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engineering
chemical engineering

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

Consider the following electrochemical cell:a. If silver metal is a product of the reaction, is the cell a galvanic cell or electrolytic cell? Label the cathode and anode, and describe the direction of the electron flow. b. If copper metal is a product of the reaction, is the cell a galvanic cell
An experimental fuel cell has been designed that uses carbon monoxide as fuel. The overall reaction is 2CO(g) + O2(g) → 2CO2(g) The two half cell reactions are CO + O2- → CO2 + 2e- O2 + 4e– → 2O2- The two half reactions are carried out in separate compartments connected with a solid
Batteries are galvanic cells. What happens to ϐ cell as a battery discharges? Does a battery represent a system at equilibrium? Explain. What is ϐ cell when a battery reaches equilibrium? How are batteries and fuel cells alike? How are they different? The U. S. space program uses
A fuel cell designed to react grain alcohol with oxygen has the following net reaction: C2H5OH(l) + 3O2(g) → 2CO2(g) + 3H2O(l) The maximum work 1 mole of alcohol can yield by this process is 1320 kJ. What is the theoretical maximum voltage this cell can achieve?
What is the maximum work that can be obtained from a hydrogen– oxygen fuel cell at standard conditions that produces 1.00 kg of water at 25oC? Why do we say that this is the maximum work that can be obtained? What are the advantages and disadvantages in using fuel cells rather than the
The overall reaction and standard cell potential at 25oC for the rechargeable nickel–cadmium alkaline battery is Cd(s) + NiO2(s) + 2H2O(l) → Ni(OH)2(s) + Cd(OH)2(s) ϐo = 1.10 V For every mole of Cd consumed in the cell, what is the maximum useful work that can be obtained at standard
Not all spontaneous redox reactions produce wonderful results. Corrosion is an example of a spontaneous redox process that has negative effects. What happens in the corrosion of a metal such as iron? What must be present for the corrosion of iron to take place? How can moisture and salt increase
Explain how the following protect metals from corrosion. a. Paint b. Durable oxide coatings c. Galvanizing d. Sacrificial metal e. Alloying f. Cathodic protection
Consider the following galvanic cells:For each galvanic cell, give the balanced cell equation and determine Ïo. Standard reduction potentials are found in Table 11.1. Table 11.1
In theory, most metals should easily corrode in air. Why? A group of metals called the noble metals are relatively difficult to corrode in air. Some noble metals include gold, platinum, and silver. Reference Table 11.1 to come up with a possible reason why the noble metals are relatively difficult
In 1973 the wreckage of the Civil War ironclad USS Monitor was discovered near Cape Hatteras, North Carolina. [The Monitor and the CSS Virginia (formerly the USS Merrimack) fought the first battle between iron-armored ships.] In 1987 investigations were begun to see whether the ship could be
A standard galvanic cell is constructed so that the overall cell reaction is 2Al3+(aq) + 3M(s) → 3M2+(aq) + 2Al(s) where M is an unknown metal. If ΔGo = –411 kJ for the overall cell reaction, identify the metal used to construct the standard cell.
Consider the following half reactions: Pt2+ + 2e– → Pt ϐo = 1.188 V PtCl42– + 2e– → Pt + 4Cl2 ϐo = 0.755 V NO3- + 4H+ + 3e– → NO + 2H2O ϐo = 0.96 V Explain why platinum metal will dissolve in aqua regia (a mixture of hydrochloric and nitric acids) but not in either concentrated
Consider the following reduction potentials: Co3+ + 3e– → Co ϐo = 1.26 V Co2+ + 2e– → Co ϐo = 20.28 V a. When cobalt metal dissolves in 1.0 M nitric acid, will Co3+ or Co2+ be the primary product (assuming standard conditions)? b. Is it possible to change the concentration of HNO3 to
The measurement of pH using a glass electrode obeys the Nernst equation. The typical response of a pH meter at 25.00oC is given by the equation ϐmeas = ϐ ref 1 0.05916 pH where ϐref contains the potential of the reference electrode and all other potentials that arise in the cell that are not
Consider the standard galvanic cell based on the following half reactions Cu2+ + 2e- → Cu Ag+ + e- → Ag The electrodes in this cell are Ag(s) and Cu(s). Does the cell potential increase, decrease, or remain the same when the following changes occur to the standard cell? a. CuSO4(s) is added
Give the standard line notation for each cell in Exercise 21.Exercise 21.
