# 3.0E: Exercises

3.0E: Exercises

## 3.E: The Schrödinger Equation (Exercises)

• Contributed by David M. Hanson, Erica Harvey, Robert Sweeney, Theresa Julia Zielinski
• Quantum States of Atoms and Molecules at Chemical Education Digital Library (ChemEd DL)

Prove Euler's formula is correct by expanding (e^<±i&theta>), (cos heta), and (sin heta) each in terms of a Maclaurin series and showing that corresponding terms are identical.

The following table gives the results of many measurements of the length of a laser cavity. Complete the table by calculating the probability for each value. Use the probabilities that you calculated to compute the average value for the length, the average of the length squared, the variance, and the standard deviation in the measurements.

length (cm) number of times the value was obtained probability
100.05 4
100.04 3
100.03 6
100.02 9
100.01 8
100.00 9
99.99 9
99.98 8
99.97 2
99.96 3

Consider an electron trapped by a positively charged point defect in a one-dimensional world. The following wavefunction with &alpha = 20/nm describes the distance x of the electron from the point defect located at x=0. Note that in 1, 2, and 3 dimensions, r = |x|, (<(x^2+y^2)>^<1/2>), and (<(x^2+y^2+z^2)>^<1/2>), respectively.

1. Evaluate the normalization constant N.
2. Graph the probability density for this electron.
3. Calculate the expectation value for x and |x|.
4. If the electron were in a two or three-dimensional world, such as on the surface of a crystal or in a free atom, would the average distance of the electron from the origin <r> be less, the same, or larger than the value you found for one dimension?
5. Determine whether the expectation value for r depends upon the dimensionality of the world (1, 2, or 3) in which the atom lives.

David M. Hanson, Erica Harvey, Robert Sweeney, Theresa Julia Zielinski ("Quantum States of Atoms and Molecules")

## 3.E: First Law of Thermodynamics (Exercises)

• Contributed by Patrick Fleming
• Assistant Professor (Chemistry and Biochemistry) at California State University East Bay

In the attempt to measure the heat equivalent of mechanical work (as Joule did in his famous experiment) a student uses an apparatus similar to that shown below:

The 1.50 kg weight is lifted 30.0 cm against the force due to gravity (9.8 N). If the specific heat of water is 4.184 J/(g °C), what is the expected temperature increase of the 1.5 kg of water in the canister?

1.00 mol of an ideal gas, initially occupying 12.2 L at 298 K, expands isothermally against a constant external pressure of 1.00 atm until the pressure of the gas is equal to the external pressure. Calculate (Delta p), (q), (w), (Delta U), and (Delta H) for the expansion.

Consider 1.00 mol of an ideal gas expanding isothermally at 298 K from an initial volume of 12.2 L to a final volume of 22.4 L. Calculate (Delta p), (q), (w), (Delta U), and (Delta H) for the expansion.

Consider 1.00 mol of an ideal gas (CV = 3/2 R) Occupying 22.4 L that undergoes an isochoric (constant volume) temperature increase from 298 K to 342 K. Calculate (Delta p), (q), (w), (Delta U), and (Delta H) for the change.

Consider 1.00 mol of an ideal gas (Cp = 5/2 R) initially at 1.00 atm that undergoes an isobaric expansion from 12.2 L to 22.4 L. Calculate (Delta T), (q), (w), (Delta U), and (Delta H) for the change.

Consider 1.00 mol of an ideal gas (CV = 3/2 R) initially at 12.2 L that undergoes an adiabatic expansion to 22.4 L. Calculate (Delta T), (q), (w), (Delta U), and (Delta H) for the change.

Derive an expression for the work of an isothermal, reversible expansion of a gas that follows the equation of state (in which (a) is a parameter of the gas)

Use the following data [Huff, Squitieri, and Snyder, J. Am. Chem. Soc., 70, 3380 (1948)] to calculate the standard enthalpy of formation of tungsten carbide, (WC(s)).

Reaction (Delta H^o) (kJ)
(C(gr) + O_2(g) ightarrow CO_2(g)) -393.51
(WC(s) + 5/2 O_2(g) ightarrow WO_3(s) + CO_2(g)) -1195.79
(W(s) + 3/2 O_2(g) ightarrow WO_3(s)) -837.42

The standard molar enthalpy of combustion ((Delta H_c)) of propane gas is given by

[C_3H_8(g) + 5 O_2(g) ightarrow 3 CO_2(g) + 4 H_2O(l)]

with (Delta H_c = -2220 ,kJ/mol)

The standard molar enthalpy of vaporization ((Delta H_)) for liquid propane

[C_3H_8(l) ightarrow C_3H_8(g)]

1. Calculate the standard enthalpy of combustion of liquid propane.
2. Calculate the standard internal energy change of vaporization ((Delta U_)) for liquid propane.
3. Calculate the standard internal energy change of combustion ((Delta H_c)) for liquid propane.

The enthalpy of combustion ((Delta H_c)) of aluminum borohydride, (Al(BH_4)_3(l)), was measured to be -4138.4 kJ/mol [Rulon and Mason, J. Am. Chem. Soc., 73, 5491 (1951)]. The combustion reaction for this compound is given by

[ Al(BH_4)_3(l) + 6 O_2(g) ightarrow ½ Al_2O_3(s) + 3/2 B_2O_3(s) + 6 H_2O(l)]

Given the following additional data, calculate the enthalpy of formation of (Al(BH_4)_3(g)).

