Unit 0 Measurements and Calculations in Chemistry3 1. SI units and prefixes d. There are few other units that are useful to chemists. For atomic mases, use atomic mass unit: 1 amu

1

Measurements and Calculations

in Chemistry

Unit 0

* Normal

** Difficult

*** Very difficult

Question Difficulty:

A. Measurements and Units (O-0.2 O-0.5)

1. SI units and prefixes

a. A measured quantity/property characterized by a number requires the use of the appropriate unit.

2


b. The SI unit system is a set of consistent units for physical properties.

Base quantity (SI) Unit Symbol

mass kilogram kg length meter m time second s

temperature kelvin K amount of substance mole mol


c. There are a number of prefixes (to the unit symbol) used in SI.

Prefix Symbol Meaning

Tera- T 1012 Giga- G 109 Mega- M 106 Kilo- k 103 Deci- d 10–1 Centi- c 10–2 Milli- m 10–3 Micro- 10–6 Nano- n 10–9 Pico- p 10–12

3


d. There are few other units that are useful to chemists.

For atomic mases, use atomic mass unit: 1 amu = 1.66 10–27 kg

For atomic distances, use angstrom: 1 A = 1 10–10 m

2. Temperature scales

a. There are three scales of (or units for) temperature.

Kelvin scale using kelvin denoted K – this is the SI unit

Celsius scale using Celsius (or centigrade) denoted C

Fahrenheit scale using Fahrenheit denoted F

4


b. There are formulas that can be used to transfer a temperature from one scale to another:

or

or

273.15C K 273.15K C

235

9C F

9

5 32FC


c. Formulas can de deduced based on the relationships between the three temperature scales.

C FK

32

212373

273H2O

melting

H2Oboiling

0

100

a

A

b

BC F B

b

A

a

32212

32F

0100

0C

5


d. One degree difference on Celsius scale is the same as one degree difference on Kelvin scale but is not the same as one degree difference on Fahrenheit scale.

1) Below is a list of common prefixes used in the SI and metric systems. Included with each is an abbreviation and meaning. Which set contains an error? a.deci- d 10-1

b.kilo- k 103

c.centi- c 10-2

d.mega- M 106

e.micro- m 10-6

**O-0.2

6

2) The normal boiling point of radon is -95.8°F. What is this temperature in kelvins?

a. 190 K b. 202 K c. 294 K d. 224 K e. 249 K

**O-0.3

3. Derived units

a. Units for all other quantities can be determined from the base SI units.

Area = (length)2 so it has SI unit of m2.

Volume = (length)3 so it has SI unit of m3.

b. Although the SI unit for volume is m3, because 1 m3 is a big volume, other units are typically used.

1 dm3 = 10–3 m3 = 1 L

1 cm3 = 10–6 m3 = 10–3 L = 1 mL = 1 cc

7

4. Density

a. An important quantity is density (denoted d or D) defined as mass (denoted m or mass) over (unit of) volume (V).

or or

b. Although the SI unit for density is kg/m3, the typical unit is g/cm3 or g/mL.

Typical values of density are in the 0.5-15 g/cm3

range.

Density of water is around 1 g/cm3 and varies with temperature.

V

md

d

mV Vdm

4. Density

c. Specific gravity is the numerical value (i.e., the value with no unit) of density when expressed in g/cm3.

d. Density is an intensive property.

e. Properties can be classified as:

extensive – when they are dependent on the amount

intensive – when they are independent on the amount

8

3) Which of the following statements about density is incorrect? a. If oil and water are placed in a container, they form two

layers with oil as the top layer because it has the greater density.

b. The densities of liquids are usually expressed in units of g/mL (or g/cm3).

c. The intensive property density can be calculated from the two extensive properties: mass and volume.

d. Densities of gases change greatly with changes in temperature and pressure.

e. The densities of gases are usually expressed in units of g/L.

*O-0.4

4) What is the specific gravity of nickel if 2.35 cm3 of nickel has the same mass as 20.9 mL of water at room temperature?

a. 19.7 b. 2.14 c. 49.2 d. 8.89 e. 0.112

**O-0.4

9

a. Energy can be defined as the capacity to do work or transfer heat.

b. In general, there are two forms of energy:

Kinetic energy (K or KE or Ek = mv2/2) is the energy associated with the motion of particles or objects,

Potential energy (V or PE or Ep) is the energy associated with the position of particles in a field of forces.

c. Potential energy can sometimes be seen as stored energy like the energy stored in chemical bonds.

5. Energy and energy changes


d. Both of these forms of energy are relative meaning that they should be defined with respect to a zero of energy.

The change in thermal energy is measured by measuring T.

e. Thermal energy is the kinetic energy associated to random motion of atoms and molecules.

10


f. The SI unit of energy is joule (J), and another accepted (and highly used) unit of energy is calorie (cal).

energy = force distance;

1 cal = 4.184 J exactly

2

2

2 s

mkgm

s

mkgmNJ


g. The first law of thermodynamics states that, during a process, energy is not created or destroyed but just transferred.