An electrochemical cell is set up using the following unbalanced reaction: Ma+(aq) + N(s) → N2+(aq) + M(s) The standard reduction potentials are Ma+ + ae– → M ϐo = 10.400 V N2+ + 2e- → N ϐo = 10.240 V The cell contains 0.10 M N2+ and produces a voltage of 0.180 V. If the
A zinc–copper battery is constructed as follows: Zn | Zn2+(0.10 M) | | Cu2+(2.50 M) | Cu The mass of each electrode is 200 g. a. Calculate the cell potential when this battery is first connected.
The measurement of F- ion concentration by ion-selective electrodes at 25.00oC obeys the equation ϐmeas = ϐref – 0.05916 log[F–]
When copper reacts with nitric acid, a mixture of NO(g) and NO2(g) is evolved. The volume ratio of the two product gases depends on the concentration of the nitric acid according to the equilibrium 2H+(aq) + 2NO3–(aq) + NO(g) ⇌ 3NO2(g) + H2O(l) Consider the following standard reduction
Consider the following galvanic cell:Calculate the concentrations of Ag+(aq) and Ni2+(aq) once the cell is €œ dead.€
A galvanic cell is based on the following half reactions: Fe2+ + 2e– → Fe(s) ϐo = 20.440 V 2H+ + 2e– → H2(g) ϐo = 0.000 V In this cell the iron compartment contains an iron electrode and [Fe2+] = 1.00 × 10–3 M, and the hydrogen compartment contains a platinum electrode, PH2 = 1.00 atm
You have a concentration cell with Cu electrodes and [Cu2+] = 1.00 M (right side) and 1.0 × 1024 M (left side). a. Calculate the potential for this cell at 25oC. b. The Cu21 ion reacts with NH3 to form Cu(NH3)42+, where the stepwise formation constants are K1 = 1.0 × 103, K2 = 1.0 × 104, K3 =
A galvanic cell is based on the following half reactions: Ag+ + e2 → Ag(s) ϐo = 0.80 V Cu2+ + 2e2 → Cu(s) ϐo = 0.34 V In this cell the silver compartment contains a silver electrode and excess AgCl(s) (Ksp = 1.6 × 10–10), and the copper compartment contains a copper electrode and [Cu2+] =
Consider the following galvanic cell:Calculate the Ksp value for Ag2SO4(s). Note that to obtain silver ions in the right compartment (the cathode compartment), excess solid Ag2SO4 was added and some of the salt dissolved.
Consider the following galvanic cell:
Microwave radiation has a wavelength on the order of 1.0 cm. Calculate the frequency and the energy of a single photon of this radiation. Calculate the energy of an Avogadro’s number of photons (called an einstein) of this electromagnetic radiation.
What experimental evidence supports the quantum theory of light? Explain the wave–particle duality of all matter. For what size particle must one consider both the wave and the particle properties?
Write equations corresponding to the following energy terms.a. The fourth ionization energy of Seb. The electron affinity of S-c. The electron affinity of Fe3+d. The ionization energy of Mge. The work function of Mg (see Exercise 27)Exercise 127.
The successive ionization energies for an unknown element are I1 = 896 kJ/mol I2 = 1752 kJ/mol I3 = 14,807 kJ/mol I4 = 17,948 kJ/mol To which family in the periodic table does the unknown element most likely belong?
An unknown element is a nonmetal and has a valence electron configuration of ns2np4. a. How many valence electrons does this element have? b. What are some possible identities for this element? c. What is the formula of the compound this element would form with potassium? d. Would this element have
An ion having a 41 charge and a mass of 49.9 amu has two electrons with n = 1, eight electrons with n = 2, and ten electrons with n = 3. Supply the following properties for the ion. (Hint: In forming ions, the 4s electrons are lost before the 3d electrons.) a. The atomic number b. Total number of s
Consider the following ionization energies for aluminum. Al(g) → Al+(g) + e- I1 = 580 kJ/mol Al+(g) → Al2+(g) + e- I2 = 1815 kJ/mol Al2+(g) → Al3+(g) + e- I3 = 2740 kJ/mol Al3+(g) → Al4+(g) + e- I4 = 11,600 kJ/ mol a. Account for the increasing trend in the values of the ionization
Answer the following questions, assuming that ms has four values rather than two and that the normal rules apply for n, ℓ, and mℓ. a. How many electrons could an orbital hold? b. How many elements would be contained in the first and second periods of the periodic table? c. How many elements
Although Mendeleev predicted the existence of several undiscovered elements, he did not predict the existence of the noble gases, the lanthanides, or the actinides. Propose reasons why Mendeleev was not able to predict the existence of the noble gases.
