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chemistry
physical chemistry

Chemical Principles 7th edition Steven S. Zumdahl, Donald J. DeCoste - Solutions

Consider the reaction 3A + B + C †’ D + E where the rate law is defined asAn experiment is carried out where [B]0 = [C]0 = 1.00 M and [A]0 = 1.00 Ã— 10-4 M. a. If after 3.00 minutes [A] = 3.26 Ã— 10-5 M, calculate the value of k. b. Calculate the half- life for
Define each of the following. a. Elementary step b. Molecularity c. Reaction mechanism d. Intermediate e. Rate-determining step
Define what is meant by unimolecular and bimolecular steps. Why are termolecular steps infrequently seen in chemical reactions?
What two requirements must be met to call a mechanism plausible? Why say a “plausible” mechanism instead of the “correct” mechanism? Is it true that most reactions occur by a one- step mechanism? Explain.
Write the rate laws for the following elementary reactions. a. CH3NC(g) → CH3CN(g) b. O3(g) + NO(g) → O2(g) + NO2(g) c. O3(g) → O2(g) + O(g) d. O3(g) + O(g) → 2O2(g) e. 614C → 714N + β particle (nuclear decay)
A possible mechanism for the decomposition of hydrogen peroxide is H2O2 → 2OH H2O2 + OH → H2O + HO2 HO2 + OH → H2O + O2 Using your results fom Exercise 31, specify which step is the rate- determining step. What is the overall balanced equation for the reaction?
A proposed mechanism for a reaction is C4H9Br → C4H9+ + Br2 Slow C4H9+ + H2O → C4H9OH2+ Fast C4H9OH2+ + H2O → C4H9OH + H3O+ Fast Write the rate law expected for this mechanism. What is the overall balanced equation for the reaction? What are the intermediates in the proposed mechanism?
Is the mechanism NO + Cl2 → NOCl2 NOCl2 + NO → 2NOCl Consistent with the results you obtained in Exercise 17? If so, which step is the rate-determining step?
The reaction 2NO(g) + O2(g) → 2NO2(g) exhibits the rate law Rate = k[NO]2[O2] Which of the following mechanisms is consistent with this rate law? a. NO + O2 → NO2 + O Slow O + NO → NO2 Fast b. NO + O2 ⇌ NO3 Fast equilibrium NO3 + NO → 2NO2 Slow c. 2NO → N2O2 Slow N2O2 + O2 → N2O4
The gas-phase reaction between Br2 and H2 to form HBr is assumed to proceed by the following mechanism:a. Under what conditions does the rate law have the form rate = k€™[Br2]? b. Under what conditions does the rate law have the form rate = k€[H2][Br2]1/2? c. Give expressions
The reaction5Br2(aq) + BrO3-(aq) + 6H+(aq) †’ 3Br2(l) + 3H2O(l)is expected to obey the mechanismBr2(aq) + H2BrO3+(aq) †’ (Br€“BrO2)(aq) + H2O(l) Slow (Br€“BrO2)(aq) + 4H+(aq) + 4Br2(aq) †’ products Fast Write the rate law for this reaction.
The rate law for the reactionBrO3-(aq) + 3SO32-(aq) †’ Br2(aq) + 3SO4 2-(aq) is Rate = k[BrO3-][SO32-][H+]The first step in a proposed mechanism isThe second step is rate determining. Write a possible second step for the mechanism.
The reaction I2(aq) + OCl2(aq) †’ IO2(aq) + Cl2(aq) is believed to occur by the following mechanism:Write the rate law for this reaction.
In the gas phase, the production of phosgene from chlorine and carbon monoxide is assumed to proceed by the following mechanism:a. Write the rate law for this reaction. b. Which species are intermediates?
The following mechanism is proposed for the reduction of NO3- by MoCl62-:a. What is the intermediate? b. Derive an expression for the rate law (rate = d[NO2-]/dt) for the overall reaction using the steady-state approximation.