• (Al_2O_3(s)): (Delta H_f = -1669.8 , kJ/mol)
• (B_2O_3(s)): (Delta H_f = -1267.8 , kJ/mol)
• (H_2O(l)): (Delta H_f = -285.84 , kJ/mol)
• (Al(BH_4)_3(l)): (Delta H_ = 30.125 , kJ/mol)

The standard enthalpy of formation ((Delta H_f^o)) for water vapor is -241.82 kJ/mol at 25 °C. Use the data in the following table to calculate the value at 100 °C.

Substance (C_p) (J mol -1 K -1 )
H2(g) 28.84
O2(g) 29.37
H2O(g) 33.58

(Delta C_p = (1.00 + 2.00 imes 10^ <-3>T), J/K) and (Delta H_ <298>= -5.00, kJ) for a dimerization reaction

Find the temperature at which ( Delta H = 0).

From the following data, determine the lattice energy of (BaBr_2).

[Ca(s) + Br_2^-(l) ightarrow CaBr_2(s)]

with (Delta H_f = -675 , kJ/mol)

Using average bond energies (Table T3) estimate the reaction enthalpy for the reaction

[C_2H_4 + HBr ightarrow C_2H_5Br]

## 3.3: Parts of the Nervous System

The nervous system can be divided into two major subdivisions: the central nervous system (CNS) and the peripheral nervous system (PNS), shown in the figure below. The CNS is comprised of the brain and spinal cord the PNS connects the CNS to the rest of the body. In this section, we focus on the peripheral nervous system later, we look at the brain and spinal cord.

### Review Questions

Our ability to make our legs move as we walk across the room is controlled by the ________ nervous system.

If your ________ is activated, you will feel relatively at ease.

1. somatic nervous system
2. sympathetic nervous system
3. parasympathetic nervous system
4. spinal cord

The central nervous system is comprised of ________.

1. sympathetic and parasympathetic nervous systems
2. organs and glands
3. somatic and autonomic nervous systems
4. brain and spinal cord

Sympathetic activation is associated with ________.

1. pupil dilation
2. storage of glucose in the liver
3. increased heart rate
4. both A and C

### Critical Thinking Questions

What are the implications of compromised immune function as a result of exposure to chronic stress?

Examine Fig. 3.3.2, illustrating the effects of sympathetic nervous system activation. How would all of these things play into the fight or flight response?

### Personal Application Questions

Hopefully, you do not face real physical threats from potential predators on a daily basis. However, you probably have your fair share of stress. What situations are your most common sources of stress? What can you do to try to minimize the negative consequences of these particular stressors in your life?

### Solution

Chronic stress can lead to increased susceptibility to bacterial and viral infections, and potentially an increased risk of cancer. Ultimately, this could be a vicious cycle with stress leading to increased risk of disease, disease states leading to increased stress and so on.

Most of these effects directly impact energy availability and redistribution of key resources and heightened sensory capacity. The individual experiencing these effects would be better prepared to fight or flee.

## 3.E: Matter and Energy (Exercises)

A pot of water is set on a hot burner of a stove. What is the direction of heat flow?

Some uncooked macaroni is added to a pot of boiling water. What is the direction of heat flow?

How much energy in calories is required to heat 150 g of H2O from 0°C to 100°C?

How much energy in calories is required to heat 125 g of Fe from 25°C to 150°C?

If 250 cal of heat were added to 43.8 g of Al at 22.5°C, what is the final temperature of the aluminum?

If 195 cal of heat were added to 33.2 g of Hg at 56.2°C, what is the final temperature of the mercury?

A sample of copper absorbs 145 cal of energy, and its temperature rises from 37.8°C to 41.7°C. What is the mass of the copper?

A large, single crystal of sodium chloride absorbs 98.0 cal of heat. If its temperature rises from 22.0°C to 29.7°C, what is the mass of the NaCl crystal?

If 1.00 g of each substance in Table 7.3 were to absorb 100 cal of heat, which substance would experience the largest temperature change?

If 1.00 g of each substance in Table 7.3 were to absorb 100 cal of heat, which substance would experience the smallest temperature change?

Determine the heat capacity of a substance if 23.6 g of the substance gives off 199 cal of heat when its temperature changes from 37.9°C to 20.9°C.

What is the heat capacity of gold if a 250 g sample needs 133 cal of energy to increase its temperature from 23.0°C to 40.1°C?

## 3.2: Determining Empirical and Molecular Formulas

What information do we need to determine the molecular formula of a compound from the empirical formula?

Calculate the following to four significant figures:

1. (a) the percent composition of ammonia, NH3
2. (b) the percent composition of photographic &ldquohypo,&rdquo Na2S2O3
3. (c) the percent of calcium ion in Ca3(PO4)2

Determine the following to four significant figures:

1. the percent composition of hydrazoic acid, HN3
2. the percent composition of TNT, C6H2(CH3)(NO2)3
3. the percent of SO4 2&ndash in Al2(SO4)3

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

Determine the percent water in CuSO4𕓿H2O to three significant figures.

