formal homework exercise mechanics & properties of matter

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Properties of matter (Essentials) - Class 11th

Course: properties of matter (essentials) - class 11th   >   unit 1, properties of matter (course intro).

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Mechanical properties of matter

• stress, strain, Young modulus
• force-extension graphs, energy stored

For many students, this topic will be the first time in physics they have been asked to explicitly link microscale structure (molecular bonds) with observed behaviour (stiffness and other characteristics). Their familiarity with the language used will vary depending on previous study, which will include design and technology, engineering and science. It's often worth spending a little time making sure that everyone is happy using the scientific terms precisely, as many of them have everyday uses which are not quite correct. You may like to remind them that they already know the terms mass, weight and gravity are used in a very particular way by physicists; the terms stiffness, stress and strength are the same. A possible structure might include:

• to recap Hooke's Law and other previous work done describing the behaviour of materials that stretch
• having students calculate stiffness of lab springs/materials using obtained data and apply experimental language to their work
• being precise when introducing and defining the terms stress and strain . You can show how they are related by the Young modulus for a given material, and how this is independent of the shape of the sample
• checking understanding of mathematical relationships, units and symbols is a good opportunity to discuss techniques for revision, as well as having a clear physics benefit
• students taking practical measurements to calculate Young modulus and compare this to accepted values
• discussing the relevance of material characteristics to their uses, being sure to include a range of applications from prosthetics, sports equipment design and consumer products as well as civil engineering
• students are often keen to use simulations and computer models in design and analysis; discussions of the benefits and limitations of this can be illuminating
• students being confident with the derivation and calculation of energy stored by a spring and knowing they must be able to find an approximate answer by using the area under a force-extension graph

Whilst this list provides a source of information and ideas for experimental work, it is important to note that recommendations can date very quickly. Do NOT follow suggestions which conflict with current advice from CLEAPSS or recent safety guides. eLibrary users are responsible for ensuring that any activity, including practical work, which they carry out is consistent with current regulations related to Health and Safety and that they carry an appropriate risk assessment. Further information is provided in our Health and Safety guidance.

Episode 227: Hooke’s Law

Quality Assured Category: Science Publisher: Institute of Physics

Most students will have encountered Hooke's law before, as it is covered in most KS3 courses. Some will have revisited it during GCSE when it will have been linked to the idea of calculating elastic potential energy. The practical guidance here from the IoP focuses on reminding students of the measurements to be made and the calculations that can then be performed.

Some of the practical work described may be familiar to students as stretching carrier bags has featured in GCSE assessed practical work several times. The terms are carefully distinguished and the idea of springs in series and parallel is introduced as - excuse the pun - extension.

Mechanics of Elastic Solids

An informative website with many material and mechanical science explanations.

Stretching copper wire

In this classic experiment students learn how to measure a small change in length accurately which gives rise to interesting discussions about the challenges faced by experimental physicists.

Episode 228: The Young Modulus

Another IoP resource (the complete mechanics set is on the eLibrary ) this moves on from Hooke's law to the relationship between stress and strain. Different practical approaches are compared and student materials include guidance on creating and interpreting stress/strain graphs. Sample data is supplied for various materials.

Of particular interest to most colleagues will be the suggestions for different ways to measure extension during the practicals. This would be an excellent stimulus for discussion about experimental methods in general and the application of scientific language to a particular practical.

Modulus of Elasticity

This page is one from the School Physics website created by an experienced teacher and author, Keith Gibbs. It is intended for students to access independently and is a useful explanation of the three main ways in which 'modulus of elasticity' may be used in textbooks. In most cases the Young modulus is intended but for those with an interest in engineering the understanding of other approaches will be useful. Be clear with students about what concepts they will need for their exam.

Masses and Springs

This simulation of a spring being stretched by adding masses allows students to change the stiffness of the spring as well as the strength of gravity. Results can be collected, plotted and compared to those from 'hands-on' practicals. In itself, this may prompt a useful discussion of the value of scientific modelling. You may choose to set tasks using this as preparation for the practical lesson, or as a follow-up to consolidate their knowledge. The reference to damping will be useful when you cover oscillations and the discussion of energy will help link the topics together.

Elastic Energy

Hyper Physics explains key concepts in physics, this webpage covers elastic potential energy.