It is known as the law of conservation of energy.

exothermic – when the system loses thermal energy

h. The transfer of energy is seen from the point of view of the system under observation, and processes can be classified as:

endothermic – when the system gains thermal energy

11

a. Accuracy is a measure of how close measurements are to the real value.

b. Precision is a measure of how close measurements are to each other.

6. Accuracy and precision in measurements

B. Significant Figures (O-0.6 & O-0.7)

1. Identifying the number of significant figures

a. Carrying out measurements of various properties are associated with uncertainty so the reported number should contain only the number of digits that are significant.

b. Significant figures are the meaningful digits in a reported number.

12


c. In general, numbers can be classified as:

exact – when there is an infinite number of significant figures

inexact – when there is a finite number of significant figures

d. The exact numbers are:

integers – examples: 1, 10, 25, 100

exact numbers by definition: 1 in = 2.54 cm and 1 cal = 4.184 J


e. The number of significant figures in inexact numbers can be determined based on the following rules:

digits other than 0 are always significant

digit 0 between other digits is always significant

leading digit 0 (i.e., before other digits) is not significant

digit 0 to the right of a non-zero digit is significant if after or before the decimal point (i.e., if the decimal point is written)

digit 0 to the right of a non-zero digit is ambiguous if it is before the decimal point and the decimal point is not shown

13


f. Scientific notation might need to be used to write a number with the proper number of significant figures.

2 significant figures and it should be written as 1.2 103



g. For example 1200 can have:

5) How many significant figures are in 0.020480?a. 3 b. 4 c. 5 d. 6 e. 7

*O-0.6

14

2. Significant figures in calculations

a. For multiplications and divisions of two or more numbers, the final result should have the same number of significant figures as the smallest number of significant figures in the starting numbers.

Equivalently, the final result should not have more decimal digits (i.e, the digits to the right of the decimal point) than any of the starting numbers.

b. For additions and subtractions of two or more numbers, the final result should have the last digit as the highest power of 10 among the last digit of the starting numbers.

c. One should carry out the calculation and round off the final result to the right number of significant figures.

6) Perform the indicated mathematical operations and express the answer in scientific notation rounded off to the proper number of significant figures: (8.001 102 ) (2.88 103 ) (2.4 10-3) =

a. 9.6 10-2

b. 9.6 102

c. 9.60 108

d. 9.6 108

e. 9.601 108

*O-0.7

15

7) The sum 2.834 + 5.71520 + 2.12 + 178.1 + 250.2619 expressed to the proper number of significant figures is: a. 439.0311 b. 439.03c. 439.031d. 439e. 439.0

*O-0.7

8) Do the arithmetic and give the answer to the correct number of significant figures:

0.00015 54.6 + 1.002

a. 1.01019 b. 1.0102c. 1.010d. 1.01e. 1.0

**O-0.7

16

9) Do the arithmetic and give the answer to the correct number of significant figures:

0.00015 (54.6 + 1.002)

a. 0.0083403 b. 0.008340c. 0.00834d. 0.0083e. 0.008

**O-0.7

C. Unit and Quantity Conversion (O-0.8)

1. Unit-factor method

a. The unit-factor method is also called factor-label method.

b. The method can be used to transform a quantity from one unit to another using conversion factors (or unit ratios).

Conversion factors are fractions (equal to 1) in which the same quantity is expressed one way in the numerator and another way in the denominator.

17

1. Unit-factor method

c. The method can also be used to transform a quantity to another equivalent (or stoichiometric) quantity.

Example: transform mass into volume using the density.

d. The fraction should have:

the unit to be transformed from in the denominator

the unit to be transform into in the numerator

2. Applications

a. To transform between in and cm, use the equality: 1 in = 2.54 cm

Use to transform from in into cm.

b. To transform between m and cm, use the equality: 1 m = 100 cm.

Use to transform from cm into in.

in 1

cm 54.2

cm 54.2

in 1

18

10) What is the kinetic energy of 2.0 grams of H2 moving at 2000 m/s?

a. 2.0 × 103 Jb. 4.0 × 103 Jc. 8.0 × 103 Jd. 4.0 × 106 Je. 8.0 × 106 J

**O-0.5 & O-0.8

11) What is the kinetic energy of a 1800-lb car traveling at 59 miles per hour? (1 lb = 0.4536 kg, 1 mi = 1.609 km)

a. 4.2 × 10–8 Jb. 2.8 × 105 Jc. 4.8 × 1019 Jd. 1.4 × 106 Je. 2.8 × 10–7 J

**O-0.5 & O-0.8

19

12) Convert 1,285 cm2 to m2?

a. 1.285 107 m2

b. 12.85 m2

c. 0.1285 m2

d. 1.285 105 m2

e. 1.285 10-3 m2

**O-0.8

13) The density of mercury is 13.6 g/cm3. What is the mass of 0.397 in3 of mercury?

a. 0.478 g b. 1.10 102 g c. 88.5 g d. 5.40 g e. 13.7 g

**O-0.4 & O-0.8

20

14) If 5.76 1013 neon atoms (spherical) were laid in a line, each touching the next, the line would measure 2.54 miles. What is the diameter of a neon atom in Å?

a. 1.86 Å b. 0.92 Å c. 1.44 Åd. 0.71 Å e. 1.74 Å

***O-0.8

= 0.71 Å2.54 mile5.76 1013

1.609 km1 mile

103 m1 km

1010 Å 1 m

15) Assuming that a lithium atom is spherical, calculate its volume in cm3. The volume of a sphere is given by V = (4/3) r3. The radius of a lithium atom is 1.52 Å.

