Using a Gabriel synthesis, propose an efficient synthesis for each of the following transformations. In each case, you will need to use reactions from previous chapters to convert the starting...

Why is the total energy of a many-electron atom not equal to the sum of the orbital energies for each electron?

How can you tell if one basis set is better than another in calculating the total energy of an atom?

Give examples of AOs for which the overlap reaches its maximum value only as the internuclear separation approaches zero in a diatomic molecule. Also give examples of AOs for which the overlap goes...

Phencyclidine (PCP) was originally developed as an anesthetic for animals, but it has since become an illegal street drug because it is a powerful hallucinogen. Treatment of PCP with excess methyl...

The total energy of a molecule is lowered if the orbital energy of the anti-bonding MO is negative, and raised if the orbital energy of the anti-bonding MO is positive. The zero of energy is the...

Explain why the nodal structures of the 1 g MOs in H 2 and F 2 differ.

Calculate the value for the coefficients of the AOs in Example Problem 23.4 for S 12 = 0.45. How are they different from the values calculated in that problem for S 12 = 0.3? Can you offer an...

Calculate the dipole moment of HF for the bonding MO in Equation (23.33). Use the method outlined in Section 23.8 to calculate the charge on each atom. The bond length in HF is 91.7 pm. The...

The bond dissociation energies of the species NO, CF , and CF + follow the trend CF + > NO > CF . Explain this trend using MO theory.

Show that the determinantal property used in the discussion of localized and delocalized orbitals in Section 24.6 is correct. ya + c a la b yb + d 9.

Explain why only two peaks are observed in the infrared spectrum of methane although six of the nine normal modes are infrared active.

The 1 H 35 Cl molecule can be described by a Morse potential with D e = 7.41 10 -19 J. The force constant k for this molecule is 516 N m 1 and v = 8.97 10 13 s 1 . a. Calculate the lowest four...

Can a molecule with C 3 h symmetry have a dipole moment? Give an example of a molecule with this symmetry and explain your reasoning.

Can a molecule with D 2 h symmetry have a dipole moment? Give an example of a molecule with this symmetry and explain your reasoning.

What is the difference between a symmetry element and a symmetry operation?

How do the results shown in Figure 20.10 differ from the predictions of the Bohr model of the H atom? Figure 20.10 1s 2p 2s d 3s d 3s 2p 2s 1s 10 15 20 rlag Radial distribution function

Consider the case of 10 oscillators and eight quanta of energy. Determine the dominant configuration of energy for this system by identifying energy configurations and calculating the corresponding...

The exact energy of a ground-state He atom is 79.01 eV. Calculate the correlation energy and the ratio of the correlation energy to the total energy for He using the results in Table 21.1. TABLE 21.1...

(Challenging) Building on the concept of equipartition, demonstrate that for any energy term of the form ax 2 , where α is a constant, the contribution to the internal energy is equal...

Determine the standard molar Gibbs energy for 35 Cl 35 Cl, where v = 560. cm 1 , B = 0.244 cm 1 , and the ground electronic state is non-degenerate.

Consider the molecular electrostatic potential map for the BH 3 molecule shown here. Is the hydrogen atom (shown as a white sphere) an electron acceptor or an electron donor in this molecule?

Why is the stoichiometry of a reaction generally not sufficient to determine reaction order?

What is the difference between the order of a reaction with respect to a given species and the overall order?

What is an elementary chemical step, and how is one used in kinetics?

What is the difference between chemical and physical methods for studying chemical kinetics?

Identify the molecular orbitals for F 2 in the images shown here in terms of the two designations discussed in Section 23.7. The molecular axis is the z axis, and the y axis is tilted slightly out of...

One issue confronting the use of 14 C decay to date materials is that of obtaining a standard. One approach to this issue is found in the field of dendrochronology, or using tree rings to determine...

For a type II second-order reaction, the reaction is 60% complete in 60 seconds when [A] 0 = 0.1 M and [B] 0 = 0.5 M. a. What is the rate constant for this reaction? b. Will the time for the reaction...