The Study of Matter

A collection of short discussion pieces about the role of materials science in teaching, it may provide useful contexts and anecdotes for what we teach our students. It is interesting to see how quickly some parts have become almost standard, for example the discussion on page 38 about 'virtual' materials testing.

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• Neutral vs. Charged Objects

Not only do electrostatic occurrences permeate the events of everyday life, without the forces associated with static electricity, life as we know it would be impossible. Electrostatic forces - both attractive and repulsive in nature - hold the world of atoms and molecules together in perfect balance. Without this electric force, material things would not exist. Atoms as the building blocks of matter depend upon these forces. And material objects, including us Earthlings, are made of atoms and the acts of standing and walking, touching and feeling, smelling and tasting, and even thinking is the result of electrical phenomenon. Electrostatic forces are foundational to our existence.

One of the primary questions to be asked in this unit of The Physics Classroom is: How can an object be charged and what affect does that charge have upon other objects in its vicinity? The answer to this question begins with an understanding of the structure of matter. Understanding charge as a fundamental quantity demands that we have an understanding of the structure of an atom. So we begin this unit with what might seem to many students to be a short review of a unit from a Chemistry course.

History of Atomic Structure

The early Greeks were simply philosophers. They did not perform experiments to test their theories. In fact, science as an experimental discipline did not emerge as a credible and popular practice until sometime during the 1600s. So the search for the atom remained a philosophical inquiry for a couple of millennia. From the 1600s to the present century, the search for the atom became an experimental pursuit. Several scientists are notable; among them are Robert Boyle, John Dalton, J.J. Thomson, Ernest Rutherford, and Neils Bohr.

Boyle's studies (middle to late 1600s) of gaseous substances promoted the idea that there were different types of atoms known as elements. Dalton (early 1800s) conducted a variety of experiments to show that different elements can combine in fixed ratios of masses to form compounds. Dalton subsequently proposed one of the first theories of atomic behavior that was supported by actual experimental evidence.

English scientist J.J. Thomson's cathode ray experiments (end of the 19th century) led to the discovery of the negatively charged electron and the first ideas of the structure of these indivisible atoms. Thomson proposed the Plum Pudding Model , suggesting that an atom's structure resembles the favorite English dessert - plum pudding. The raisins dispersed amidst the plum pudding are analogous to negatively charged electrons immersed in a sea of positive charge.

Nearly a decade after Thomson, Ernest Rutherford's famous gold foil experiments led to the nuclear model of atomic structure. Rutherford's model suggested that the atom consisted of a densely packed core of positive charge known as the nucleus surrounded by negatively charged electrons. While the nucleus was unique to the Rutherford atom, even more surprising was the proposal that an atom consisted mostly of empty space. Most the mass was packed into the nucleus that was abnormally small compared to the actual size of the atom.

Neils Bohr improved upon Rutherford's nuclear model (1913) by explaining that the electrons were present in orbits outside the nucleus. The electrons were confined to specific orbits of fixed radius, each characterized by their own discrete levels of energy. While electrons could be forced from one orbit to another orbit, it could never occupy the space between orbits.

Bohr's view of quantized energy levels was the precursor to modern quantum mechanical views of the atoms. The mathematical nature of quantum mechanics prohibits a discussion of its details and restricts us to a brief conceptual description of its features. Quantum mechanics suggests that an atom is composed of a variety of subatomic particles. The three main subatomic particles are the proton, electron and neutron. The proton and neutron are the most massive of the three subatomic particles; they are located in the nucleus of the atom, forming the dense core of the atom. The proton is charged positively. The neutron does not possess a charge and is said to be neutral. The protons and neutrons are bound tightly together within the nucleus of the atom. Outside the nucleus are concentric spherical regions of space known as electron shells . The shells are the home of the negatively charged electrons. Each shell is characterized by a distinct energy level. Outer shells have higher energy levels and are characterized as being lower in stability. Electrons in higher energy shells can move down to lower energy shells; this movement is accompanied by the release of energy. Similarly, electrons in lower energy shells can be induced to move to the higher energy outer shells by the addition of energy to the atom. If provided sufficient energy, an electron can be removed from an atom and be freed from its attraction to the nucleus.