Human color vision is €œproduced€ by the nervous system based on how three different cone receptors interact with photons of light in the eye. These three different types of cones interact with photons of different frequency light, as indicated in the following chart:What
Assume that four electrons are confined to a one-dimensional box 5.64 × 10-10 m in length. If two electrons can occupy each allowed energy level, calculate the wavelength of electromagnetic radiation necessary to promote the highest- energy electron into the first excited state.
The figure below represents part of the emission spectrum for a one- electron ion in the gas phase. All the lines result from electronic transitions from excited states to the n = 3 state.a. What electronic transitions correspond to lines A and B? b. If the wavelength of line B is 142.5 nm,
Explain the photoelectric effect.
An atom moving at its root mean square velocity at 100oC has a wavelength of 2.31 × 10-11 m. Which atom is it?
The ground state ionization energy for the one electron ion Xm+ is 4.72 × 104 kJ/ mol. Identify X and m.
When the excited electron in a hydrogen atom falls from n = 5 to n = 2, a photon of blue light is emitted. If an excited electron in He1 falls from n = 4, which energy level must it fall to so that a similar blue light (as with hydrogen) is emitted? Prove it.
The treatment of a particle in a one-dimensional box can be extended to a two-dimensional box of dimensions Lx and Ly yielding the following expression for energy:The two quantum numbers independently can assume only integer values. Consider an electron confined to a two-dimensional box that is
The following numbers are the ratios of second ionization energy to first ionization energy: Na: 9.2 P: 1.8 Mg: 2.0 S: 2.3 Al: 3.1 Cl: 1.8 Si: 2.0 Ar: 1.8 Explain these relative numbers.
For a hydrogen atom in its ground state, calculate the relative probability of finding the electron in the area described. a. In a sphere of volume 1.0 × 10-3 pm3 centered at the nucleus b. In a sphere of volume 1.0 × 10-3 pm3 centered on a point 1.0 × 10-11 m from the nucleus c. In a sphere of
The treatment of a particle in a one-dimensional box can be extended to a rectangular box of dimensions Lx, Ly, and Lz, yielding the following expression for energy:The three quantum numbers nx, ny, and nz independently can assume only integer values. a. Determine the energies of the three lowest
Assume that eight electrons are placed into the allowed energy levels of a cubic box where two electrons can occupy each allowed energy level. (See Exercise 148 for the appropriate energy equation.) Calculate the wavelength of light necessary to promote the highest-energy ground-state electron into
Assume that we are in another universe with different physical laws. Electrons in this universe are described by four quantum numbers with meanings similar to those we use. We will call these quantum numbers p, q, r, and s. The rules for these quantum numbers are as follows: p = 1, 2, 3, 4, 5, . .
The ionization energy for a 1s electron in a silver atom is 2.462 × 106 kJ/ mol. a. Determine an approximate value for Zeff for the Ag 1s electron. You will first have to derive an equation that relates Zeff to ionization energy. b. How does Zeff from part a compare to Z for Ag? Rationalize the
Calculate the de Broglie wavelength for each of the following. a. An electron with a velocity 10% of the speed of light b. A tennis ball (55 g) served at 35 m/s (80 mi/h)
Without looking at data in the text, sketch a qualitative graph of the third ionization energy versus atomic number for the elements Na through Ar, and explain your graph.
From the information below, identify element X. a. The wavelength of the radiowaves sent by an FM station broadcasting at 97.1 MHz is 30 million (3.00 × 107) times greater than the wavelength corresponding to the energy difference between a particular excited state of the hydrogen atom and the
Neutron diffraction is used in determining the structures of molecules. a. Calculate the de Broglie wavelength of a neutron moving at 1.00% of the speed of light. b. Calculate the velocity of a neutron with a wave-length of 75 pm (1 pm = 10-12 m).
Calculate the velocities of electrons with de Broglie wavelengths of 1.0 × 102 nm and 1.0 nm, respectively.
An atom of a particular element is traveling at 1% of the speed of light. The de Broglie wavelength is found to be 3.31 × 10-3 pm. Which element is this?