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

(a) 15.8% carbon and 84.2% sulfur

(b) 40.0% carbon, 6.7% hydrogen, and 53.3% oxygen

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

(a) 43.6% phosphorus and 56.4% oxygen

(b) 28.7% K, 1.5% H, 22.8% P, and 47.0% O

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?

Dichloroethane, a compound that is often used for dry cleaning, contains carbon, hydrogen, and chlorine. It has a molar mass of 99 g/mol. Analysis of a sample shows that it contains 24.3% carbon and 4.1% hydrogen. What is its molecular formula?

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.

Polymers are large molecules composed of simple units repeated many times. Thus, they often have relatively simple empirical formulas. Calculate the empirical formulas of the following polymers:

1. Lucite (Plexiglas) 59.9% C, 8.06% H, 32.0% O
2. Saran 24.8% C, 2.0% H, 73.1% Cl
3. polyethylene 86% C, 14% H
4. polystyrene 92.3% C, 7.7% H
5. Orlon 67.9% C, 5.70% H, 26.4% N

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.

## 29.E: Polymers (Exercises)

• Contributed by John D. Roberts and Marjorie C. Caserio
• Professors (Chemistry) at California Institute of Technology

Exercise 29-1 Write a reasonable mechanism for the thermal depolymerization of 1,3-cyclopentadiene tetramer. How could one chemically alter the tetramer to make thermal breakdown more difficult? Explain.

Exercise 29-2 Suppose a bottle of 1,3-cyclopentadiene were held at a temperature at which polymerization is rapid but depolymerization is insignificant. Would the polymerization result in conversion of all the 1,3-cyclopentadiene into essentially one gigantic molecule? Why or why not? How would you carry on the polymerization so as to favor formation of polymer molecules with high molecular weights?

Exercise 29-3* Calculate a number-average and a weight-average molecular weight for a low-molecular-weight sample of poly-1,3-cyclopentadiene having the following composition:

Under what circumstances would you expect (overline) to be equal to (overline)? Suppose one were to determine a molecular weight for a sample of poly-1,3-cyclopentadiene by quantitative hydrogenation of the terminal double bonds. Would the resulting molecular weight be equal to (overline), (overline), or neither of these?

Exercise 29-4 Show how each of the following polymer structures may be obtained from suitable monomers either by addition or condensation. More than one step may be required.

h.

Exercise 29-5 High-pressure polyethene (Section 10-8C) differs from polyethene made with the aid of Ziegler catalysts (Section 10-8D) in having a lower density and lower (T_m). It has been suggested that this is due to branches in the chains of the high-pressure material. Explain how such branches may arise in the polymerization process and how they would affect the density and (T_m).

Exercise 29-6 Radical-induced chlorination of polyethene in the presence of sulfur dioxide produces a polymer with many chlorine and a few sulfonyl chloride (left( ce <-SO_2Cl> ight)) groups, substituted more or less randomly along the chains. Write suitable mechanisms for these substitution reactions. What kind of physical properties would you expect the chlorosulfonated polymer to have if substitution is carried to the point of having one substituent group to every 25 to 100 (ce) groups? How may this polymer be cross-linked? (A useful product of this general type is marketed under the name Hypalon.)

Exercise 29-7 When polyethene (and other polymers) are irradiated with x rays, cross-links are formed between the chains. What changes in physical properties would you expect to accompany such cross-linking? Would the polyethene become more flexible? Explain.

Suppose polyethene were cross-linked by irradiation at a temperature above (T_m). What would happen if it were then cooled?

Exercise 29-8 Answer the following questions in as much detail as you can, showing your reasoning:

a. Why is atactic polymethyl 2-methylpropenoate not an elastomer?

b. How may one make a polyamide that is an elastomer?

c. What kind of physical properties are to be expected for isotactic polyethenylbenzene (polystyrene)?

d. What would you expect to happen if a piece of high-molecular-weight polypropenoic acid, (ce<-(CH_2-CH(CO_2H))>_n-), were placed in a solution of sodium hydroxide?

e. What kind of properties would you expect for high-molecular-weight "poly-para-phenylene"?

f. Are the properties, listed in Table 29-1, of polychloroprene produced by radical polymerization of 2-chloro-1,3-butadiene such as to make it likely that trans-1,4-addition occurs exclusively?

g. A very useful oil-resistant commercial polymer called "Hytrel" is a block copolymer, having repeating units of the following basic structure:

The length of the blocks is determined by (m) and (n), and the overall molecular weight by (m + n). With appropriate average values, the material is a "thermoplastic elastomer", which means that it is elastic and can be stretched without plastic flow at ordinary temperatures but when heated becomes fluid enough to be easily molded. What physical properties would you expect for polymers of this type having (m + n) large, but with (m = 1), (n = 200) (m = 30), (n = 200) (m = 200), (n = 200) (m = 200), (n = 30) and (m = 200), (n = 1)? Which composition would you expect to correspond to Hytrel?

h. Millions of light, strong soft-drink bottles were made from a recyclable (75\%) ethenylbenzene-(25\%) propenenitrile copolymer. The mechanical strength of the polymer is increased significantly in the operation of blowing a polymer bubble to fit the mold. Why should this be so?