Application of Atomic Structure to Static Electricity

This brief excursion into the history of atomic theory leads to some important conclusions about the structure of matter that will be of utmost importance to our study of static electricity. Those conclusions are summarized here:

• All material objects are composed of atoms. There are different kinds of atoms known as elements; these elements can combine to form compounds. Different compounds have distinctly different properties. Material objects are composed of atoms and molecules of these elements and compounds, thus providing different materials with different electrical properties.
• An atom consists of a nucleus and a vast region of space outside the nucleus. Electrons are present in the region of space outside the nucleus. They are negatively charged and weakly bound to the atom. Electrons are often removed from and added to an atom by normal everyday occurrences. These occurrences are the focus of this Static Electricity unit of The Physics Classroom.
• The nucleus of the atom contains positively charged protons and neutral neutrons. These protons and neutrons are not removable or perturbable by usual everyday methods. It would require some form of high-energy nuclear occurrence to disturb the nucleus and subsequently dislodge its positively charged protons. These high-energy occurrences are fortunately not an everyday event and they are certainly not the subject of this unit of The Physics Classroom. One sure truth of this unit is that the protons and neutrons will remain within the nucleus of the atom. Electrostatic phenomenon can never be explained by the movement of protons.

A variety of phenomena will be pondered, investigated and explained through the course of this Static Electricity unit. Each phenomenon will be explained using a model of matter described by the above three statements. The phenomena will range from a rubber balloon sticking to a wooden door to the clinging together of clothes that have tumbled in the dryer to the bolt of lightning seen in the evening sky. Each of these phenomena will be explained in terms of electron movement - both within the atoms and molecules of a material and from the atoms and molecules of one material to those of another. In the next section of Lesson 1 we will explore how electron movement can be used to explain how and why objects acquire an electrostatic charge.

Check Your Understanding

Use your understanding of charge to answer the following questions. When finished, click the button to view the answers.

1. ____ are the charged parts of an atom.

a. Only electrons b. Only protons c. Neutrons only d. Electrons and neutrons e. Electrons and protons f. Protons and neutrons

Electrons are negatively charged and protons are positively charged. The neutrons do not have a charge.

• Triboelectric Charging

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FORMAL HOMEWORK EXERCISE Mechanics & Properties of Matter Attempt all 7 questions Homework is due by Monday 15 December 1. A car has its tyres inflated to a pressure of 240 kPa on a day when the temperature is 5 °C. The car is then driven for several hours, and the temperature of the tyres is found to have risen to 35 °C. (a) Assuming the mass and volume of the air in the tyres has remained constant, calculate the new pressure in the tyres. (b) Explain why this happens to the pressure as the temperature rises, making reference to the kinetic theory of gases. 3 2. In preparation for a party, a balloon is inflated to a volume of 0.5 m in a cold room (0 °C). During the party, the room temperature rises to 22 °C. Calculate the new volume of the balloon, assuming the pressure inside it remains constant. 3. An astronaut on a spacewalk has an oxygen tank strapped to his suit. The oxygen in it is pressurised to 5 5 atmospheres (5.0 x 10 Pa), and the volume of the tank is 15 litres. 5 (a) The oxygen is pumped to his mouth at atmospheric pressure (1.0 x 10 Pa). What is the maximum volume of oxygen available to the astronaut at this pressure? (b) What assumptions are made about the gas that allow us to perform this calculation? (c) In reality, the astronaut would find that he had less oxygen available to him than calculated in part (a). Why would this be the case? (Problem solving!)FORMAL HOMEWORK EXERCISE Radiation & Matter 4. Draw the electric field around the following charges. You must show the direction of the field clearly. (a) - + (b) + - 5. What is the definition of a volt? 6. Look at the following diagram. 1.5 C 300 V 100 V (a) What is the potential difference between the two plates? (b) Calculate the work done in moving the charged particle across the electric field. 7. Most vehicle assembly lines use robots...

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8.E: Chemical Bonding Basics (Exercises)

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8.1: CHEMICAL BONDS, LEWIS SYMBOLS AND THE OCTET RULE

Conceptual problems.

• The Lewis electron system is a simplified approach for understanding bonding in covalent and ionic compounds. Why do chemists still find it useful?
• Is a Lewis dot symbol an exact representation of the valence electrons in an atom or ion? Explain your answer.
• How can the Lewis electron dot system help to predict the stoichiometry of a compound and its chemical and physical properties?
• How is a Lewis dot symbol consistent with the quantum mechanical model of the atom? How is it different?