An experiment is performed on the branching reaction depicted in the text. Two things are determined: (1) The yield for B at a given temperature is found to be 0.3, and (2) the rate constants are...

A standard rule of thumb for thermally activated reactions is that the reaction rate doubles for every 10 K increase in temperature. Is this statement true independent of the activation energy...

Why does the list of elements for the D 6h group in Table 27.2 not list the elements C 2 6 , C 3 6 , and C 4 6 ? Selected Point Groups and Their Elements Symmetry Elements TABLE 27.2 Example Molecule...

Why does the list of elements for the D 6h group in Table 27.2 not list the elements S 2 6 , S 3 6 , and 6? Selected Point Groups and Their Elements Symmetry Elements TABLE 27.2 Example Molecule...

Use the 3 3 matrices for the C 2v group in Equation (27.3) to verify the group multiplication table for the following successive operations: a. v v b. v C 2 c. C 2 C 2

Draw the nucleoside formed from each of the following pairs of compounds and name the nucleoside: (a) 2-Deoxy-d-ribose and adenine (b) d-Ribose and guanine

Use the 3 Ã 3 matrices for the C 2v group in Equation (27.2) to verify the associative property for the following successive operations: a. b. ,(6,C2) = (6,6-)C () = 6,(2) %3D

Use the logic diagram of Figure 27.2 to determine the point group for allene. Indicate your decision-making process as was done in the text for NH3 1. linear? 2. C n axis? 3. more than 1C n axis? 4....

Use the logic diagram of Figure 27.2 to determine the point group for the planar molecule cisHBrC ¡ CClH. Indicate your decision-making process as was done in the text for NH 3 . a. linear? b....

CH 4 belongs to the T d point group with the following symmetry elements: E, 4C 3 , 4C 2 3 , 3C 2 , 3S 4 , 3S 3 4 , and 6Ï. Make a drawing similar to Figure 27.1 showing these elements. C2, S....

Four bases (A, C, T, and G) appear in DNA. Assume that the appearance of each base in a DNA sequence is random. a. What is the probability of observing the sequence AAGACATGCA? b. What is the...

The natural abundance of 13 C is roughly 1%, and the abundance of deuterium ( 2 H or D) is 0.015%. Determine the probability of finding the following in a mole of acetylene: a. H- 13 C- 13 C-H b. D-...

Draw a mechanism for the biosynthesis of α-farnesene starting with dimethylallyl pyrophosphate and isopentenyl pyrophosphate. a-Farnesene

The lowest four energy levels for atomic vanadium (V) have the following energies and degeneracies: What is the contribution to the average energy from electronic degrees of freedom for V when T =...

The reaction rate as a function of initial reactant pressures was investigated for the reaction 2NO(g) + 2H 2 (g) N 2 (g) + 2H 2 O(g), and the following data were obtained: What is the rate law...

For the sequential reaction k A = 1.00 Ã 10 -3 s -1 . Using a computer spreadsheet program such as Excel, plot the concentration of each species for cases where k B = 10k A , k B = 1.5k A ,...

Predict the product that is obtained when cellobiose is treated with each of the following reagents: (a) NaBH 4 , H 2 O (b) Br 2 , H 2 O (pH = 6) (c) CH 3 OH, HCl (d) Ac 2 O, pyridine

Determine the resultant internal loadings acting on section bb through the centroid C on the beam. B' 900 Ib/ft 60 3 ft 30 A 6 ft

When d-glucose is treated with aqueous sodium hydroxide, a complex mixture of carbohydrates is formed, including d-mannose and d-fructose. Over time, almost all aldohexoses will be present in the...

The rigid pipe is supported by a pin at A and an A-36 guy wire BD. If the wire has a diameter of 0.25 in., determine the load P if the end C is displaced 0.075 in. downward. 4 ft 3 ft 3 ft

The brake pads for a bicycle tire are made of rubber. If a frictional force of 50 N is applied to each side of the tires, determine the average shear strain in the rubber. Each pad has...