Characterize the Bohr model of the atom. In the Bohr model, what do we mean when we say something is quantized? How does the Bohr model of the hydrogen atom explain the hydrogen emission spectrum? Why is the Bohr model fundamentally incorrect?
The following is an energy- level diagram illustrating three different electronic transitions in the Bohr hydrogen atom.a. Explain why the energy levels get closer together as they increase. Provide mathematical support for this. b. Verify that the colors given in the diagram are correct. Provide
Calculate the wavelength of light emitted when each of the following transitions occur in the hydrogen atom. What type of electromagnetic radiation is emitted in each transition? a. n = 4 → n = 3 b. n = 5 → n = 4 c. n = 5 → n = 3
Assume that a hydrogen atom’s electron has been excited to the n = 5 level. How many different wavelengths of light can be emitted as this excited atom loses energy?
Consider the following waves representing electromagnetic radiation:Which wave has the longer wavelength? Calculate the wavelength. Which wave has the higher frequency and larger photon energy? Calculate these values. Which wave has the greater velocity? What type of electromagnetic radiation does
An electron is excited from the ground state to the n = 3 state in a hydrogen atom. Which of the following state-ments are true? Correct any false statements. a. It takes more energy to ionize (remove) the electron from n = 3 than from the ground state. b. The electron is farther from the nucleus
Does a photon of visible light (l = 400 – 700 nm) have sufficient energy to excite an electron in a hydrogen atom from the n = 1 to the n = 5 energy state? From the n = 2 to the n = 6 energy state?
An excited hydrogen atom emits light with a wavelength of 397.2 nm to reach the energy level for which n = 2. In which principal quantum level did the electron begin?
An excited hydrogen atom with an electron in the n = 5 state emits light having a frequency of 6.90 × 1014 s-1. Determine the principal quantum level for the final state in this electronic transition.
Consider an electron for a hydrogen atom in an excited state. The maximum wavelength of electromagnetic radiation that can completely remove (ionize) the electron from the H atom is 1460 nm. Determine the initial excited state for the electron (n = ?).
Calculate the energy (in kJ/ mol) required to remove the electron in the ground state for each of the following one- electron species using the Bohr model. a. H b. He+ c. Li2+ d. C5+ e. Fe25+
One of the emission spectral lines for Be3+ has a wave-length of 253.4 nm for an electronic transition that begins in the state with n = 5. What is the principal quantum number of the lower-energy state corresponding to this emission?
The Heisenberg uncertainty principle can be expressed in the formwhere E represents energy and t represents time. Show that the units for this form are the same as the units for the form used in this chapter:
Using the Heisenberg uncertainty principle, calculate Δx for each of the following. a. An electron with Δv = 0.100 m/s b. A baseball (mass = 145 g) with Δv = 0.100 m/ s How does the answer in part a compare with the size of a hydrogen atom? How does the answer in part b correspond to the size of
One type of electromagnetic radiation has a frequency of 107.1 MHz, another type has a wavelength of 2.12 × 10-10 m, and another type of electromagnetic radiation has photons with energy equal to 3.97 × 10-19 J/ photon. Identify each type of electromagnetic radiation, and place them in order of
We can represent both probability and radial probability versus distance from the nucleus for a hydrogen 1s orbital as depicted below.What does each graph tell us about the electron in a hydrogen 1s orbital? Describe the significance of the radial probability distribution.
Calculate the wavelength of the electromagnetic radiation required to excite an electron from the ground state to the level with n = 5 in a one-dimensional box 40.0 pm in length.
An electron in a one- dimensional box requires a wavelength of 8080 nm to excite an electron from the n = 2 to the n = 3 energy level. Calculate the length of this box.
An electron in a 10.0 nm one-dimensional box is excited from the ground state into a higher- energy state by absorbing a photon of electromagnetic radiation with a wavelength of 1.374×10-5 m. Determine the final energy state for this transition.
Discuss what happens to the energy levels for an electron trapped in a one-dimensional box as the length of the box increases.
What is the total probability of finding a particle in a one-dimensional box in level n = 3 between x = 0 and x = L/ 6?
Which has the lowest (ground-state) energy, an electron trapped in a one dimensional box of length 10-6 m or one with length 10-10 m?
What are quantum numbers? What information do we get from the quantum numbers n, ℓ, and mℓ? We define a spin quantum number (ms)ℓ but do we know that an electron literally spins?
How do 2p orbitals differ from each other? How do 2p and 3p orbitals differ from each other? What is a nodal surface in an atomic orbital?