The following mechanism has been proposed to account for the rate law of the decomposition of ozone to O2(g):Apply the steady-state hypothesis to the concentration of atomic oxygen, and derive the rate law for the decomposition of ozone. (M stands for an atom or molecule that can exchange kinetic
Consider the hypothetical reaction B †’ E + F which is assumed to occur by the mechanismWhere B* represents a B molecule with enough energy to surmount the reaction energy bar70. Consider the following potential energy plotsrier. a. Derive the rate law for the production of E using the
How is the rate of a reaction affected by each of the following. a. Activation energy b. Temperature c. Frequency of collisions d. Orientation of collisions
The central idea of the collision model is that molecules must collide in order to react. Give two reasons why not all collisions of reactant molecules result in product formation.
Consider the following potential energy plotsa. Rank the reactions from fastest to slowest, and explain your answer. If any reactions have equal rates, explain why. b. Label the reactions as endothermic or exothermic, and supply your answer. c. Rank the exothermic reactions from greatest to least
The graph below shows the number of collisions with a particular energy for two different temperatures.a. Which is greater, T2 or T1? How can you tell? b. What does this graph tell us about the temperature dependence of the rate of a chemical reaction? Explain your answer.
Which of the following reactions would you expect to have the larger rate at room temperature? Why? (Hint: Think of which would have the lower activation energy.) 2Ce4+(aq) + Hg22+(aq) → 2Ce3+(aq) + 2Hg2+(aq) H3O+(aq) + OH2(aq) → 2H2O(l)
The activation energy for the decomposition of HI(g) to H2(g) and I2(g) is 186 kJ/ mol. The rate constant at 555 K is 3.52 × 10-7 Lmol-1s-1. What is the rate constant at 645 K?
The decomposition of iodoethane in the gas phase proceeds according to the following equation: C2H5I(g) → C2H4(g) + HI(g) At 660. K, k = 7.2 × 10-4 s-1; at 720. K, k = 1.7 × 10-2 s-1. What is the rate constant for this first- order decomposition at 325oC? If the initial pressure of iodoethane
A certain reaction has an activation energy of 54.0 kJ/ mol. As the temperature is increased from 22oC to a higher temperature, the rate constant increases by a factor of 7.00. Calculate the higher temperature.
Chemists commonly use a rule of thumb that an increase of 10 K in temperature doubles the rate of a reaction. What must the activation energy be for this statement to be true for a temperature increase from 25oC to 35oC?
The reaction (CH3)3CBr + OH- → (CH3)3COH + Br2 in a certain solvent is first order with respect to (CH3)3CBr and zero order with respect to OH-. In several experiments the rate constant k was determined at different temperatures. A plot of ln(k) versus 1/T was constructed that resulted in a
The rate constant for the gas- phase decomposition of N2O5, N2O5 †’ 2NO2 + 1/2O2 has the following temperature dependence:Make the appropriate graph using these data, and deter-mine the activation energy for this reaction.
What are intermolecular forces? How do they differ from intramolecular forces? What are dipole–dipole forces? How do typical dipole–dipole forces differ from hydrogen-bonding interactions? In what ways are they similar? What are London dispersion forces? How do typical London dispersion forces
Rationalize the following differences in physical properties in terms of intermolecular forces. Compare the first three substances with each other, compare the last three with each other, and then compare all six. Can you account for any anomalies?
A certain oxide of titanium is 28.31% oxygen by mass and contains a mixture of Ti2+ and Ti3+ ions. Determine the formula of the compound and the relative numbers of Ti2+ and Ti3+ ions.
Spinel is a mineral that contains 37.9% aluminum, 17.1% magnesium, and 45.0% oxygen, by mass, and has a density of 3.57 g/cm3. The edge of the cubic unit cell measures 809 pm. How many of each type of atom are present in the unit cell?
A metallic solid with atoms in a face-centered cubic unit cell with an edge length of 392 pm has a density of 21.45 g/cm3. Calculate the atomic mass and the atomic radius of the metal. Identify the metal.
The unit cell for a pure xenon fluoride compound is shown below. What is the formula of the compound?