The rod has a diameter of 1 in. and a weight of 15 lb/ft. Determine the maximum torsional stress in the rod at a section located at B due to the rods weight. 4.5 ft -1.5 ft 1.5t B. 1.5 ft 4 ft

A tension test was performed on a steel specimen having an original diameter of 0.503 in. and gage length of 2.00 in. The data is listed in the table. Plot the stressstrain diagram and determine...

Data taken from a stressstrain test for a ceramic are given in the table. The curve is linear between the origin and the first point. Plot the diagram, and determine the modulus of elasticity and the...

Data taken from a stressstrain test for a ceramic are given in the table. The curve is linear between the origin and the first point. Plot the diagram, and determine approximately the modulus of...

The stressstrain diagram for a steel alloy having an original diameter of 0.5 in. and a gage length of 2 in. is given in the figure. Determine approximately the modulus of resilience and the modulus...

The elastic portion of the tension stressstrain diagram for an aluminum alloy is shown in the figure. The specimen used for the test has a gage length of 2 in. and a diameter of 0.5 in. When the...

Determine the resultant internal loadings acting on the cross sections at points F and G of the frame. 4 ft 75 Ib/ft B. -2 ft 1 ft -2 ft 1 ft 30 '1 ft 150 lb to

When the temperature is at 30°C, the A-36 steel pipe fits snugly between the two fuel tanks. When fuel flows through the pipe, it causes the temperature to vary along the pipe as T = (5/3 x 2 -...

When the temperature is at 30°C, the A-36 steel pipe fits snugly between the two fuel tanks. When fuel flows through the pipe, the temperatures at ends A and B rise to 130°C and 80°C,...

The brace and drill bit is used to drill a hole at O. If the drill bit jams when the brace is subjected to the forces shown, determine the resultant internal loadings acting on the cross section of...

The assembly has the diameters and material indicated. If it fits securely between its fixed supports when the temperature is T 1 = 70F, determine the average normal stress in each material when the...

If P = 15 kN, determine the average shear stress in the pins at A, B, and C. All pins are in double shear, and each has a diameter of 18 mm. 4P 4P 2P 0.5 m 0.5,m -1.5 m -1 m--1.5 m 307

The solid shaft is subjected to the distributed and concentrated torsional loadings shown. Determine the required diameter d of the shaft if the allowable shear stress for the material is Ï...

The copper pipe has an outer diameter of 3 in. and an inner diameter of 2.50 in. If it is tightly secured to the wall at C and it is subjected to the uniformly distributed torque along its entire...

The copper pipe has an outer diameter of 2.50 in. and an inner diameter of 2.30 in. If it is tightly secured to the wall and three torques are applied to it, determine the shear stress developed at...

A shaft is made of an aluminum alloy having an allowable shear stress of Ï allow = 100 MPa. If the diameter of the shaft is 100 mm, determine the maximum torque T that can be transmitted. What...

The solid shaft of radius r is subjected to a torque T. Determine the radius r­' of the inner core of the shaft that resists one-quarter of the applied torque (T/4). Solve the problem two ways:...

The solid shaft of radius r is subjected to a torque T. Determine the radius r­ of the inner core of the shaft that resists one-half of the applied torque (T>2). Solve the problem two ways: (a)...

The blade of the hacksaw is subjected to a pretension force of F = 100 N. Determine the resultant internal loadings acting on section aa that passes through point D. -225 mm 30%, D 150 mm

Determine the required minimum thickness t of member AB and edge distance b of the frame if P = 9 kip and the factor of safety against failure is 2. The wood has a normal failure stress of Ï...

If the allowable tensile stress for the bar is (Ï t ) allow = 21 ksi, and the allowable shear stress for the pin is Ï allow = 12 ksi, determine the diameter of the pin so that the load P...

A thin strip of rubber has an unstretched length of 15 in. If it is stretched around a pipe having an outer diameter of 5 in., determine the average normal strain in the strip.

