the element Minebro has two isotopes 79Mr and 81Mr, whose masses (78.9183 and 80.9163 amu) and abundances (49.31% and 50.69%) were determined in earlier experiments. Calculate the average atomic mass of Minebro based on these experiments.

 Isotope Mass Percent Abundance Fraction 79Br 78.9183amu 49.31% 0.4931 81Br 80.9163 amu 50.69% 0.5069

${X_A}{(m_A)} +{X_B}{(m_B)} = {m_{ave}}$

${X_{79Br}}{(m_{79Br})} +{X_{81Br}}{(m_{81Br})} = {m_{ave}}$

${0.4931}{(78.9183amu)} +{0.5069}{(80.9163 amu)} = {m_{ave}}$

${m_{ave}}= 79.931amu$

Exercise $$\PageIndex{3.f}$$

In an alternate universe on the planet Htrae, the element Robber has an average atomic mass of 64.494 amu. Robber has two isotopes 63Ru and 65Ru. The mass of 63Ru was determined in an earlier experiment and found to be 62.930 amu. The abundance of 63Ru was found to be 21.72%. Calculate the mass and abundance of 65Ru.

 Isotope Mass Percent Abundance Fraction 63Cu 62.930 amu 21.72% 0.2172 65Cu $$m_B\nonumber$$ $$%_B\nonumber$$ $$X_B\nonumber$$

$X_A + X_B=1$

$X_B=1-X_A$

$X_B=1-0.2172=0.7828=78.28%$

${X_A}{(m_A)} +{X_B}{(m_B)} = {m_{ave}}$

$m_B=\frac{m_{ave}-X_A(m_A)}{X_B}$

$m_B=\frac{64.494amu-0.2172(62.930 amu)}{0.7828}$

$m_B= 64.928$

## Identify Isotopes

Exercise $$\PageIndex{4.a}$$

The following are properties of isotopes of two elements that are essential in our diet. Determine the number of protons, neutrons and electrons in each and name them.

1. atomic number 26, mass number 58, charge of 2+
2. atomic number 53, mass number 127, charge of 1−

Iron, 26 protons, 24 electrons, and 32 neutrons

Iodine, 53 protons, 54 electrons, and 74 neutrons

## Isotope Notation

Exercise $$\PageIndex{5.a}$$

Give the number of protons, electrons, and neutrons in neutral atoms of each of the following isotopes:

1. $$_{3}^{7}\textrm{Li}$$
2. $$_{52}^{125}\textrm{Te}$$
3. $$_{47}^{109}\textrm{Ag}$$
4. $$_{7}^{15}\textrm{N}$$
5. $$_{15}^{31}\textrm{P}$$

3 protons, 3 electrons, 4 neutrons

52 protons, 52 electrons, 73 neutrons

47 protons, 47 electrons, 62 neutrons

7 protons, 7 electrons, 8 neutrons

15 protons, 15 electrons, 16 neutrons

Exercise $$\PageIndex{5.b}$$

Write a symbol for each of the following neutral isotopes. Include the atomic number and mass number for each.

1. the alkali metal with 11 protons and a mass number of 23
2. the noble gas element with and 75 neutrons in its nucleus and 54 electrons in the neutral atom
3. the isotope with 33 protons and 40 neutrons in its nucleus
4. the alkaline earth metal with 88 electrons and 138 neutrons

$$_{11}^{23}\textrm{Na}$$

$$_{54}^{129}\textrm{Xe}$$

$$_{33}^{73}\textrm{As}$$

$$_{88}^{226}\textrm{Ra}$$

## Isotope Abundance and Average Atomic Mass

Exercise $$\PageIndex{6.a}$$

Average atomic masses listed by IUPAC are based on a study of experimental results. Bromine has two isotopes 79Br and 81Br, whose masses (78.9183 and 80.9163 amu) and abundances (50.69% and 49.31%) were determined in earlier experiments. Calculate the average atomic mass of bromine based on these experiments.