1 Å = 10-8 cm and = 3.14.

a. 1.47 10-23 cm3

b. 3.06 10-17 cm3

c. 6.14 10-22 cm3

d. 4.68 10-24 cm3

e. 4.78 10-8 cm3

***O-0.8

V = (4/3) 1.52 Å)3

V = 14.7 Å3

V = 14.7 Å3 10-8 cm1 Å

10-8 cm1 Å

10-8 cm1 Å

1

Atoms

Unit I

* Normal

** Difficult

*** Very difficult


A. Matter and Properties (O-I.2 & O-I.3)

1. Matter

a. Matter is anything that occupied space and has mass.

b. Matter can be classified as:

a substance – matter that has a definite (i.e., constant) composition and properties

a mixture – matter that is a combination of two or more substances

2

1. Matter

c. Substances can be:

an element – a substance that cannot be broken down into simpler substances by any means

a compound – a substance composed of two or more elements combined in a specific ration that cannot be separated into simpler substances using physical methods

1. Matter

d. Mixtures can be:

homogeneous – when the composition is uniform throughout

heterogeneous – when the composition is not uniform throughout

e. The physical states of matter are solid, liquid and gas.

3

2. Properties

a. There are two types of properties (or changes) of matter:

chemical – when the chemical nature of matter changes

physical – when the chemical nature of matter does not change

b. Chemical changes are chemical reactions.

2. Properties

c. The properties can be:

qualitative – when there is no number associated with the property

quantitative – when there is a number associated with the property

4

3. Early experimental laws and early atomic theory

a. Experiments led to some early laws: the law of conservation of mass, the law of definite proportions, and the law of multiple proportions.

3. Early experimental laws and early atomic theory

Each element is composed of tiny, indestructible particles called atoms.

All atoms of the same element have the same mass and properties that distinguish them from the atoms of other elements.

b. Dalton proposed an early atomic theory in 1808.

Atoms combined in simple, whole-number ratios to form compounds.

Atoms of one element cannot change into atoms of another element; a chemical reaction involves changing the way that atoms are bound with each other.

5

1) Which of the following is not a mixture?

a. seawater b. steel c. gasoline d. oxygen e. air

*O-I.2

2) Which statement is false?

a. A compound is a substance that can be decomposed by chemical means into simpler substances.

b. An example of a homogeneous mixture is one prepared by mixing two liquids, ethyl alcohol (grain alcohol) and water.

c. All samples of a particular pure substance have the same composition and properties.

d. Different mixtures of the same two substances can have different compositions.

e. An example of a heterogeneous mixture is one prepared by dissolving the solid, sodium chloride (table salt), in the liquid, water.

*O-I.2

6

3) All of the following are properties of antimony. Which one is not a physical property? a. It burns in an atmosphere of chlorine. b. It has both yellow and gray forms (allotropes) in

the solid state. c. It is one of the few substances that expands upon

freezing. d. It is a solid at room temperature. e. The gray form melts at 631°C

*O-I.3

B. Atoms and Elements (O-I.2 O-I.6)

1. Atomic particles and structure

a. An atom is the smallest quantity of matter that still retains the properties of matter.

b. Atoms contain three types of subatomic particles.

electron – negative charge, mass of 5.485810–4 amu

proton – positive charge, mass of 1.0073 amu

Atom means indivisible in Greek.

neutron – neutral charge, mass of 1.0086 amu

7


c. Protons and neutron are heavier particles and are located in the atomic nucleus, which contains the large majority of the atom weight.

Protons and neutrons are called nucleons.

d. The size of the nucleus is about 10–14 m while the size of atoms (or electrons in atoms) is about 10–10 m.


e. The historic discoveries of subatomic particles and atomic structure can be summarized in the table below.

Scientist Experiment Discovery

J. J. Thomson cathode rays charge/mass ratio of electron

Millikan oil-drop experiment charge and mass of electron

Becquerel radioactivity , , and rays

Rutherford gold foil experiment nuclear model of atom

Chadwick existence of neutron

8

2. Elements and element symbols

a. An element is a substance that cannot be broken down into simpler substances by chemical means.

Elements contain the same type of atoms.

b. Each element has a name and a symbol.

c. An element symbol has one or two letters in which the first one is a capital letter while the second one is not.

Example: Ca not CA or ca.

d. Element symbols are very important and need to be known for elements 136, elements from principal groups and selected transitional metals.