Conceptual Answer

8.2: ionic bonding.

Describe the differences in behavior between NaOH and CH 3 OH in aqueous solution. Which solution would be a better conductor of electricity? Explain your reasoning.

What is the relationship between the strength of the electrostatic attraction between oppositely charged ions and the distance between the ions? How does the strength of the electrostatic interactions change as the size of the ions increases?

Which will result in the release of more energy: the interaction of a gaseous sodium ion with a gaseous oxide ion or the interaction of a gaseous sodium ion with a gaseous bromide ion? Why?

Which will result in the release of more energy: the interaction of a gaseous chloride ion with a gaseous sodium ion or a gaseous potassium ion? Explain your answer.

What are the predominant interactions when oppositely charged ions are

• at internuclear distances close to r 0 ?
• very close together (at a distance that is less than the sum of the ionic radii)?

Several factors contribute to the stability of ionic compounds. Describe one type of interaction that destabilizes ionic compounds. Describe the interactions that stabilize ionic compounds.

What is the relationship between the electrostatic attractive energy between charged particles and the distance between the particles?

The interaction of a sodium ion and an oxide ion. The electrostatic attraction energy between ions of opposite charge is directly proportional to the charge on each ion ( Q 1 and Q 2 in Equation 9.1). Thus, more energy is released as the charge on the ions increases (assuming the internuclear distance does not increase substantially). A sodium ion has a +1 charge; an oxide ion, a −2 charge; and a bromide ion, a −1 charge. For the interaction of a sodium ion with an oxide ion, Q 1 = +1 and Q 2 = −2, whereas for the interaction of a sodium ion with a bromide ion, Q 1 = +1 and Q 2 = −1. The larger value of Q 1 × Q 2 for the sodium ion–oxide ion interaction means it will release more energy.

Numerical Problems

How does the energy of the electrostatic interaction between ions with charges +1 and −1 compare to the interaction between ions with charges +3 and −1 if the distance between the ions is the same in both cases? How does this compare with the magnitude of the interaction between ions with +3 and −3 charges?

How many grams of gaseous MgCl 2 are needed to give the same electrostatic attractive energy as 0.5 mol of gaseous LiCl? The ionic radii are Li + = 76 pm, Mg +2 = 72 pm, and Cl − = 181 pm.

Sketch a diagram showing the relationship between potential energy and internuclear distance (from r = ∞ to r = 0) for the interaction of a bromide ion and a potassium ion to form gaseous KBr. Explain why the energy of the system increases as the distance between the ions decreases from r = r 0 to r = 0.

Calculate the magnitude of the electrostatic attractive energy ( E , in kilojoules) for 85.0 g of gaseous SrS ion pairs. The observed internuclear distance in the gas phase is 244.05 pm.

What is the electrostatic attractive energy ( E , in kilojoules) for 130 g of gaseous HgI 2 ? The internuclear distance is 255.3 pm.

Numerical Answers

According to Equation 9.1, in the first case Q 1 Q 2 = (+1)(−1) = −1; in the second case, Q 1 Q 2 = (+3)(−1) = −3. Thus, E will be three times larger for the +3/−1 ions. For +3/−3 ions, Q 1 Q 2 = (+3)(−3) = −9, so E will be nine times larger than for the +1/−1 ions.

At r < r 0 , the energy of the system increases due to electron–electron repulsions between the overlapping electron distributions on adjacent ions. At very short internuclear distances, electrostatic repulsions between adjacent nuclei also become important.

8.3: COVALENT BONDING

• Which would you expect to be stronger—an S–S bond or an Se–Se bond? Why?
• Which element—nitrogen, phosphorus, or arsenic—will form the strongest multiple bond with oxygen? Why?
• Why do multiple bonds between oxygen and period 3 elements tend to be unusually strong?
• What can bond energies tell you about reactivity?
• Bond energies are typically reported as average values for a range of bonds in a molecule rather than as specific values for a single bond? Why?
• If the bonds in the products are weaker than those in the reactants, is a reaction exothermic or endothermic? Explain your answer.
• A student presumed that because heat was required to initiate a particular reaction, the reaction product would be stable. Instead, the product exploded. What information might have allowed the student to predict this outcome?