Exercise 29-9 The material popularly known as "Silly Putty" is a polymer having an (ce<-O-Si(R)_2-O-Si(R)_2-O>-) backbone. It is elastic in that it bounces and snaps back when given a quick jerk, but it rapidly loses any shape it is given when allowed to stand. Which of the polymers listed in Table 29-1 is likely to be the best candidate to have anything like similar properties? Explain. What changes would you expect to take place in the properties of Silly Putty as a function of time if it were irradiated with x rays (see Exercise 29-7)?

Exercise 29-10* Suppose one had a sample of completely isotactic polypropene prepared from nonoptically active substances with the structure (ce-C(CH_3)=CH_2>).

a. Would the material theoretically cause a net rotation of the plane of polarized light? Explain.

b. Suppose one could make this polypropene with all (D) orientations of the (ce-) groups. Would the resulting material have an optical rotation theoretically? Practically?

Exercise 29-11 What kind of polymer would you expect to be formed if 4-methylbenzenol were used in place of benzenol in the Bakelite process?

Exercise 29-12 Write a reasonable mechanism for the base-catalyzed condensation of urea with methanal to give bis-methyleneurea, (ce).

Exercise 29-13 Show the reaction whereby butenedioic anhydride would be able to cross-link an epoxy prepolymer with (n = 1).

Exercise 29-14 The terminal carbon of the epoxide ring of epichlorohydrin generally is quite a bit more reactive toward nucleophilic agents than is the carbon bonded to chlorine. Work out a mechanism for the following reaction that takes account of this fact (review Section 15-11D):

Exercise 29-15 Polymerization of methyl 2-methylpropenoate with benzoyl peroxide labeled with (ce<^<14>C>) in the aromatic ring gives a polymer from which only (57\%) of the (ce<^<14>C>) can be removed by vigorous alkaline hydrolysis. Correlation of the (ce<^<14>C>) content of the original polymer with its molecular weight shows that, on the average, there are 1.27 initiator fragments per polymer molecule. Write mechanism(s) for this polymerization that are in accord with the experimental data, and calculate the ratios of the different initiation and termination reactions.

Exercise 29-16 The radical polymerization of ethenylbenzene gives atactic polymer. Explain what this means in terms of the mode of addition of monomer units to the growing-chain radical.

Exercise 29-17 Polyvinyl alcohol prepared by hydrolysis of polyethenyl ethanoate (polyvinyl acetate Table 29-1) does not react with measurable amounts of periodic acid or lead tetraethanoate (Sections 16-9A and 20-4A). However, periodic acid or lead tetraethanoate treatment of the polymer does decrease the number-average molecular weight, for a typical sample from 25,000 to 5000. Explain what these results mean in terms of the polymer structures and the mechanism of the polymerization.

Exercise 29-18 Treatment of polychloroethene with zinc in alcohol removed (85\%) of the chlorine as zinc chloride without formation of unsaturated polymer. What does this result indicate about the polymer structure? Would you have expected that all of the chlorine would be removed by the zinc treatment? Explain. (See Section 14-10C.)

Exercise 29-19 Ozonizations of natural rubber and gutta-percha, which are both poly-2-methyl-1,3-butadienes, give high yields of (ce) and no (ce). What are the structures of these polymers?

Exercise 29-20* What conditions would you choose for producing the highest possible yield of (phenylmethylthio)phenylethane by radical-induced addition of phenylmethanethiol to ethenylbenzene? What structure would you expect the product to have? Explain.

Exercise 29-21* The rate of radical polymerization of ethenylbenzene, induced by benzoyl peroxide in mixtures of tetrachloromethane and benzene, is independent of the concentration of tetrachloromethane. At high concentrations of tetrachloromethane, the average molecular weight of the polymer is greatly reduced and chlorine is found in the polymer. Explain.

Exercise 29-22* 2-Propenyl ethanoate with radical initiators gives a rather short-chain polymer in a relatively slow polymerization. Deuterated 2-propenyl ethanoate of the structure (ce). Gives higher-molecular-weight polymer at a faster rate. Explain.

Exercise 29-23 Devise a synthesis of polyethenamine, remembering that ethenamine (vinylamine) itself is unstable.

Exercise 29-24* Write an equation for the dimerization of sodium naphthalenide analogous to dimerization of the ethenylbenzene radical anion (1) to give (2). Show why you may expect that this dimerization would not be as energetically favorable as the dimerization of (1).

Exercise 29-25* How could you use the living-polymer technique to synthesize (ce)?

Exercise 29-26* What physical properties would you expect for a 2-methylpropene-butenedioic anhydride copolymer? (Review Section 29-3.)

Exercise 29-27* What would be the expected structure of a copolymer of ethenylbenzene and propene made by a Ziegler catalyst if the growing chain is transferred to the monomer as a radical? As an anion?

Exercise 29-28* Devise a synthesis of a block polymer with poly-1,2-ethanediol and nylon 66 segments. What kind of physical properties would you expect such a polymer to have?