NOTE: This problem is also in 2.2: Atomic Number, Mass Number, and Atomic Mass Unit

79.904 amu

Exercise $$\PageIndex{6.b}$$

The average atomic masses of some elements may vary, depending upon the sources of their ores. Naturally occurring boron consists of two isotopes with accurately known masses (10B, 10.0129 amu and 11B, 11.0931 amu). The actual atomic mass of boron can vary from 10.807 to 10.819, depending on whether the mineral source is from Turkey or the United States. Calculate the percent abundances leading to the two values of the average atomic masses of boron from these two countries.

Turkey source: 0.2649 (of 10.0129 amu isotope)

US source: 0.2537 (of 10.0129 amu isotope)

## Metal or Nonmetal

Exercise $$\PageIndex{7.a}$$

Using the periodic table, classify each of the following elements as a metal or a nonmetal, and then further classify each as a main-group (representative) element, transition metal, or inner transition metal:

1. uranium
2. bromine
3. strontium
4. neon
5. gold
6. americium
7. rhodium
8. sulfur
9. carbon
10. potassium

metal, inner transition metal

nonmetal, representative element

metal, representative element

nonmetal, representative element

metal, transition metal

metal, inner transition metal

metal, transition metal

nonmetal, representative element

nonmetal, representative element

metal, representative element

## Periodic Table: Groups

Exercise $$\PageIndex{8.a}$$

Using the periodic table, identify the lightest and heaviest member of each of the following groups:

1. noble gases
2. alkaline earth metals
3. alkali metals
4. chalcogens

He, Og

Be, Ra

Li, Fr

O, Lv

## Periodic Table: Periods

Exercise $$\PageIndex{9.a}$$

Use the periodic table to give the name and symbol for each of the following elements:

1. the noble gas in the same period as germanium
2. the alkaline earth metal in the same period as selenium
3. the halogen in the same period as lithium
4. the chalcogen in the same period as cadmium

krypton, Kr

calcium, Ca

fluorine, F

tellurium, Te

## Diatomic Elements

Exercise $$\PageIndex{10.a}$$

Explain why the symbol for an atom of the element oxygen and the formula for a molecule of oxygen differ.

The symbol for the element oxygen, O, represents both the element and one atom of oxygen. A molecule of oxygen, O2, contains two oxygen atoms; the subscript 2 in the formula must be used to distinguish the diatomic molecule from two single oxygen atoms.

## Isomers

Exercise $$\PageIndex{11.a}$$

Draw or build a molecule with two carbons, six hydrogens, and one oxygen.

1. Draw the structural formula of this molecule and state its name.
2. Can you arrange these atoms to make a different molecule? If so, draw its structural formula and state its name.
3. How are the molecules drawn in (a) and (b) the same? How do they differ? What are they called (the type of relationship between these molecules, not their names).

Ethanol

Methoxymethane, more commonly known as dimethly ether

These molecules has the same chemical composistion (types and number of atoms) but have different chemical structures. They are structural isomers

## Ionic or Covalent Compounds

Exercise $$\PageIndex{12.a}$$

Using the periodic table, predict whether the following chlorides are ionic or covalent: KCl, NCl3, ICl, MgCl2, PCl5, and CCl4.

Ionic: KCl, MgCl2

Covalent: NCl3, ICl, PCl5, CCl4

Exercise $$\PageIndex{12.b}$$

For each of the following compounds, state whether it is ionic or covalent. If it is ionic, write the symbols for the ions involved:

1. NF3
2. BaO
3. (NH4)2CO3
4. Sr(H2PO4)2
5. IBr
6. Na2O

covalent

ionic, Ba2+, O−2

ionic, NH4+, CO3−2

ionic, Sr2+, H2PO4-

covalent

ionic, Na+, O−2

## Ions to Compounds

Exercise $$\PageIndex{13.a}$$

For each of the following pairs of ions, write the symbol for the formula of the compound they will form:

1. Ca2+, S2−
2. $$NH_{4}^{+}$$, $$SO_{4}^{2-}$$
3. Al3+, Br
4. Na+, $$HPO_{4}^{2-}$$
5. Mg2+, $$PO_{4}^{3-}$$

CaS

(NH4)2SO4

AlBr3

Na2HPO4

Mg3(PO4)2

## Name from Molecular Formula

Exercise $$\PageIndex{14.a}$$

Name the following compounds:

1. CsCl
2. BaO
3. K2S
4. BeCl2
5. HBr
6. AlF3

cesium chloride

barium oxide

potassium sulfide

beryllium chloride

hydrogen bromide

aluminum fluoride

Exercise $$\PageIndex{14.b}$$

Each of the following compounds contains a metal that can exhibit more than one ionic charge. Name these compounds:

1. Cr2O3
2. FeCl2
3. CrO3
4. TiCl4
5. CoO
6. MoS2

chromium(III) oxide

iron(II) chloride

chromium(VI) oxide

titanium(IV) chloride

cobalt(II) oxide

molybdenum(IV) sulfide

## Molecular Formula from Name

Exercise $$\PageIndex{15.a}$$

Write the formulas of the following compounds:

1. rubidium bromide
2. magnesium selenide
3. sodium oxide
4. calcium chloride
5. hydrogen fluoride
6. gallium phosphide
7. aluminum bromide
8. ammonium sulfate
RbBr
MgSe
Na2O
CaCl2
HF
GaP
AlBr3
(NH4)2SO4

Exercise $$\PageIndex{15.b}$$

Write the formulas of the following compounds:

1. chlorine dioxide
2. dinitrogen tetraoxide
3. potassium phosphide
4. silver(I) sulfide
5. aluminum nitride
6. silicon dioxide
ClO2
N2O4
K3P
Ag2S
AlN
SiO2

Exercise $$\PageIndex{15.c}$$

The following ionic compounds are found in common household products. Write the formulas for each compound:

1. potassium phosphate
2. copper(II) sulfate
3. calcium chloride
4. titanium dioxide
5. ammonium nitrate
6. sodium bisulfate (the common name for sodium hydrogen sulfate)
K3PO4
CuSO4
CaCl2
TiO2
NH4NO3
NaHSO4

## Common Names to IUPAC Names

Exercise $$\PageIndex{16.a}$$

What are the IUPAC names of the following compounds?

1. manganese dioxide
2. mercurous chloride (Hg2Cl2)
3. ferric nitrate [Fe(NO3)3]
4. titanium tetrachloride
5. cupric bromide (CuBr2)
manganese(IV) oxide
mercury(I) chloride
iron(III) nitrate
titanium(IV) chloride
copper(II) bromide

## Atoms and the Mole

Exercise $$\PageIndex{17.a}$$

What is the total mass (amu) of carbon in each of the following molecules?

1. CH4
2. CHCl3
3. C12H10O6
4. CH3CH2CH2CH2CH3

$$12.01\;amu$$

$$12.01\;amu$$

$$12(12.01)\;=\;144.12\;amu$$

$$5(12.01)\;=\;60.05\;amu$$

Exercise $$\PageIndex{17.b}$$

Calculate the molecular or formula mass of each of the following:

1. CH4
2. CHCl3
3. C12H10O6
4. CH3CH2CH2CH2CH3

$$12.01 \;+\;4(1.007)\;=\;16.04\;amu$$

$$12.01 \;+\;1.007\;+\;3(35.45)\;=\;119.37\;amu$$

$$12(12.01)\;+\;10(1.007)\;+\;6(16.00)\;=\;250.19\;amu$$

$$5(12.01)\;+\;12(1.007)\;=\;72.13\;amu$$

Exercise $$\PageIndex{17.c}$$

Calculate the molecular or formula mass of each of the following:

1. P4
2. H2O
3. Ca(NO3)2
4. CH3CO2H (acetic acid)
5. C12H22O11 (sucrose, cane sugar)

$$4(30.974)\;=\;123.896\;amu$$

$$2(1.007)\;+\;15.999\;=\;18.015\;amu$$

$$40.078\;+\;2(14.007\;+\;3(15.99))\;=\;164.086\;amu$$

$$2(12.011)\;+\;2(15.999)\;+\;4(1.007)\;=\;60.052\;amu$$

$$12(12.011)\;+\;22(1.007)\;+\;11(15.999)\;=\;342.297\;amu$$

Exercise $$\PageIndex{17.d}$$

Determine the molecular mass of the following compounds:

$$4(12.011)\;+\;8(1.007)\;=\;56.107\;amu$$

$$4(12.011)\;+\;6(1.007)\;=\;54.091\;amu$$

$$2(28.085)\;+\;4(35.45)\;+\;2(1.007)\;=\;199.998\;amu$$

$$30.974\;+\;4(15.99)\;3(1.007)\;=\;97.995\;amu$$

## Mass, Moles, and Number of Particles

Exercise $$\PageIndex{18.a}$$

Which contains the greatest mass of oxygen: 0.75 mol of ethanol (C2H5OH), 0.60 mol of formic acid (HCO2H), or 1.0 mol of water (H2O)? Explain why.

Formic acid. Its formula has twice as many oxygen atoms as the other two compounds (one each). Therefore, 0.60 mol of formic acid would be equivalent to 1.20 mol of a compound containing a single oxygen atom.

Exercise $$\PageIndex{18.b}$$

Calculate the molar mass of each of the following:

1. S8
2. C5H12
3. Sc2(SO4)3
4. CH3COCH3 (acetone)
5. C6H12O6 (glucose)

$$8(32.070)\;=\;256.560\;g/mol$$

$$5(12.011)\;+\;12(1.008)\;=\;72.150\;g/mol$$

$$2(44.956)\;+\;3(32.07+4(15.999)\;=\;378.110\;g/mol$$

$$3(12.011)\;+\;6(1.008)\;+\;15.999\;=\;58.080\;g/mol$$

$$6(12.011)\;+\;12(1.008)\;+\;6(15.999)\;=\;180.156\;g/mol$$

Exercise $$\PageIndex{18.c}$$

Calculate the molar mass of each of the following:

1. the anesthetic halothane, C2HBrClF3
2. the herbicide paraquat, C12H14N2Cl2
3. caffeine, C8H10N4O2
4. urea, CO(NH2)2
5. a typical soap, C17H35CO2Na

$$2(12.011)\;+\;1.008\;+\;79.900\;+\;35.45\;+\;3(18.998)\;=\;197.382\;g/mol$$

$$12(12.011)\;+\;14(1.008)\;+\;2(14.007)\;2(35.45)\;=\;257.158 g/mol$$

$$8(12.011)\;+\;10(1.008)\;4(14.007)\;+\;2(15.999)\;=\;194.194 g/mol$$

$$12.011\;+\;15.999\;+\;2(14.007\;+\;2(1.008))\;=\;60.056 g/mol$$

$$18(12.011)\;+\;35(1.008)\;+\;2(15.999)\;+\;22.990\;=\;306.466 g/mol$$

Exercise $$\PageIndex{18.d}$$

Determine the mass of each of the following:

1. 0.0146 mol KOH
2. 10.2 mol ethane, C2H6
3. 1.6 × 10⁻³mol Na2SO4
4. 6.854 × 10³ mol glucose, C6H12O6
5. 2.86 mol Co(NH3)6Cl3

$$38.098\;+\;15.999\;+\;1.008\;=\;55.105\;g/mol\\55.105\;g/mol\;\times\;.0146\;mol\;=\;0.805\;g$$

$$2(12.011\;+\;6(1.008)\;=\;30.070\;g/mol\\30.070\;g/mol\;\times\;10.2\;mol\;=306.714\;g$$

$$2(22.990)\;+\;32.07\;+\;4(15.999)\;=\;142.046\;g/mol\\142.046\;g/mol\;\times\;1.6\;\times10^{-3}\;mol\;=\;.227\;g$$

$$6(12.011)\;+\;12(1.008)\;+\;6(15.999)\;=\;180.156\;g/mol\\180.156\;g/mol\;\times\;6.854\;\times\;10^{3}\;mol\;=\;1.235*10^6\;g$$

$$58.933\;+\;6(14.007\;+\;3(1.007))\;+\;3(35.45)\;=\;267.451\;g/mol\\267.451\;g/mol\;\times\;2.86mol\;=\;764.909\;g$$