What is the bond order about the central atom(s) of hydrazine (N 2 H 4 ), nitrogen, and diimide (N 2 H 2 )? Draw Lewis electron structures for each compound and then arrange these compounds in order of increasing N–N bond distance. Which of these compounds would you expect to have the largest N–N bond energy? Explain your answer.

What is the carbon–carbon bond order in ethylene (C 2 H 4 ), BrH 2 CCH 2 Br, and FCCH? Arrange the compounds in order of increasing C–C bond distance. Which would you expect to have the largest C–C bond energy? Why?

From each pair of elements, select the one with the greater bond strength? Explain your choice in each case.

• P–P, Sb–Sb
• Cl–Cl, I–I
• O–O, Se–Se
• S–S, Cl–Cl
• Al–Cl, B–Cl
• Te–Te, S–S
• C–H, Ge–H
• Si–Si, P–P
• Cl–Cl, F–F
• Ga–H, Al–H

Approximately how much energy per mole is required to completely dissociate acetone [(CH 3 ) 2 CO] and urea [(NH 2 ) 2 CO] into their constituent atoms?

Approximately how much energy per mole is required to completely dissociate ethanol, formaldehyde, and hydrazine into their constituent atoms?

Is the reaction of diimine (N 2 H 2 ) with oxygen to produce nitrogen and water exothermic or endothermic? Quantify your answer.

Numerical Answer

N 2 H 4 , bond order 1; N 2 H 2 , bond order 2; N 2 , bond order 3; N–N bond distance: N 2 < N 2 H 2 < N 2 H 4 ; Largest bond energy: N 2 ; Highest bond order correlates with strongest and shortest bond.

8.4: BOND POLARITY AND ELECRONEGATIVITY

Why do ionic compounds such as KI exhibit substantially less than 100% ionic character in the gas phase?

Of the compounds LiI and LiF, which would you expect to behave more like a classical ionic compound? Which would have the greater dipole moment in the gas phase? Explain your answers.

Predict whether each compound is purely covalent, purely ionic, or polar covalent.

Based on relative electronegativities, classify the bonding in each compound as ionic, covalent, or polar covalent. Indicate the direction of the bond dipole for each polar covalent bond.

• the C=O bond in acetone
• the S–S bond in CH 3 CH 2 SSCH 2 CH 3
• the C–Cl bond in CH 2 Cl 2
• the O–H bond in CH 3 OH
• PtCl 4 2 −

Classify each species as having 0%–40% ionic character, 40%–60% ionic character, or 60%–100% ionic character based on the type of bonding you would expect. Justify your reasoning.

If the bond distance in HCl (dipole moment = 1.109 D) were double the actual value of 127.46 pm, what would be the effect on the charge localized on each atom? What would be the percent negative charge on Cl? At the actual bond distance, how would doubling the charge on each atom affect the dipole moment? Would this represent more ionic or covalent character?

Calculate the percent ionic character of HF (dipole moment = 1.826 D) if the H–F bond distance is 92 pm.

Calculate the percent ionic character of CO (dipole moment = 0.110 D) if the C–O distance is 113 pm.

Calculate the percent ionic character of PbS and PbO in the gas phase, given the following information: for PbS, r = 228.69 pm and µ = 3.59 D; for PbO, r = 192.18 pm and µ = 4.64 D. Would you classify these compounds as having covalent or polar covalent bonds in the solid state?

8.5: DRAWING LEWIS STRUCTURES

Compare and contrast covalent and ionic compounds with regard to

• volatility.
• melting point.
• electrical conductivity.
• physical appearance.

What are the similarities between plots of the overall energy versus internuclear distance for an ionic compound and a covalent compound? Why are the plots so similar?

Which atom do you expect to be the central atom in each of the following species?

• SO 4 2 −

Which atom is the central atom in each of the following species?

What is the relationship between the number of bonds typically formed by the period 2 elements in groups 14, 15, and 16 and their Lewis electron structures?

Although formal charges do not represent actual charges on atoms in molecules or ions, they are still useful. Why?

Give the electron configuration and the Lewis dot symbol for the following. How many more electrons can each atom accommodate?

Based on Lewis dot symbols, predict the preferred oxidation state of Be, F, B, and Cs.

Based on Lewis dot symbols, predict the preferred oxidation state of Br, Rb, O, Si, and Sr.