In solid KCl the smallest distance between the centers of a potassium ion and a chloride ion is 314 pm. Calculate the length of the edge of the unit cell and the density of KCl, assuming it has the same structure as sodium chloride.
The temperature inside a pressure cooker is 115oC. Calculate the vapor pressure of water inside the pressure cooker. What would be the temperature inside the pressure cooker if the vapor pressure of water was 3.50 atm?
Dry nitrogen gas is bubbled through liquid benzene (C6H6) at 20.0oC. From 100.0 L of the gaseous mixture of nitrogen and benzene, 24.7 g of benzene is condensed by passing the mixture through a trap at a temperature where nitrogen is gaseous and the vapor pressure of benzene is negligible. What is
A sample of dry nitrogen gas weighing 100.0 g is bubbled through liquid water at 25.0oC. The gaseous mixture of nitrogen and water vapor escapes at a total pressure of 700. torr. What mass of water has vaporized? (The vapor pressure of water at 25oC is 23.8 torr.)
The molar enthalpy of vaporization of water at 373 K is 41.16 kJ/mol. What fraction of this energy is used to change the internal energy of the water, and what fraction is used to do work against the atmosphere? (Assume that water vapor is an ideal gas.)
You are asked to help set up a historical display in the park by stacking some cannonballs next to a Revolutionary War cannon. You are told to stack them by starting with a triangle in which each side is composed of four touching cannonballs. You are to continue stacking them until you have a
Consider the compounds Cl2, HCl, F2, NaF, and HF. Which compound has a boiling point closest to that of argon? Explain.
Consider the ionic solid AxBy, which has the unit cell below. The B ions are packed in a cubic arrangement, where each face has this structure:There is one B in the center of the cube. The structure can also be described in terms of three parallel planes of B€™s of the type shown above.
Mn crystallizes in the same type of cubic unit cell as Cu. Assuming that the radius of Mn is 5.6% larger than the radius of Cu and the density of Cu is 8.96 g/cm3, calculate the density of Mn.
An electron is trapped in an octahedral hole in a closest packed array of aluminum atoms (assume they behave as uniform hard spheres). In this situation the energy of the electron is quantized and the lowest-energy transition corresponds to a wavelength of 9.50 nm. Assuming that the hole can be
You and a friend each synthesize a compound with the formula XeCl2F2. Your compound is a liquid, and your friend’s compound is a gas (at the same conditions of temperature and pressure). Explain how the two compounds with the same formulas can exist in different phases at the same conditions of
A metal burns in air at 600oC under high pressure to form an oxide with formula MO2. This compound is 23.72% oxygen by mass. The distance between the centers of touching atoms in a cubic closest packed crystal of this metal is 269.0 pm. What is this metal? What is its density?
Consider a perfectly insulated and sealed container. Determine the minimum volume of a container such that a gallon of water at 25oC will evaporate completely. If the container is a cube, determine the dimensions in feet. Assume the density of water is 0.998 g/cm3.
The vapor pressure of water at 30.0oC is 31.824 torr; at this temperature the density of liquid water is 0.99567 g/cm3. What is the ratio of the average distance between water molecules in the liquid and in the saturated vapor at this temperature?
For a simple cubic array, solve for the volume of an interior sphere (cubic hole) in terms of the radius of a sphere in the array.
Consider the following melting point data:Account for the trends in melting points for the two series of compounds in terms of interparticle forces.
The structures of another class of high-temperature ceramic superconductors are shown below.a. Determine the formula of each of these four superconductors. b. One of the structural features that appears to be essential for high-temperature superconductivity is the presence of planar sheets of
Consider the following electrostatic potential diagrams:Rank the compounds from lowest to highest boiling point, and explain your answer.
Consider two different compounds, each with the formula C2H6O. One of these compounds is a liquid at room conditions and the other is a gas. Write Lewis structures consistent with this observation, and explain your answer.