Exercise $$\PageIndex{18.e}$$

Determine the mass of each of the following:

1. (a) 2.345 mol LiCl
2. (b) 0.0872 mol acetylene, C2H2
3. (c) 3.3 × 10−2 mol Na2 CO3
4. (d) 1.23 × 103 mol fructose, C6 H12 O6
5. (e) 0.5758 mol FeSO4(H2O)7

$$7.0\;+35.45\;=\;42.45\;g/mol\\42.45\;g/mol\;\times\;2.345\;mol\;=99.545\;g$$

$$2(12.011)\;+\;2(1.008)\;=\;26.038\;g/mol\\26.038\;g/mol\;\times\;0.0872\;mol\;=2.271\;g$$

$$2(22.99)\;+\;12.011\;+\;3(15.999)\;=\;105.988\;g/mol\\105.988\;g/mol\;\times\;3.3\;\times\;10^{-2}\;mol\;=\;3.498\;g$$

$$6(12.011)\;+\;12(1.008)\;+\;6(15.999)\;=\;180.156\;g/mol\\180.156\;g/mol\;\times\;1.23\;\times\;10^3\;mol\;=2.216\;\times\;10^5\;g$$

$$55.84\;+\;32.07\;+\;4(15.999)\;+\;7(2(1.008)\;+\;15.999)\;=\;278.011\;g/mol\\278.011\;g/mol\;\times\;0.5758\;mol\;=\;160.079\;g$$

Exercise $$\PageIndex{18.f}$$

Determine the mass in grams of each of the following:

1. 0.600 mol of oxygen atoms
2. 0.600 mol of oxygen molecules, O2
3. 0.600 mol of ozone molecules, O3

$$15.999\;g/mol\;\times\;0.600\;mol\;=\;9.599\;g$$

$$2(15.999)\;g/mol\;\times\;0.600\;mol\;=\;19.199\;g$$

$$3(15.999)\;g/mol\;\times\;0.600\;mol\;=\;28.798\;g$$

Exercise $$\PageIndex{18.g}$$

Determine which of the following contains the greatest mass of aluminum: 122 g of AlPO4, 266 g of Al2Cl6, or 225 g of Al2S3.

$$26.982\;+\;30.974\;+\;4(15.999)\;=\;121.952\;g/mol\\ \frac{122\;g}{121.952\;g/mol}\;=\;1\;mol\;AlPO_4\\1\;mol\;Al\;in\;AlPO_4\\1.000\;\times\;1\;=\;1\;mol\;Al$$

$$2(26.982)\;+\;6(35.45)\;=\;266.664\;g/mol\\ \frac{266\;g}{266.664\;g/mol}\;=\;0.998\;mol\;Al_2Cl_6\\2\;mol\;Al\;in\;Al_2Cl_6\\0.998\;\times\;2\;=\;1.996\;mol\;Al$$

$$2(26.982)\;+\;3(32.07)\;=\;150.174\;g/mol\\ \frac{225\;g}{150.174\;g/mol}\;=\;1.498\;mol\;Al_2S_3\\2\;mol\;Al\;in\;Al_2S_3\\1.498\;\times\;2\;=\;2.996\;mol\;Al$$

Exercise $$\PageIndex{18.h}$$

The Cullinan diamond was the largest natural diamond ever found (January 25, 1905). It weighed 3104 carats (1 carat = 200 mg). How many carbon atoms were present in the stone?

$$3104\;carats\;\times\;200\;mg\;=\;\frac{620800\;mg}{1000\;g}\;=\;620.8\;g\\\frac{620.8\;g}{12.011}\;=\;51.686\;mol\;C\\51.686\;times\;6.022\;\times\;10^{23}\;=\;3.113\;\times\;10^{25}$$

Exercise $$\PageIndex{18.i}$$

A certain nut crunch cereal contains 11.0 grams of sugar (sucrose, C12H22O11) per serving size of 60.0 grams. How many servings of this cereal must be eaten to consume 0.0278 moles of sugar?