4) Atoms consist principally of what three fundamental particles? a. elements, protons, and neutrons b. electrons, protons, and neutrons c. electrons, protons, and molecules d. electrons, positrons, and neutrons e. elements, positrons, and neutrons

*O-I.4

9

5) Which statement is false?

a. The charge on a proton is positive, the charge on a neutron is negative.

b. Electrons are smaller particles than protons. c. The nucleus of an atom is very small and massive. d. Molecules are the smallest unit of a compound. e. Compounds consist of more than one type of

element.

*O-I.4

6) The Rutherford "gold foil experiment" suggested __________.

a. that electrons have negative charges b. the ratio of the mass of an electron to the charge of

the electron c. the existence of canal rays d. that atoms have a tiny, positively charged, massive

center e. that protons have charges equal in magnitude but

opposite in sign to those of electrons

**O-I.4

10

7) The cathode rays experiment of J. J. Thomson suggested __________.

a. that electrons have negative charges b. the ratio of the mass of an electron to the charge of

the electron c. the existence of canal rays d. that atoms have a tiny, positively charged, massive

center e. that protons have charges equal in magnitude but

opposite in sign to those of electrons

**O-I.4

8) Which of the following statements is incorrect? a. The heavy particles constituting an atom are

present in the nucleus. b. Negative particles are present in the nucleus. c. The chemical symbol of sodium is Na. d. Both negative and positive particles are present in

atoms. e. The charge on an electron is negative, and the

charge on a proton is positive.

**O-I.4

11

9) What is the symbol for the element selenium?

a. S b. Snc. Sid. See. Sl

*O-I.5

3. Atomic and mass numbers

a. Atomic number (denoted Z) is equal to the number of protons in an atom.

It is an integer.

b. Mass number (denoted A) is equal to the number of protons and neutrons in an atom (i.e., the number of heavy particles in an atom).

Atomic number is also equal to the number of electrons in an atom but not equal in an ion.

It is an integer.

Mass number is equal to the number of nucleons.

12


c. Isotopes are different forms of an atom having same Zbut different A (i.e., same number of protons but different number of neutrons).

d. Nuclide refers to a particular isotope (or a particular nucleus) namely an atom/element with a particular mass number.

Example: hydrogen is a mixture of three isotopes: protium, deuterium, and tritium.


e. A nuclide or an isotope is denoted by the chemical symbol with the mass number on the top left corner (and sometimes with the atomic number on the bottom left corner) or by name-A or by symbol-A.

f. Ions are charged particles in which the number of electrons is different than the number of protons.

Example: or Cu-64 64-copperor Cu or Cu 646429

A positive ion is called a cation, and it has less electrons than protons.

A negative ion is called an anion, and it has more electrons than protons.

13

10) Which of the following nuclides have 18 neutrons?

a. 18O b. 32Sc. 34Sd. 31Pe. 32P

*O-I.6

11) Which of the following nuclides have 18 nucleons?

a. 18O b. 32Sc. 34Sd. 31Pe. 32P

*O-I.6

14

12) What is the symbol for a species composed of 19 protons, 20 neutrons, and 18 electrons?

a. 40Ar b. 40Ca c. 34S2-

d. 39K+

e. 40Ca2+

**O-I.6

13) Which of the following statements is false?

a. 17O nuclide has 8 electrons. b. 32S2- nuclide has 32 nucleons.c. 32S2- ion has 16 electrons.d. 18O nuclide has 10 neutrons.e. 2H2

16O molecule has 10 protons.

**O-I.6

15

14) Give the number of protons, neutrons, and electrons in the 34S nuclide.

a. 16 p, 18 n, 15 e b. 16 p, 18 n, 16 e c. 16 p, 16 n, 16 e d. 16 p, 18 n, 18 e e. 34 p, 16 n, 18 e

*O-I.6

15) Give the number of protons, neutrons, and electrons in the ion.

a. 16 p, 18 n, 15 e b. 16 p, 18 n, 16 e c. 16 p, 16 n, 19 e d. 16 p, 18 n, 18 e e. 34 p, 16 n, 18 e

S3416

**O-I.6

16

4. Atomic masses

a. The atomic mass of an element, in the periodic table, is the average mass (in amu or g/mol) of an element based on the natural abundance of element’s isotopes and the isotope masses.

It is a weighted average.

It is not the same as the mass number A.


b. For example, consider an atom with three isotopes with masses a, b, and c and percentage natural abundances x, y, and z, respectively.

The sum of all abundances should be 100: x + y + z = 100

100

mass Atomicczbyax

zyx

czbyax

Generalizing, Atomic mass = 100

)mass isotopeabundance(

17

16) If an element consisted of three isotopes in the following relative abundance, what would the atomic weight of the element be? This is a hypothetical example.

30.00% 37.00 amu 50.00% 38.00 amu 20.00% 40.00 amu

a. 39.98 amu b. 38.76 amu c. 38.20 amu d. 38.10 amu e. 38.00 amu

**O-I.7

C. Mole and Molar Mass (O-I.8 & O-I.9)

1. The mole and molar mass

a. One mole is the amount of substance having Avogadro number of particles (i.e., atoms, ions, molecules, etc.).

b. Molar mass (denoted MM or ) is the mass of 1 mole of substance.