The edge of the LiCl unit cell is 514 pm in length. Assum-ing that the Li+ ions just fit in the octahedral holes of the closest packed Cl- ions, calculate the ionic radii for the Li+ and Cl- ions. Compare them with the radii given in Fig. 13.8, and discuss the significance of any
The table below lists the ionic radii for the cations and anions in three different ionic compounds.Each compound has either the NaCl, CsCl, or ZnS type cubic structure. Predict the type of structure formed (NaCl, CsCl, or ZnS) and the type and fraction of holes filled by the cations, and estimate
Consider the following enthalpy changes:F2(g) + HF(g) †’ FHF2(g) Î”H = €“155 kJ/ molH2O(g) + HOH(g) †’ H2O---HOH (in ice) Î”H = €“21 kJ/ mol How do the strengths of hydrogen bonds vary with the electronegativity of the element to which
Using the heats of fusion and vaporization for water, calculate the change in enthalpy for the sublimation of water: H2O(s) → H2O(g) Using the ΔH value given in Exercise 24 and the number of hydrogen bonds formed to each water molecule, estimate what portion of the intermolecular forces in ice
List some physical characteristics that distinguish solids from liquids from gases.
Define the following terms, and describe how each depends on the strength of the intermolecular forces. a. Surface tension b. Viscosity c. Melting point d. Boiling point e. Vapor pressure
The shape of the meniscus of water in a glass tube is different from that of mercury in a glass tube. Why?
Explain why water forms into beads on a waxed car finish.
Hydrogen peroxide (H2O2) is a syrupy liquid with a relatively low vapor pressure and a normal boiling point of 152.2oC. Rationalize the differences between these physical properties and those of water.
List the major types of intermolecular forces in order of increasing strength. Is there some overlap? That is, can the strongest London dispersion forces be greater than some dipole–dipole forces? Give examples of such instances.
Carbon diselenide (CSe2) is a liquid at room temperature. The normal boiling point is 125oC, and the melting point is –45.58C. Carbon disulfide (CS2) is also a liquid at room temperature, with normal boiling and melting points of 46.5oC and –111.6oC, respectively. How do the strengths of the
Distinguish between the solids in the following pairs. a. Crystalline solid and amorphous solid b. Ionic solid and molecular solid c. Molecular solid and network solid d. Metallic solid and network solid
What is closest packing? What is the difference between hexagonal closest packing and cubic closest packing? What is the unit cell for each closest packing arrangement?
Compare and contrast the structures of the following solids. a. Diamond and graphite b. Silica, silicates, and glass
Compare and contrast the structures of the following solids. a. CO2(s) and H2O(s) b. NaCl(s) and CsCl(s)
Will a crystalline solid or an amorphous solid give a simpler X-ray diffraction pattern? Why?
What type of solid will each of the following substances form? a. CO2 b. SiO2 c. Si d. CH4 e. Ru f. I2 g. KBr h. H2O i. NaOH j. U k. CaCO3 l. PH3 m. GaAs n. BaO o. NO p. GeO2
A topaz crystal has an interplanar spacing (d) of 1.36 Å (1Å = 1 × 10–10 m). Calculate the wavelength of the X ray that should be used if u = 15.08 (assume n = 1).
X rays of wavelength 2.63 Å were used to analyze a crystal. The angle of first-order diffraction (n = 1 in the Bragg equation) was 15.558. What is the spacing between crystal planes, and what would be the angle for second-order diffraction (n = 2)?
X rays from a copper X-ray tube (l = 1.54 Å) were diffracted at an angle of 14.228 by a crystal of silicon. Assuming first-order diffraction (n = 1 in the Bragg equation), what is the interplanar spacing in silicon?
Why is ΔHvap for water much greater than ΔHfus? What does this reveal concerning changes in intermolecular forces in going from solid to liquid to vapor?
In what array (simple cubic, body-centered cubic, and face-centered cubic) do atoms pack most efficiently (greatest percent of space occupied by spheres)? Support your answer mathematically.
Calcium has a cubic closest packed structure as a solid. Assuming that calcium has an atomic radius of 197 pm, calculate the density of solid calcium.
A certain form of lead has a cubic closest packed structure with an edge length of 492 pm. Calculate the value of the atomic radius and the density of lead.