Carbon absorbs energy at a wavelength of 150 nm. The total amount of energy emitted by a carbon sample is 1.98 × 105 J. Calculate the number of carbon atoms present in the sample, assuming that each atom emits one photon.
Identify each of the following orbitals, and determine the n and l quantum numbers. Explain your answers.
Which of the following orbital designations are incorrect: 1s, 1p, 7d, 9s, 3f, 4f, 2d?
Which of the following sets of quantum numbers are not allowed in the hydrogen atom? For the sets of quantum numbers that are incorrect, state what is wrong in each set. a. n = 3, ℓ = 2, mℓ = 2 b. n = 4, ℓ = 3, mℓ = 4 c. n = 0, ℓ = 0, mℓ = 0 d. n = 2, ℓ = 21, mℓ = 1
Which of the following sets of quantum numbers are not allowed? For each incorrect set, state why it is incorrect. a. n = 3, ℓ = 3, mℓ = 0, ms = - 1/2 b. n = 4, ℓ = 3, mℓ = 2, ms = - 1/2 c. n = 4, ℓ = 1, mℓ = 1, ms = + 1/2 d. n = 2, ℓ = 1, mℓ = 21, ms = - 1 e. n = 5, ℓ = 24, mℓ
How many orbitals can have the designation 5p, 3dz2, 4d, n = 5, and n = 4?
How many electrons in an atom can have the designation 1p, 6dx2-y2, 4f, 7py, 2s, and n = 3?
From the diagrams of 2p and 3p orbitals in Fig.19 and Fig.20, respectively, draw a rough graph of the square of the wave function for these orbitals in the direction of one of the lobes.Figure 12.19Figure 20
The wave function for the 2pz orbital in the hydrogen atom isWhere a0 is the value for the radius of the first Bohr orbit in meters (5.29 Ã— 10-11), Ïƒ is Zr/a0, r is the value for the distance from the nucleus in meters, and Î¸ is an angle. Calculate the value of
For hydrogen atoms, the wave function for the state n = 3, „“ = 0, and m„“ = 0 iswhere Ïƒ = r/a0 and a0 is the Bohr radius (5.29 Ã— 10-11 m). Calculate the position of the nodes for this wave function.
Total radial probability distributions for the helium, neon, and argon atoms are shown in the following graph. How can the shapes of these curves be interpreted in terms of electron configurations, quantum numbers, and nuclear charges?
A carbon–oxygen double bond in a certain organic molecule absorbs radiation that has a frequency of 6.0 × 1013 s-1. a. What is the wavelength of this radiation? b. To what region of the spectrum does this radiation belong? c. What is the energy of this radiation per photon? Per mole of
The relative orbital levels for the hydrogen atom can be represented asDraw the relative orbital energy levels for atoms with more than one electron, and explain your answer. Also explain how the following radial probability distributions support your answer.
What is the difference between core electrons and valence electrons? Why do we emphasize the valence electrons in an atom when discussing atomic properties? What is the relationship between valence electrons and elements in the same group of the periodic table?
The periodic table consists of four blocks of elements that correspond to s, p, d, and f orbitals being filled. After f orbitals come g and h orbitals. In theory, if a g block and an h block of elements existed, how long would the rows of g and h elements be in this theoretical periodic table?
What is the maximum number of electrons in an atom that can have these quantum numbers? a. n = 4 b. n = 5, mℓ = +1 c. n = 5, ms = + 1/2 d. n = 3, ℓ = 2 e. n = 2, ℓ = 1 f. n = 0, ℓ = 0, mℓ = 0 g. n = 2, ℓ = 1, mℓ = –1, ms = – 1/2 h. n = 3, ms = + 1/2 i. n = 2, ℓ = 2 j. n = 1, ℓ
The elements of Si, Ga, As, Ge, Al, Cd, S, and Se are all used in the manufacture of various semiconductor devices. Write the expected electron configurations for these atoms.
Write the expected electron configurations for the following atoms: Sc, Fe, P, Cs, Eu, Pt, Xe, and Br.
Write the expected electron configurations for each of the following atoms: Cl, As, Sr, W, Pb, and Cf.
Write the expected ground-state electron configuration for the following. a. The element with one unpaired 5p electron that forms a covalent compound with fluorine. b. The (as yet undiscovered) alkaline earth metal after radium c. The noble gas with electrons occupying 4f orbitals d. The first-row

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