Avogadro number: NA = 6.023 1023

Avogadro number is the number of 12C atoms in 12 g of 12C.

18

1. The mole and molar mass

c. Transformations between mass, number of moles, and number of particles can be done based on the following equalities:

NA particles = 1 mole = MM g (or MM amu)

2. The mass of an atom

a. The mass of an atom in grams is the molar mass divided by NA.

1 amu = 1 g / NA

b. The molar mass in grams has the same numerical value of (atomic) mass in amu.

19

17) How many grams are in a mole of carbon?

a. 6.02 1023

b. 16 c. 40 d. 52 e. 12

*O-I.8

18) Calculate the number of moles of nitrogen atoms in 35 grams of nitrogen. a. 1.3 moles b. 1.7 moles c. 0.63 moles d. 2.5 moles e. 5.0 moles

**O-I.8

1 mol N = 14 g

11 mol =14 g

114 g =1 mol

35 g = 2.5 mol1 mol14 g

20

19) How many grams of Mo equal 2.50 moles of Mo? a. 59.8 g b. 238 g c. 178 g d. 150 g e. 95.3 g

*O-I.8

1 mol Mo = 95.9 g

195.9 g =1 mol

2.5 mol = 239 g95.9 g1 mol

? g =95.9 g1 mol

2.5 mol

20) Suppose you have a 10-gram sample of each of the following elements. Which sample contains the smallest number of moles?

a. Crb. Nac. Pd. Ne. Pb

***O-I.8

21

21) The mass of one oxygen atom is

a. 2.657 10-22 g b. 5.314 10-22 g c. 5.314 10-23 g d. 2.657 10-23 g e. 1.327 10-22 g

***O-I.9

1 mol O = 16 g = 6.022 1023 atoms

1 atom = 2.657 10-23 g 16.00 g6.022 1023 atoms

1

Quantum Theory

Unit II

* Normal

** Difficult

*** Very difficult


A. Energy and Light (O-II.2 O-II.4)

1. Electromagnetic radiation

a. Electromagnetic radiation (or wave) has an oscillating electric field perpendicular to a magnetic field.

Light (or visible light) is part of electromagnetic spectrum.

Waves have the property of interference.

2


b. Electromagnetic radiation (or wave) is characterized by:

Wavelength () – the distance between two maximum in amplitude

Frequency () – number of oscillations per unit time Energy (E) Wavenumbers ( )~

c. There are relations between the properties of waves: = c where c is the speed of light (c = 3.00 108

m/s) E = h = hc/ where h is Planck’s constant (h = 6.63

10–34 Js)

1~


d. The SI unit of wavelength is m, the SI unit of frequency is s–1 = Hz, and the SI unit of wavenumber is m–1.

3

2. Regions of electromagnetic spectrum

a. Electromagnetic spectrum includes all wavelengths of radiation.

b. Electromagnetic spectrum contains the following regions:

gamma-rays (-rays) X-rays UV visible IR microwave radio

*1) Which of the following regions of

electromagnetic spectrum has the largest wavelength?

a. visibleb. infraredc. ultravioletd. microwavee. X-rays

O-II.2

4

2) Which statement about electromagnetic radiation is false?

a. As frequency increases, wavelength decreases. b. As wavelength increases, energy increases. c. As wavelength increases, frequency decreases. d. Wavelength and frequency are inversely

proportional. e. Wavelength and energy are inversely proportional.

*O-II.3

3) A police officer is measuring traffic speed with radar operating at 1.0 1019 Hz. What is the wavelength of this electromagnetic energy?

a. 0.30 m b. 0.30 nm c. 0.30 Å d. 3.30 m e. 3 1017 m

*O-II.3

5

4) What is the frequency of light having a wavelength of 4.50 10-6 cm?

a. 2.84 10-12 s1

b. 2.1 104 s1

c. 4.29 1014 s1

d. 1.06 1022 s1

e. 6.67 1015 s1

*O-II.3

5) A tanning booth uses ultraviolet light at a wavelength of 1000 Å. What is the frequency of this light?

a. 3.3 1016 s-1

b. 2.48 1013 s-1

c. 1.5 1026 s-1

d. 6.63 1016 s-1

e. 3.0 1015 s-1

*O-II.3

6

6) What is the wavelength in Ångstroms of radiation used by an x-ray technician, with a frequency of 6.00 1018 s1?

a. 0.50 Å b. 2.00 Å c. 1.80 1017 Å d. 3.98 105 Å e. 5.56 1018 Å

**O-II.3

B. Development of Quantum Theory (O-II.5 O-II.7)

1. Quantum theory discoveriesa. A series of discoveries at the beginning of the 20th

century led to the development of quantum theory.Scientist Property Development

Plank blackbody radiation quantized energy

Einstein photoelectric effect light behaving as particle

Rutherford gold foil experiment nuclear model of atom

Bohr line spectra of H atom quantized energy of electron

Schrödinger describing particles wave function for electron

de Broglie wave nature of particle de Broglie wavelength

Heisenberg location of particles uncertainty principle

7

1. Quantum theory discoveries

b. Plank introduced the idea of quantized energy for oscillating particles given by E = h, where h is Planck’s constant.