Exercise 29-29* Suppose one were to synthesize two block copolymers with the following structures:

What difference in physical properties would you expect for these two materials? (Review Sections 29-3 and 13-4.)

Exercise 29-30* What would you expect for the physical and chemical properties of the following ladder polymer?

Exercise 29-31* Fibers made from aromatic polyamides such as from 1,4-benzenedicarboxylic acid and 1,4-benzenediamine are at least as strong as steel wire with the same ratio of weight to length. What are the structural features of this kind of polyamide that contribute to the strength?

Exercise 29-32 The economically important chain reaction, wool (+) moths ( ightarrow) holes (+) more moths, has, as a key step, scission of the disulfide linkages of cystine in the polypeptide chains by the digestive enzymes of the moth larva. Devise a method of mothproofing wool that would involve chemically altering the disulfide linkages in such a way as to make it unlikely that they would be attacked by the moth enzymes.

## 3.E: Molecules, Compounds and Chemical Equations (Exercises)

These are homework exercises to accompany the Textmap created for Chemistry: A Molecular Approach by Nivaldo Tro. Complementary General Chemistry question banks can be found for other Textmaps and can be accessed here. In addition to these publicly available questions, access to private problems bank for use in exams and homework is available to faculty only on an individual basis please contact Delmar Larsen for an account with access permission.

Classify each compound as ionic or molecular

1. First you need to have good understanding of the difference between Ionic and Molecular.
2. Ionic compound is formed between a metal and a non-metal
3. Molecular compound is formed between two non-metals
4. Then you need to figure out which elements are metals and non-metals by looking at the periodic table

Question: How many types of each atom are in each formula?

What We Know: A chemical formula gives the number of atoms in a compound and the element ratio within a compound.

What It's Asking For: Determine the number of each atom in the given compounds.

Strategy: The subscripts after each atom give the number of atoms in the compound. If the subscript is outside of the parenthesis, the subscript is applied to each atom within the parenthesis.

Write four different ionic compounds that can be formed using the following elements: Sodium, Chlorine, Aluminum and Sulfur.

Identify which elements are the metals and which are the nonmetals that will be arranged to form the ionic compounds.

Ionic compounds always contain positive and negative ions therefore identify the positive charge of each metal identified in the above step and the negative charge of each nonmetal identified in the above step using the Periodic Table for reference.

Combine each metal with each nonmetal to form the initial foundation for the ionic compound. The sum of the positive charges must equal the sum of the negative charges within the compound which means that the number of each ion may have to be adjusted to achieve the balance of ions. If so, then the formula of the ionic compound will always reflect the smallest whole number ratio of ions. For example: 2:1, 2:3, etc.

Write the formula for the compound that forms between Potassium and each of the polyatomic ions listed below:

1. Identify the compound listed
2. Write out the chemical equation for each reaction
3. Balance the equations
• The formula for Sulfate is SO4 2-
• The formula for Perchlorate is ClO4 -
• The formula for Nitrate is NO3 -
• The formula for Phosphate is PO4 3-
1. (2K^+ + SO_4^ <2-> ightarrow K_2SO_4)
2. (K^+ + ClO_4^- ightarrow K_2CLO_4)
3. (K^+ + NO_3^- ightarrow KNO_3)
4. (3K^+ + PO_4^ <3-> ightarrow K_3PO_4)

Write the name from the formula of the formula from the name for each hydrated ionic compound

1. Iron(III) phosphate tetrahydrate
2. (CsBr cdot 4H_2O)
3. Cobalt(II) chloride hexahydrate
4. (LiI cdot 3H_2O)
1. Name the cation and anion combination in the first part of the equation, or if the name is given, name the element combination with the anion first, then the cation. The anion is capitalized, while the cation remains lowercase.
2. If the compound involves a metal that forms more than one cation, the number of cations it forms goes in between parentheses in roman numeral form. If the compound does not involve a metal, than list cation charges as normal.
3. For each hydrate at the end of the compound, the prefix at the beginning indicates the number of hydrates. Name the appropriate prefix or number needed for each formula or compound name. Make sure the hydrate is lowercase.

(1) Iron(III) phosphate tetrahydrate

1. Iron phosphate as an element is written as FePO4,since both parts have a charge of 3, they are not needed in the equation.
2. The prefix tetra stands for "4", so therefore tetrahydrate as an element is written as 4H2O
3. The two parts combined make the final formula (FePO_4 cdot 4H_2O)

(2) (CsBr cdot 4H_2O)

1. Cs and Br with 1 charge stands for Cesium Bromide
2. 4 as a prefix is Tetra, so the end of the formula is tetrahydrate
3. The final name of the compound is Cesium bromide tetrahydrate

(3) Cobalt(II) chloride hexahydrate ​

1. Cobalt Chloride has a compound formula of (CoCl), and with Cobalt's charge of 2 involved, a subscript of 2 is added to the end to make (CoCl_2)
2. The "hexa" prefix stands for 6, meaning there are 6 hydrates or 6H2O
3. The two parts put together makes the final compound, (CoCl_2 cdot 6H_2O)

(4) (LiI cdot 3H_2O)

1. Li and I both with single charges make up the compound Lithium iodide
2. 3 as a prefix i labled as "tri", so with 3 hydrates, the compound is named as trihydrate
3. The final compound put together makes Lithium iodide trihydrate

Write the name for each molecular compound.