Nickel has a face-centered cubic unit cell. The density of nickel is 6.84 g/ cm3. Calculate a value for the atomic radius of nickel.
You are given a small bar of an unknown metal X. You find the density of the metal to be 10.5 g/ cm3. An X-ray diffraction experiment measures the edge of the face-centered cubic unit cell as 4.09 Å (1 Å = 10–10 m). Identify X.
Titanium metal has a body-centered cubic unit cell. The density of titanium is 4.50 g/cm3. Calculate the edge length of the unit cell and a value for the atomic radius of titanium. (Hint: In a body-centered arrangement of spheres, the spheres touch along the body diagonal.)
Barium has a body-centered cubic structure. If the atomic radius of barium is 222 pm, calculate the density of solid barium.
The radius of gold is 144 pm and the density is 19.32 g/cm3. Does elemental gold have a face-centered cubic structure or a body-centered cubic structure?
The radius of tungsten is 137 pm and the density is 19.3 g/cm3. Does elemental tungsten have a face-centered cubic structure or a body-centered cubic structure?
Use the band model to describe differences among insulators, conductors, and semiconductors. Also use the band model to explain why each of the following increases the conductivity of a semiconductor. a. Increasing the temperature b. Irradiating with light c. Adding an impurity How do conductors
Rationalize why chalk (calcium carbonate) has a higher melting point than motor oil (large compounds made from carbon and hydrogen), which has a higher melting point than water, which engages in relatively strong hydrogen-bonding interactions.
How can an n-type semiconductor be produced from pure germanium? How can a p-type semiconductor be produced from pure germanium? Explain how n-type and p-type semiconductors increase electrical conductivity over that of pure germanium.
Explain how a p–n junction makes an excellent rectifier.
What is an alloy? Explain the differences in structure between substitutional and interstitial alloys. Give an example of each type.
The Group 3A/ Group 5A semiconductors are composed of equal amounts of atoms from Group 3A and Group 5A— for example, InP and GaAs. These types of semi-conductors are used in light-emitting diodes and solid-state lasers. What would you add to make a p-type semi-conductor from pure GaAs? How would
The band gap in aluminum phosphide (AlP) is 2.5 electron-volts (1 eV = 1.6 × 10–19 J). What wavelength of light is emitted by an AlP diode?
An aluminum antimonide solid-state laser emits light with a wavelength of 730 nm. Calculate the band gap in joules.
The structures of some common crystalline substances follow. Show that the net composition of each unit cell corresponds to the correct formula of each substance.
The unit cell for nickel arsenide is shown below. What is the formula of this compound?
Describe, in general, the structures of ionic solids. Com-pare and contrast the structures of sodium chloride and zinc sulfide. How many tetrahedral holes and octahedral holes are there per closest packed anion? In zinc sulfide, why are only one-half of the tetrahedral holes filled with cations?
Assume the two-dimensional structure of an ionic com-pound MxAy isWhat is the empirical formula of this ionic compound?
Identify the most important types of interparticle forces present in the solids of each of the following substances. a. Ar b. HCl c. HF d. CaCl2 e. CH4 f. CO g. NaNO3 h. NH4Cl i. Teflon, CF3(CF2CF2)nCF3 j. polyethylene, CH3(CH2CH2)nCH3 k. CHCl3 l. NH3 m. NO n. BF3
Cobalt fluoride crystallizes in a closest packed array of fluoride ions, with the cobalt ions filling one-half of the octahedral holes. What is the formula of this compound?
The compounds Na2O, CdS, and ZrI4 all can be described as cubic closest packed anions with the cations in tetrahedral holes. What fraction of the tetrahedral holes is occupied for each case?
The structure of manganese fluoride can be described as a simple cubic array of manganese ions with fluoride ions at the center of each edge of the cubic unit cell. What is the charge of the manganese ions in this compound?
The unit cell of MgO is shown below.Does MgO have a structure like that of NaCl or ZnS? If the density of MgO is 3.58 g/cm3, estimate the radius (in centimeters) of the O2- anions and the Mg2+ cations.

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