Energy of photon is given by Ephoton = h

c. To explain photoelectric effect, Einstein introduced the idea of light behaving like particle called photon.

d. De Broglie introduced the idea of moving particles behaving like wave and having a de Broglie wavelength associated with it.

where is de Broglie wavelength, m is the mass, and u is the speed.

um

h

1. Quantum theory discoveries

e. Heisenberg realized that the position and the momentum of a particle cannot be determined simultaneously with any desired precision.

where x is uncertainty in position and p is uncertainty in momentum.

f. Schrödinger proposed that particles should be described by wave functions () that can be obtained from the Schrodinger equation.

4h

px

8

7) All of the following are true statements about electromagnetic radiation (light) except?

a. As wavelength increases frequency decreases. b. As energy increases frequency decreases. c. As wavelength increases energy decreases. d. The product of wavelength and frequency is

constant. e. Amplitude is independent of frequency.

*O-II.4

8) Radio waves are very low energy forms of electromagnetic radiation. What is the energy of a photon of radio waves with a wavelength of 150 m?

a. 1.33 10-27 J b. 2.22 10-19 J c. 1.38 10-26 J d. 3.30 10-27 J e. 1.10 10-17 J

*O-II.4

9

9) The energy of a photon is 4.10 1019 J. What is the wavelength of the corresponding light?

a. 485 nm b. 485 108 m c. 4.85 10 md. 485 pme. 485 10 m

*O-II.4

10) The photoelectric work function of a metal is the minimum energy needed to eject an electron by irradiating the metal with light. For calcium, this work function equals 4.34 10-19

J. What is the minimum frequency of light for the photoelectric effect in calcium? a. 6.55 1011 s1

b. 6.55 1012 s1

c. 6.55 1013 s1

d. 6.55 1014 s1

e. 6.55 1015 s1

**O-II.4

10

11) The emission spectrum of mercury shows a line of wavelength 579 nm. How much energy is emitted as the excited electron falls to a lower energy level?

a. 3.43 1019 J/atom b. 1.07 1020 J/atom c. 6.05 1019 J/atom d. 3.60 1020 J/atom e. 5.16 1020 J/atom

**O-II.4

12) What is the energy, in J/photon, of ultraviolet light with a frequency of 2.70 1016 Hz?

a. 6.00 108 J/photon b. 8.00 106 J/photon c. 2.46 1018 J/photon d. 4.07 1019 J/photon e. 1.79 1017 J/photon

**O-II.4

11

13) Who developed an explanation for the photoelectric effect?

a. Einstein b. Planck c. Rutherford d. Millikan e. Bohr

*O-II.5

14) Which statement regarding the photoelectric effect is false? a. Electrons can be ejected only if the light is of

sufficiently short wavelength. b. The current increases with increasing intensity of

the light. c. Electrons can be ejected only if the light is of

sufficiently high energy. d. The current does not depend on the color of the

light as long as the wavelength is short enough. e. The wavelength limit sufficient for the ejection of

electrons is the same for all metals.

**O-II.5

12

15) Which of the following has the lowest de Broglie wavelength?

a. A proton moving with a speed of 500 ms–1.b. A proton moving with a speed of 200 ms–1.c. An electron moving with a speed of 1000 ms–1.d. An electron moving with a speed of 500 ms–1.e. An electron moving with a speed of 200 ms–1.

**O-II.6

16) An electron of mass 9.11 10-28 g is traveling at 2.50 106 m/s. Calculate its de Broglie wavelength (in Å).

a. 0.14 Å b. 2.90 10-3 Åc. 345 Å d. 0.029 Å e. 2.91 Å

***O-II.6

13

2. Bohr model of H atom

a. Bohr extended the nuclear model of atom proposed by Rutherford to explain the line spectrum of H atom.

Line spectrum means that only certain wavelength (or frequency) are emitted or absorbed by H atom.

b. The experimentally determined wavelengths were described by Rydberg equation.

where n2 > n1.

R = 109700 cm–1 is the Rydberg constant.

2

22

1

111

nnR


c. Bohr proposed that only certain energy levels for the electron in H atom are possible.

where constant = 2.18 10–18 J.

2

constant

nE

n is called quantum number, and possible values are n = 1, 2, 3,…

n = 1

n = 2

n = 3n = 4n = 5 E = 0

14



The lowest-energy state (obtained when n = 1) is called ground state.

n = 1

n = 2

n = 3n = 4n = 5 E = 0



All other states (obtained when n = 2,3,…) are higher in energy and are called excited states.

n = 1

n = 2

n = 3n = 4n = 5 E = 0

15


d. Bohr proposed that radiation is emitted (or absorbed) when the electron moves from one energy state (or level) to another.

c

hhnn

EEE nn

22

21

111

constant2

2

22

12

22

1

1111constant1

nnR

nnhc

A photon is emitted when ninitial > nfinal and energy is lost by the H atom.