First, you have to know how to name a molecular compound. To name a compound, its the prefix, name of first element, prefix and name of the second element with the suffix -ide. The prefixes are as follows:

• mono=1
• di=2
• tri=3
• tetra=4
• penta=5
• hexa=6
• hepta=7
• octa=8
• nona=9
• deca=10

After finding the elements and suffixes, just put it together and you have a molecular compound.

1. CO: Since we only have one of each, the carbon does not have a suffix, so we would just use Carbon and there is only one oxygen so the suffix is mono. So the answer is Carbon Monoxide
2. H2S: The hydrogen has a coefficient of 2, so the suffix would be di and the sulfur has no coefficients. Therefore, the answer would be dihydrogen monosulfide.
3. SF6: The sulfur has no coefficients, so it does not change. The fluoride has a coefficient of 6. Therefore, the answer is Sulfur Hexafluoride
4. N2O2: The nitrogen has a coefficient of 2, while the oxygen has a coefficient of 3. The compounds name is Dinitrogen trioxide.

### Q5.75a

Find the amount of moles contained in each specimen.

A. First, determine the units that are given for each sample. In order to convert these measurements to moles, each sample should first be written in grams. Two of the given samples are measured in kilograms. Use the following conversion factor to convert kilograms to grams, with (x) representing the given mass:

B. Next, find the atomic masses of all the atoms in each compound by using the Periodic Table. Then, add these atomic masses together for each compound. The resulting value will be the number of grams of each sample that make up one mole.

C. Convert the mass in grams of each sample to moles by multiplying it by the following conversion factor, called the molar mass, with x representing the mass of the given specimen and (y) representing the calculated atomic mass found in step B:

A Numbers 1 and 2 first need to be converted into grams.

B The following are the calculated molar masses of each of the given compounds. The atomic mass of each element has been rounded to 4 significant figures in these calculations.

1. H2O2: [2, (1.008, g, H)+2, (16.00, g, O)=dfrac<34.02, g><1, mole>, H_2O_2]
2. NaCl: [(22.99, g, Na)+(35.45, g, Cl)=dfrac<58.44, g><1, mole>, NaCl]
3. C2H6O: [2, (12.01, g, C)+6, (1.008, g, H)+left ( 16.00, g, O ight )=dfrac<46.07, g><1, mole>, C_2H_6O]
4. NH3: [(14.01, g, N)+3, (1.008, g, H)=dfrac<17.03, g><1, mole>, NH_3]

C The number of moles in each specimen can now be calculated by multiplying the mass in grams of each sample by its molarity.

1. [7,870, g, H_2O_2cdot dfrac<1, mole, H_2O_2><34.02, g, H_2O_2>=231, moles, H_2O_2]
2. [2,340, g, NaClcdot dfrac<1, mole, NaCl><58.44, g, NaCl>=40.0, moles, NaCl]
3. [12.5, g, C_2H_6Ocdot dfrac<1, mole, C_2H_6O><46.07, g, C_2H_6O>=0.271, moles, C_2H_6O]
4. [85.72, g, NH_3cdot dfrac<1, mole, NH_3><17.03, g, NH_3>=5.033, moles, NH_3]

### Q5.75b

Calculate the number of moles in each of the following examples.

First, calculate the molar mass of NO2.

14.007g/mol N + 2 (15.999 g/mol O) = 46.0055 g/mol

Now, convert the sample from mg to g.

 402.5 mg NO2 1 g 0.4025 g NO2 1000 mg

Finally, use the molar mass to determine how many moles your sample size contains.

 0.4025 g NO2 1 mol 0.0087 moles of NO2 46.0055 g

This gives us the final answer, 0.0087 moles of NO2.

From this, we can deduce that:

For each substance, convert the given molecules to mass in grams:

1. 3.2 x 10 24 Cl2 molecules
2. 8.25 x 10 18 CH2O molecules
3. 1 carbon dioxide molecule

Step 1: Convert the given molecules to moles by dividing by Avogadro's number.

Step 2: Multiply the number of moles by the Molar Mass of the substance to determine the grams.

Step 3: Through correct Dimensional Analysis, the molecules and moles will cancel to leave grams.

[dfrac ightarrow moles ightarrow moles cdot MM ightarrow grams]

• Avogadro's number: 6.022 x 10 23 mol of a substance
• Molar mass (MM): the weight of a substance in the units g/mol, found by adding the atomic masses of each element.
• Example: MM of H2O --> H(1.008 x 2) + O(15.999)= 18 g/mol

### Q5.105

Write the empirical formula and molecular formula for the compound with the given percent composition and molecular weight.

Molecular Weight &asymp 240 g/mol

1. Calculate amount of grams of each element we have.
2. Convert amount of grams into number of moles of each element.
3. Obtain molecular formula.
4. Find the common factor among the number of atoms each elements has, then obtain the empirical formula.

1. Calculate amount of grams in each element:

2. Convert amount of grams into number of moles of each elements:

3. Obtain molecular formula:

4. Find common factor and obtain empirical formula:

### Q5.106

For several compounds both the molar mass and and empirical formulas are listed. What is the molecular formula for each compound.