0.865 servings, or about 1 serving

Exercise $$\PageIndex{18.j}$$

Which of the following represents the least number of molecules?

1. 20.0 g of H2O (18.02 g/mol)
2. 77.0 g of CH4 (16.06 g/mol)
3. 68.0 g of CaH2 (42.09 g/mol)
4. 100.0 g of N2O (44.02 g/mol)
5. 84.0 g of HF (20.01 g/mol)

a. 20.0 g H2O represents the least number of molecules since it has the least number of moles.

## Percent Composition

Exercise $$\PageIndex{19.a}$$

Calculate the following to four significant figures:

1. the percent composition of ammonia, NH3
2. the percent composition of photographic “hypo,” Na2S2O3
3. the percent of calcium ion in Ca3(PO4)2

a.

$$M_N: \;1\;\times\;14.007 \;=\;14.007 \; \\M_H:\;3\;\times\;1.008\;=\;3.024 \\M_T\;= \; 1(14.007)+ 3(1.008)=17.031\\\; \\ \%\; N\;=\;\frac{M_N}{M_T}\;=\;82.24\;\%\\\%\;H\;=\;\frac{M_H}{M_T}\;=\;17.76\;\%$$\

b.

$$M_{Na}: \;2\;\times\;22.99\;=\;45.98\\M_{S}:\;2\;\times\;32.07\;=\;64.14\\M_O:\;3\;\times\;15.999\;=\;47.997\\M_T\;=\;2(22.99)\;+\;2(32.07)\;=\;158.117\\\%\; Na\;=\;\frac{M_{Na}}{M_T}\;=\;29.07\;\%\\\%\; S\;=\;\frac{M_{S}}{M_T}\;=\;40.56\;\%\\\%\; O\;=\;\frac{M_{O}}{M_T}\;=\;30.36\;\%$$

c.

$$M_{Ca^{+2}}: \;3\;\times\;40.08\;=\;120.24\\P:\;2\;\times\;30.974\;=\;61.948\\O:\;8\;\times\;15.999\;=\;127.992\\M_T\;=\;3(40.08)\;+\;2(30.974)\;+8(15.999)\;=\;310.18\\\%\; Ca^{+2}\;=\;\frac{M_{Ca^{+2}}}{M_T}\;=\;38.76\;\%$$

Exercise $$\PageIndex{19.b}$$

Determine the percent ammonia, NH3, in Co(NH3)6Cl3, to three significant figures.

$$NH_3: \;6\;\times\;(14.007\;+\;3(1.008))\;=\;102.186\\Co:\;1\;\times\;58.933\;=\;58.933\\Cl:\;3\;\times\;35.45\;=\;106.35\\M_T\;=267.469\\M_{NH_{3}}\;=\;6(14.007\;+\;3(1.008))\\ \%\; NH_{3}\;=\;\frac{M_{NH_{3}}}{M_T}\;=\;38.20\;\%$$

Exercise $$\PageIndex{19.c}$$

Determine the empirical formulas for compounds with the following percent compositions:

1. 15.8% carbon and 84.2% sulfur
2. 40.0% carbon, 6.7% hydrogen, and 53.3% oxygen

$$C\;100\;\times\;.158\;=\;15.8/12.011\;=\;1.315/1.315\;=\;1\\ S\;100\;\times\;.842\;=\;84.2/32.07\;=\;2.62/1.315\;=\;2\\CS_2$$

$$C\;100\;\times\;.400\;=\;40.0/12.011\;=\;3.33/3.33\;=\;1\\ H\;100\;\times\;.067\;=\;6.7/1.008\;=\;6.64/3.33\;=\;2\\O\;100\;\times\;.533\;=\;55.3/15.999\;=\;3.46/3.33\;=\;1\\CH_2O$$

Exercise $$\PageIndex{19.d}$$

A compound of carbon and hydrogen contains 92.3% C and has a molar mass of 78.1 g/mol. What is its molecular formula?

$$78.1\;\times\;.923\;=\;72.08/12.011\;=\;6\\78.1\;-\;72.08\;=\;6.02/1.008\;=\;6\\C_6H_6$$

Exercise $$\PageIndex{19.e}$$

Determine the empirical and molecular formula for chrysotile asbestos. Chrysotile has the following percent composition: 28.03% Mg, 21.60% Si, 1.16% H, and 49.21% O. The molar mass for chrysotile is 520.8 g/mol.