A photon is absorbed when ninitial < nfinal and energy is gained by the H atom.


e. Bohr model/theory of H atom explained the spectrum of H atom that contains a series of lines.

Lyman series in UV is due to n = 2, 3, 4, … to n = 1 transitions.

Balmer series in visible is due to n = 3, 4, 5, … to n = 2 transitions.

Pashen series in IR is due to n = 4, 5, 6, … to n = 3 transitions.

Bracket series in IR is due to n = 5, 6, 7, … to n = 4 transitions.

16

17) When an electron of an excited hydrogen atom falls from level n = 2 to level n = 1, what wavelength of light is emitted?

R = 1.097 107 m-1

a. 18.2 Å b. 1215 Å c. 4800 Å d. 970 Å e. 1820 Å

**O-II.7

18) What is the frequency of the first line in the Paschen series?

a. 1.60 1014 Hz b. 4.57 1014 Hz c. 6.17 1014 Hz d. 24.7 1014 Hz e. 29.2 1014 Hz

**O-II.7

17

C. Quantum Mechanical Treatment of H Atom (O-II.8 & O-II.9)

1. Wave functions and orbitals

a. Schrodinger equation provides the wave function for electron in hydrogen atom.

b. The wave function contains all possible information about the electron in hydrogen atom.

c. The location of the electron is not completely known so one need to discuss the probability of finding the electron or electron density, which is determined by 2.

Wave function ()

Obtained by solving Schrödinger equation

Schrödinger equation for H atom in spherical coordinates

),,(),,(),,(2 2

2

2

2

2

22zyxEzyxzyxV

zyxm

Er

e

rm

rmrr

rrm

re

ree

0

2

,2

2

22

2

,2

2

,

22

2

4sin

1

2

sinsin

1

2

1

2

18

Wave function () for H atom

),()(),,( mlnlnlm YrRr

0

12/2/3

0

2/1

322

!2

!1)( 0

na

rLer

nalnn

lnrR l

lnnarl

l

nl

imml

ml eP

ml

mllY cos

)!(

)!(

4

)12(),(

2/1

)()1()( 22 xPdx

dxxP lm

mmm

l

!7)(

)6(!6)(

)2

1510(!5)(

)6

1264(!4)(

!5)(

)4(!4)(

)2

133(!3)(

!3)(

)2(!2)(

1)(

77

56

235

3214

55

34

213

33

12

11

xL

xxL

xxxL

xxxxL

xL

xxL

xxxL

xL

xxL

xL

1. Wave functions and orbitals

d. Schrodinger equation introduces the concept of orbital, which very generally indicate a description of an electron, but is typically used to indicate one of the following:

the wave function – depending on three quantum numbers

the wave function square 2 – probability of finding the electron or electron density

boundary surface – a 3-dimensional representation of the probability of finding the electron or electron density

19

2. Shells, subshells and orbitals in H atom

a. The electron wave function (or the electron properties/behavior) in an atom is dependent on four quantum numbers that are described below.

Quantum Name Possible Determinesnumber values (or describes)

n principal 1, 2, 3, 4, … E or size of orbital

l angular momentum 0, 1, …, (n -1) shape of orbital

ml or m magnetic -l, …, 0, …, l orientation

ms spin +1/2 or -1/2 electron spin


a. The electron wave function (or the electron properties/behavior) in an atom is dependent on four quantum numbers that are described below. Angular momentum quantum number l is also called

azimuthal or secondary quantum number. The value of angular momentum quantum number l is

given by a letter as follows:

Various ml values are sometimes described by the Cartesian coordinates or combinations of Cartesian coordinates: x, y, and z for p orbitals, xy, xz, yz, x2-y2, and z2 for d orbitals.

l value 0 1 2 3 4 5

orbital designation s p d f g h

20


b. One can construct a diagram showing all possibilities for the electron based on possible quantum numbers.

n = 1

n = 2

n = 3

n = 4

l 0 1 2 3

ml 0 –1 0 +1 –2 –1 0 +1 +2

1s

2s 2p

3s 3p 3d


b. One can construct a diagram showing all possibilities for the electron based on possible quantum numbers.

All boxes with same energy (or n) represent a shell.

Each set of boxes represents a subshell.

Each box represents an orbital.

Each box can contain up to two electrons (with different ms).

21


c. The quantum numbers describe various quantities.

Quantum number n describes a shell, level, or period.

Quantum numbers n and l describe a subshell or sublevel.

Quantum numbers n, l and ml describe an orbital.

Quantum numbers n, l, ml, and ms describe an electron.

d. For H atom, the energy of subshells (or types of orbitals) is determined only by n and increases in the order:

1s < 2s = 2p < 3s = 3p =3d < 4s = 4p = 4d = 4f <5s=..


e. The number of orbitals into a subshell is (2l + 1) and the number of orbitals into a shell is n2.

f. The maximum number of electrons that can be accommodated or fit into an orbital is 2.