## Problems

### 3.2 Mathematics of Interference

16. At what angle is the first-order maximum for 450-nm wavelength blue light falling on double slits separated by 0.0500 mm?

17. Calculate the angle for the third-order maximum of 580-nm wavelength yellow light falling on double slits separated by 0.100 mm.

18. What is the separation between two slits for which 610-nm orange light has its first maximum at an angle of (displaystyle 30.0°)?

19. Find the distance between two slits that produces the first minimum for 410-nm violet light at an angle of (displaystyle 45.0°).

20. Calculate the wavelength of light that has its third minimum at an angle of (displaystyle 30.0°) when falling on double slits separated by (displaystyle 3.00&mum). Explicitly show how you follow the steps from the Problem-Solving Strategy: Wave Optics, located at the end of the chapter.

21. What is the wavelength of light falling on double slits separated by (displaystyle 2.00&mum) if the third-order maximum is at an angle of (displaystyle 60.0°)?

22. At what angle is the fourth-order maximum for the situation in the preceding problem?

23. What is the highest-order maximum for 400-nm light falling on double slits separated by (displaystyle 25.0&mum)?

24. Find the largest wavelength of light falling on double slits separated by (displaystyle 1.20&mum) for which there is a first-order maximum. Is this in the visible part of the spectrum?

25. What is the smallest separation between two slits that will produce a second-order maximum for 720-nm red light?

26. (a) What is the smallest separation between two slits that will produce a second-order maximum for any visible light?

27. (a) If the first-order maximum for monochromatic light falling on a double slit is at an angle of (displaystyle 10.0°), at what angle is the second-order maximum?

(b) What is the angle of the first minimum?

(c) What is the highest-order maximum possible here?

28. Shown below is a double slit located a distance x from a screen, with the distance from the center of the screen given by y. When the distance d between the slits is relatively large, numerous bright spots appear, called fringes. Show that, for small angles (where (displaystyle sin&theta&asymp&theta), with (displaystyle &theta) in radians), the distance between fringes is given by (displaystyle &Deltay=x&lambda/d)

Picture shows a double slit located a distance x from a screen, with the distance from the center of the screen given by y. Distance between the slits is d.

29. Using the result of the preceding problem,

(a) calculate the distance between fringes for 633-nm light falling on double slits separated by 0.0800 mm, located 3.00 m from a screen.

(b) What would be the distance between fringes if the entire apparatus were submersed in water, whose index of refraction is 1.33?

30. Using the result of the problem two problems prior, find the wavelength of light that produces fringes 7.50 mm apart on a screen 2.00 m from double slits separated by 0.120 mm.

31. In a double-slit experiment, the fifth maximum is 2.8 cm from the central maximum on a screen that is 1.5 m away from the slits. If the slits are 0.15 mm apart, what is the wavelength of the light being used?

32. The source in Young&rsquos experiment emits at two wavelengths. On the viewing screen, the fourth maximum for one wavelength is located at the same spot as the fifth maximum for the other wavelength. What is the ratio of the two wavelengths?

33. If 500-nm and 650-nm light illuminates two slits that are separated by 0.50 mm, how far apart are the second-order maxima for these two wavelengths on a screen 2.0 m away?

34. Red light of wavelength of 700 nm falls on a double slit separated by 400 nm.

(a) At what angle is the first-order maximum in the diffraction pattern?

(c) Which assumptions are unreasonable or inconsistent?

### 3.3 Multiple-Slit Interference

35. Ten narrow slits are equally spaced 0.25 mm apart and illuminated with yellow light of wavelength 580 nm. (a) What are the angular positions of the third and fourth principal maxima? (b) What is the separation of these maxima on a screen 2.0 m from the slits?

36. The width of bright fringes can be calculated as the separation between the two adjacent dark fringes on either side. Find the angular widths of the third- and fourth-order bright fringes from the preceding problem.

37. For a three-slit interference pattern, find the ratio of the peak intensities of a secondary maximum to a principal maximum.

38. What is the angular width of the central fringe of the interference pattern of

(a) 20 slits separated by (displaystyle d=2.0×10^<&minus3>mm)?

(b) 50 slits with the same separation? Assume that (displaystyle &lambda=600nm).

### 3.4 Interference in Thin Films

39. A soap bubble is 100 nm thick and illuminated by white light incident perpendicular to its surface. What wavelength and color of visible light is most constructively reflected, assuming the same index of refraction as water?

40. An oil slick on water is 120 nm thick and illuminated by white light incident perpendicular to its surface. What color does the oil appear (what is the most constructively reflected wavelength), given its index of refraction is 1.40?

41. Calculate the minimum thickness of an oil slick on water that appears blue when illuminated by white light perpendicular to its surface. Take the blue wavelength to be 470 nm and the index of refraction of oil to be 1.40.

42. Find the minimum thickness of a soap bubble that appears red when illuminated by white light perpendicular to its surface. Take the wavelength to be 680 nm, and assume the same index of refraction as water.