Mg3Si2H3O8 (empirical formula),

Mg6Si4H6O16 (molecular formula)

Empirical Formula

$$Mg\;100\;\times\;.2803\;=\;28.03/24.305\;=\;1.15/.77\;=\;1.5\;\times\;2\;=\;3\\ Si\;100\;\times\;.2160\;=\;21.60/28.085\;=\;.77/.77\;=\;1\;\times\;2\;=\;2\\H\;100\;\times\;.0116\;=\;1.16/1.008\;=\;1.15/.77\;=\;1.5\;\times\;2\;=\;3\\O\;100\;\times\;.4921\;=\;49.21/15.999\;=\;3.08/.77\;=\;4\;\times\;2\;=\;8\\Mg_3Si_2H_3O_{16}$$

Molecular Formula

$$Mg\;520.8\;\times\;.2803\;=\;145.98/24.305\;=6\\ Si\;520.8\;\times\;.2160\;=\;112.49/28.085\;=4\\H\;520.8\;\times\;.0116\;=\;6.04/1.008\;=6\\O\;520.8\;\times\;.4921\;=\;256.28/15.999\;=16\\Mg_6Si_4H_6O_{16}$$

Exercise $$\PageIndex{19.f}$$

A major textile dye manufacturer developed a new yellow dye. The dye has a percent composition of 75.95% C, 17.72% N, and 6.33% H by mass with a molar mass of about 240 g/mol. Determine the molecular formula of the dye.

$$C\;240\;\times\;.7595\;=\;182.28/12.011\;=15\\ H\;240\;\times\;.0633\;=\;15.19/1.008\;=15\\N\;240\;\times\;.1772\;=\;42.53/14.007\;=4\\C_{15}H_{15}N_{3}$$

## Empirical Formulas

Exercise $$\PageIndex{20.a}$$

Determine the empirical formulas for the following compounds:

1. caffeine, C8H10N4O2
2. fructose, C12H22O11
3. hydrogen peroxide, H2O2
4. glucose, C6H12O6
5. ascorbic acid (vitamin C), C6H8O6
1. C4H5N2O

2. C12H22O11

3. HO

4. CH2O

5. C3H4O3

## Molecular and Empirical Formulas from Structures

Exercise $$\PageIndex{21.a}$$

Write the molecular and empirical formulas of the following compounds:

1. molecular CO2, empirical CO2
2. molecular C2H2, empirical CH
3. molecular C2H4, empirical CH2
4. molecular H2SO4, empirical H2SO4

## Hydrates

Exercise $$\PageIndex{22.a}$$

Name the following compounds:

1. FeCl3 * 6 H2O
2. CuSO4 * 5 H2O
3. Na2SO4 * 10 H2O
1. Iron (III) chloride hexahydrate
2. Copper (II) sulfate pentahydrate
3. Sodium sulfate decahydrate

Exercise $$\PageIndex{22.b}$$

Write the formulas for the following compounds:

1. Barium chloride dihydrate
2. Magnesium sulfate heptahydrate
3. Sodium carbonate decahydrate
1. BaCl2 * 2 H2O
2. MgSO4 * 7 H2
3. Na2CO3 * 10 H2O

Exercise $$\PageIndex{22.c}$$

What is the percent composition of water in the compounds in 2b?

126.0 / 246.4 * 100 = 51.14%

Exercise $$\PageIndex{22.d}$$

If 125 grams of magnesium sulfate heptahydrate is completely dehydrated, how many grams of anhydrous magnesium sulfate will remain?

100 – 51.14 = 48.86% magnesium sulfate

0.4886 * 125 = 61.1 grams