2 in s subshell, 6 in p subshell, etc.

2 in shell 1, 8 in shell 2, 18 in shell 3, etc.

g. The maximum number of electrons that can be accommodated or fit into a subshell is 2(2l + 1).

h. The maximum number of electrons that can be accommodated or fit into a shell is 2n2.

22

3. Representing orbitals

a. Orbitals are typically represented by the boundary surface, which is the surface (of equal electron density) that contains 95% of probability to finding the electron.

They are not surfaces on which the electron moves!


b. (The boundary surfaces of) orbitals have different sizes (determined by n), different shapes (determined by l), and different orientations (determined by ml).

s orbitals “have” spherical shape

1s 2s

p orbitals “have” bilobal/dumbbell shape

2px 2py 2pz

23


b. (The boundary surfaces of) orbitals have different sizes (determined by n), different shapes (determined by l), and different orientations (determined by ml).

d orbitals “have” tetralobal shape

f orbitals “have” octalobal shape

19) Which of the following quantum numbers determine the orientation of an orbital?

a. nb. ml

c. ld. je. ms

*O-II.8

24

20) Which of the following quantum numbers determine the energy of an orbital?

a. nb. ml

c. ld. je. ms

*O-II.8

21) Which of the following quantum numbers determine the shape of an orbital?

a. nb. ml

c. ld. je. ms

*O-II.8

25

22) Which of the following sets of quantum numbers are permissible for an electron?

a. n = 1, l = 1, ml = 0, ms = –1/2b. n = 2, l = 1, ml = 2, ms = –1/2 c. n = 3, l = 1, ml = 1, ms = +1 d. n = 2, l = –1, ml = –1, ms = –1/2 e. n = 3, l = 2, ml = –1, ms = +1/2

*O-II.8

23) Which of the following sets of quantum numbers are NOT permissible for an electron?

a. n = 1, l = 0, ml = 0, ms = –1/2b. n = 2, l = 1, ml = 1, ms = –1/2 c. n = 3, l = –1, ml = 1, ms = +1/2 d. n = 2, l = 1, ml = –1, ms = –1/2 e. n = 3, l = 1, ml = 0, ms = +1/2

*O-II.8

26

24) Which of the following sets of quantum numbers (n, l, ml, ms) is permissible for an electron in an atom? a. (4, –2, 0, +1/2) b. (2, 0, –1, –1/2) c. (3, 2, 0, +1/2) d. (3, 2, 3, –1/2) e. (2, 2, 1, –1/2) f. (2, 1, 0, 0)

**O-II.8

25) Which of the following statements is false? a. The spin quantum number has values of either

+1/2 or –1/2. b. An f set of orbitals is filled with 10 electrons. c. The third energy level has 5 d orbitals. d. A set of p orbitals in a given energy level are equal

in energy. e. The magnetic quantum number has its values

restricted by the l quantum number.

***O-II.8 & O-II.9

27

26) What is the value of the azimuthal quantum number, l , for orbital?

a. 0b. 1/2 c. -1 d. 1 e. 2

*O-II.9

27) What is the value of l for the orbital aside?

a. 1/2 b. –1 c. 0 d. 3 e. 2 f. 1

*O-II.9

28

28) Which of the following sets of quantum numbers (n, l, ml) are associated with the 4psubshell? a. (4, 0, 0) b. (4, 2, 1) c. (4, 1, 1) d. (3, 2, 0) e. (3, 1, 1) f. (3, 1, –1)

**O-II.9

29) The third energy level or shell of an atom can hold a maximum of __________ electrons.

a. 25b. 18 c. 8 d. 16 e. 2

**O-II.9

29

30) One of the spectral lines in the emission spectrum of mercury has a wavelength of 6.234 107 m. How much energy is emitted if 1.00 mole of mercury atoms emits light of 6.234 107 m? Express your answer in kJ/mol. a. 127 kJ/mol b. 485 kJ/mol c. 192 kJ/mol d. 5.56 101 kJ/mol e. 1.74 101 kJ/mol

***O-II.4

31) An electron is confined to a linear region with a length of the same order as the diameter of an atom (about 100 pm). What is the minimum uncertainty in its momentum?

a. 5.8 10–5 kgms–1

b. 5.3 10–25 kgms–1

c. 1.1 10–26 kgms–1

d. 2.6 10–28 kgms–1

e. 5.3 10–28 kgms–1

***O-II.5

30

32) A moving electron has a de Broglie wavelength of 727 nm. What is its speed?

a. 1 ms–1

b. 10 ms–1

c. 100 ms–1

d. 1000 ms–1

e. 10000 ms–1

***O-II.6

33) A ground-state hydrogen atom absorbs a photon of light that has a wavelength of 93.78 nm. What is the principal quantum number of the final state of the hydrogen atom?

a. 2 b. 3 c. 4 d. 5 e. 6

***O-II.7

Documents

Unit 0 Measurements and Calculations in Chemistry3 1. SI units and prefixes d. There are few other units that are useful to chemists. For atomic mases, use atomic mass unit: 1 amu