43. A film of soapy water ((displaystyle n=1.33)) on top of a plastic cutting board has a thickness of 233 nm. What color is most strongly reflected if it is illuminated perpendicular to its surface?

44. What are the three smallest non-zero thicknesses of soapy water ((displaystyle n=1.33)) on Plexiglas if it appears green (constructively reflecting 520-nm light) when illuminated perpendicularly by white light?

45. Suppose you have a lens system that is to be used primarily for 700-nm red light. What is the second thinnest coating of fluorite (magnesium fluoride) that would be nonreflective for this wavelength?

46. (a) As a soap bubble thins it becomes dark, because the path length difference becomes small compared with the wavelength of light and there is a phase shift at the top surface. If it becomes dark when the path length difference is less than one-fourth the wavelength, what is the thickest the bubble can be and appear dark at all visible wavelengths? Assume the same index of refraction as water.

(b) Discuss the fragility of the film considering the thickness found.

47. To save money on making military aircraft invisible to radar, an inventor decides to coat them with a nonreflective material having an index of refraction of 1.20, which is between that of air and the surface of the plane. This, he reasons, should be much cheaper than designing Stealth bombers.

(a) What thickness should the coating be to inhibit the reflection of 4.00-cm wavelength radar?

(c) Which assumptions are unreasonable or inconsistent?

### 3.5 The Michelson Interferometer

48. A Michelson interferometer has two equal arms. A mercury light of wavelength 546 nm is used for the interferometer and stable fringes are found. One of the arms is moved by (displaystyle 1.5&mum). How many fringes will cross the observing field?

49. What is the distance moved by the traveling mirror of a Michelson interferometer that corresponds to 1500 fringes passing by a point of the observation screen? Assume that the interferometer is illuminated with a 606 nm spectral line of krypton-86.

50. When the traveling mirror of a Michelson interferometer is moved (displaystyle 2.40×10^<&minus5>m), 90 fringes pass by a point on the observation screen. What is the wavelength of the light used?

51. In a Michelson interferometer, light of wavelength 632.8 nm from a He-Ne laser is used. When one of the mirrors is moved by a distance D, 8 fringes move past the field of view. What is the value of the distance D?

52. A chamber 5.0 cm long with flat, parallel windows at the ends is placed in one arm of a Michelson interferometer (see below). The light used has a wavelength of 500 nm in a vacuum. While all the air is being pumped out of the chamber, 29 fringes pass by a point on the observation screen. What is the refractive index of the air?

Picture shows a schematics of a set-up utilized to measure the refractive index of a gas. The glass chamber with a gas is placed in the Michelson interferometer between the half-silvered mirror M and mirror M1. The space inside the container is 5 cm wide.

## Problem Set B

1. A company sells mulch by the cubic yard. Grade A much sells for ($150) per cubic yard and has variable costs of ($65) per cubic yard. The company has fixed expenses of ($15,000) per month. In August, the company sold (240) cubic yards of Grade A mulch. 1. Calculate the contribution margin per unit for Grade A mulch. 2. Calculate the contribution margin ratio of the Grade A mulch. 3. Prepare a contribution margin income statement for the month of August. 1. Calculate the contribution margin per unit for the (18)-inch blade. 2. Calculate the contribution margin ratio of the (18)-inch blade. 3. Prepare a contribution margin income statement for the month of January. 1. West Island distributes a single product. The company&rsquos sales and expenses for the month of June are shown. Using the information presented, answer these questions: 1. What is the break-even point in units sold and dollar sales? 2. What is the total contribution margin at the break-even point? 3. If West Island wants to earn a profit of ($21,000), how many units would they have to sell?
4. Prepare a contribution margin income statement that reflects sales necessary to achieve the target profit.
1. Wellington, Inc., reports the following contribution margin income statement for the month of May. The company has the opportunity to purchase new machinery that will reduce its variable cost per unit by ($10) but will increase fixed costs by (20\%). Prepare a projected contribution margin income statement for Wellington, Inc., assuming it purchases the new equipment. Assume sales level remains unchanged. 1. Karen&rsquos Quilts is considering the purchase of a new Long-arm Quilt Machine that will cost ($17,500) and will increase her fixed costs by ($119). What would happen if she purchased the new quilt machine to realize the variable cost savings of ($5.00) per quilt, and what would happen if she raised her price by just ($5.00)? She feels confident that such a small price increase will not decrease the sales in units that will help her offset the increase in fixed costs. Given the following current prices how would the break-even in units and dollars change? Complete the monthly contribution margin income statement for each of these cases. 1. Abilene Industries manufactures and sells three products (XX, YY, and ZZ). The sales price and unit variable cost for the three products are as follows: Their sales mix is reflected as a ratio of (4:2:1). Annual fixed costs shared by the three products are ($345,000) per year.

1. What are total variable costs for Abilene with their current product mix?
2. Calculate the number of units of each product that will need to be sold in order for Abilene to break even.
3. What is their break-even point in sales dollars?
4. Using an income statement format, prove that this is the break-even point.
1. Tim-Buck-II rents jet skis at a beach resort. There are three models available to rent: Junior, Adult, and Expert. The rental price and variable costs for these three models are as follows:

The current product mix is (5:4:1). The three models share total fixed costs of (\$114,750).