Based on Lewis dot symbols, predict how many bonds gallium, silicon, and selenium will form in their neutral compounds.

Determine the total number of valence electrons in the following.

• NO 3 −

Draw Lewis electron structures for the following.

• AlCl 4 −
• SO 3 2 −
• S 2 2 −

Draw Lewis electron structures for CO 2 , NO 2 − , SO 2 , and NO 2 + . From your diagram, predict which pair(s) of compounds have similar electronic structures.

Write Lewis dot symbols for each pair of elements. For a reaction between each pair of elements, predict which element is the oxidant, which element is the reductant, and the final stoichiometry of the compound formed.

Use Lewis dot symbols to predict whether ICl and NO 4 − are chemically reasonable formulas.

Draw a plausible Lewis electron structure for a compound with the molecular formula Cl 3 PO.

Draw a plausible Lewis electron structure for a compound with the molecular formula CH 4 O.

While reviewing her notes, a student noticed that she had drawn the following structure in her notebook for acetic acid:

Why is this structure not feasible? Draw an acceptable Lewis structure for acetic acid. Show the formal charges of all nonhydrogen atoms in both the correct and incorrect structures.

A student proposed the following Lewis structure shown for acetaldehyde.

Why is this structure not feasible? Draw an acceptable Lewis structure for acetaldehyde. Show the formal charges of all nonhydrogen atoms in both the correct and incorrect structures.

Draw the most likely structure for HCN based on formal charges, showing the formal charge on each atom in your structure. Does this compound have any plausible resonance structures? If so, draw one.

Draw the most plausible Lewis structure for NO 3 − . Does this ion have any other resonance structures? Draw at least one other Lewis structure for the nitrate ion that is not plausible based on formal charges.

At least two Lewis structures can be drawn for BCl 3 . Using arguments based on formal charges, explain why the most likely structure is the one with three B–Cl single bonds.

Using arguments based on formal charges, explain why the most feasible Lewis structure for SO 4 2 − has two sulfur–oxygen double bonds.

At least two distinct Lewis structures can be drawn for N 3 − . Use arguments based on formal charges to explain why the most likely structure contains a nitrogen–nitrogen double bond.

Is H–O–N=O a reasonable structure for the compound HNO 2 ? Justify your answer using Lewis electron dot structures.

Is H–O=C–H a reasonable structure for a compound with the formula CH 2 O? Use Lewis electron dot structures to justify your answer.

Explain why the following Lewis structure for SO 3 2 − is or is not reasonable.

[Ar]4 s 2 3 d 10 4 p 4

Selenium can accommodate two more electrons, giving the Se 2 − ion.

[Ar]4 s 2 3 d 10 4 p 6

Krypton has a closed shell electron configuration, so it cannot accommodate any additional electrons.

1 s 2 2 s 1

Lithium can accommodate one additional electron in its 2 s orbital, giving the Li − ion.

Strontium has a filled 5 s subshell, and additional electrons would have to be placed in an orbital with a higher energy. Thus strontium has no tendency to accept an additional electron.

Hydrogen can accommodate one additional electron in its 1 s orbital, giving the H − ion.

Be 2 + , F − , B 3+ , Cs +

K is the reductant; S is the oxidant. The final stoichiometry is K 2 S.

Sr is the reductant; Br is the oxidant. The final stoichiometry is SrBr 2 .

Al is the reductant; O is the oxidant. The final stoichiometry is Al 2 O 3 .

Mg is the reductant; Cl is the oxidant. The final stoichiometry is MgCl 2 .

The only structure that gives both oxygen and carbon an octet of electrons is the following:

The student’s proposed structure has two flaws: the hydrogen atom with the double bond has four valence electrons (H can only accommodate two electrons), and the carbon bound to oxygen only has six valence electrons (it should have an octet). An acceptable Lewis structure is

The formal charges on the correct and incorrect structures are as follows:

The most plausible Lewis structure for NO 3 − is:

There are three equivalent resonance structures for nitrate (only one is shown), in which nitrogen is doubly bonded to one of the three oxygens. In each resonance structure, the formal charge of N is +1; for each singly bonded O, it is −1; and for the doubly bonded oxygen, it is 0.

The following is an example of a Lewis structure that is not plausible:

This structure nitrogen has six bonds (nitrogen can form only four bonds) and a formal charge of –1.

With four S–O single bonds, each oxygen in SO 4 2 − has a formal charge of −1, and the central sulfur has a formal charge of +2. With two S=O double bonds, only two oxygens have a formal charge of –1, and sulfur has a formal charge of zero. Lewis structures that minimize formal charges tend to be lowest in energy, making the Lewis structure with two S=O double bonds the most probable.

8.6: RESONANCE STRUCTURES

• Why are resonance structures important?
• In what types of compounds are resonance structures particularly common?
• True or False, The picture below is a resonance structure?

• HSO 4 −
• HSO 3 −
• Draw the Lewis Dot Structure for SO 4 2 - and all possible resonance structures. Which of the following resonance structure is not favored among the Lewis Structures? Explain why. Assign Formal Charges.
• Draw the Lewis Dot Structure for CH 3 COO - and all possible resonance structures. Assign Formal Charges. Choose the most favorable Lewis Structure.
• Draw the Lewis Dot Structure for H PO 3 2 - and all possible resonance structures. Assign Formal Charges.
• Draw the Lewis Dot Structure for CHO 2 1 - and all possible resonance structures. Assign Formal Charges.
• Draw the Resonance Hybrid Structure for P O 4 3 - .
• Draw the Resonance Hybrid Structure for N O 3 - .

1. False, because the electrons were not moved around, only the atoms (this violates the Resonance Structure Rules).

3. Below are the all Lewis dot structure with formal charges (in red) for Sulfate ( SO 4 2 - ). There isn't a most favorable resonance of the Sulfate ion because they are all identical in charge and there is no change in Electronegativity between the Oxygen atoms.

4. Below is the resonance for CH 3 COO - , formal charges are displayed in red. The Lewis Structure with the most formal charges is not desirable, because we want the Lewis Structure with the least formal charge.

5. The resonance for HPO 3 2 - , and the formal charges (in red).

6. The resonance for CHO 2 1 - , and the formal charges (in red).

7. The resonance hybrid for PO 4 3 - , hybrid bonds are in red.

8. The resonance hybrid for NO 3 - , hybrid bonds are in red.

8.7: EXCEPTIONS TO THE OCTET RULE

• What regions of the periodic table contain elements that frequently form molecules with an odd number of electrons? Explain your answer.
• How can atoms expand their valence shell? What is the relationship between an expanded valence shell and the stability of an ion or a molecule?
• What elements are known to form compounds with less than an octet of electrons? Why do electron-deficient compounds form?
• List three elements that form compounds that do not obey the octet rule. Describe the factors that are responsible for the stability of these compounds.

What is the major weakness of the Lewis system in predicting the electron structures of PCl 6 − and other species containing atoms from period 3 and beyond?

The compound aluminum trichloride consists of Al 2 Cl 6 molecules with the following structure (lone pairs of electrons removed for clarity):

Does this structure satisfy the octet rule? What is the formal charge on each atom? Given the chemical similarity between aluminum and boron, what is a plausible explanation for the fact that aluminum trichloride forms a dimeric structure rather than the monomeric trigonal planar structure of BCl 3 ?

Draw Lewis electron structures for ClO 4 − , IF 5 , SeCl 4 , and SbF 5 .

Draw Lewis electron structures for ICl 3 , Cl 3 PO, Cl 2 SO, and AsF 6 − .

Draw plausible Lewis structures for the phosphate ion, including resonance structures. What is the formal charge on each atom in your structures?

Draw an acceptable Lewis structure for PCl 5 , a compound used in manufacturing a form of cellulose. What is the formal charge of the central atom? What is the oxidation number of the central atom?

Using Lewis structures, draw all of the resonance structures for the BrO 3 − ion.

Draw an acceptable Lewis structure for xenon trioxide (XeO 3 ), including all resonance structures.

ClO 4 − (one of four equivalent resonance structures)

The formal charge on phosphorus is 0, while three oxygen atoms have a formal charge of −1 and one has a formal charge of zero.

Practice Problems

• Draw the Lewis structure for the molecule I 3 - .
• Draw the molecule ClF 3 .
• The central atom for an expanded octet must have an atomic number larger than what?
• Draw the Lewis structure for the molecule NO 2 .
• Which Lewis structure is more likely?

Practice Answers

3. 10 (Sodium and higher)

8.8: STRENGTHS OF COVALENT BONDS