If the load P on the beam causes the end C to be displaced 10 mm downward, determine the normal strain in wires CE and BD. 4 m -2 m-2m-| 3 m- -

The nylon cord has an original length L and is tied to a bolt at A and a roller at B. If a force P is applied to the roller, determine the normal strain in the cord when the roller is at C, and at D....

The composite shaft, consisting of aluminum, copper, and steel sections, is subjected to the loading shown. Determine the displacement of end A with respect to end D and the normal stress in each...

The A-36 steel shaft has a diameter of 50 mm and is subjected to the distributed and concentrated loadings shown. Determine the absolute maximum shear stress in the shaft and plot a graph of the...

The rigid beam is supported by the three posts A, B, and C. Posts A and C have a diameter of 60 mm and are made of a material for which E = 70 GPa and Ï Y = 20 MPa. Post B is made of a material...

The bar has a cross-sectional area of 0.5 in 2 and is made of a material that has a stressstrain diagram that can be approximated by the two line segments. Determine the elongation of the bar due to...

The resulting stress distribution along section AB for the bar is shown. From this distribution, determine the approximate resultant axial force P applied to the bar. Also, what is the stress...

Determine the maximum normal stress developed in the bar when it is subjected to a tension of P = 2 kip. 0.125 in. 1.875 in. 1.25 in. r = 0.25 in. 0.75 in.

The assembly consists of two posts AB and CD each made from material 1 having a modulus of elasticity of E 1 and a cross-sectional area A1, and a central post EF made from material 2 having a modulus...

The 2014-T6 aluminum rod AC is reinforced with the firmly bonded A992 steel tube BC. If the assembly fits snugly between the rigid supports so that there is no gap at C, determine the support...

The rigid bar is pinned at A and supported by two aluminum rods, each having a diameter of 1 in. and a modulus of elasticity E al = 10(103) ksi. If the bar is initially vertical, determine the...

The shaft is made of A992 steel with the allowable shear stress of Ï allow = 75 MPa. If gear B supplies 15 kW of power, while gears A, C and D withdraw 6 kW, 4 kW and 5 kW, respectively,...

The device shown is used to mix soils in order to provide in-situ stabilization. If the mixer is connected to an A-36 steel tubular shaft that has an inner diameter of 3 in. and an outer diameter of...

The 60-mm-diameter solid shaft is made of A-36 steel and is subjected to the distributed and concentrated torsional loadings shown. Determine the angle of twist at the free end A of the shaft due to...

The steel shaft is made from two segments: AC has a diameter of 0.5 in, and CB has a diameter of 1 in. If the shaft is fixed at its ends A and B and subjected to a torque of 500 lb # ft, determine...

The Am1004-T61 magnesium tube is bonded to the A-36 steel rod. If the allowable shear stresses for the magnesium and steel are (Ï allow ) mg = 45 MPa and (Ï allow ) st = 75 MPa,...

The two shafts are made of A-36 steel. Each has a diameter of 25 mm and they are connected using the gears fixed to their ends. Their other ends are attached to fixed supports at A and B. They are...

The shaft is fixed to the wall at A and is subjected to the torques shown. Determine the maximum shear stress in the shaft. A fillet weld having a radius of 2.75 mm is used to connect the shafts at...

The 304 stainless steel tube has a thickness of 10 mm. If the applied torque is T = 50 N # m, determine the average shear stress in the tube. The mean dimensions are shown. 30 mm 70 mm

For a given maximum average shear stress, determine the factor by which the torque-carrying capacity is increased if the half-circular section is reversed from the dashed-line position to the section...

The A-36 steel circular tube is subjected to a torque of 10 kN # m. Determine the shear stress at the mean radius Ï = 60 mm and calculate the angle of twist of the tube if it is 4 m long and...

The tube has a length of 2 m and is made of an elastic perfectly plastic material as shown. Determine the torque needed to just cause the material to become fully plastic. What is the permanent angle...

If the solid shaft is made from red brass C83400 and it is subjected to a torque T = 6 kip # ft at B, determine the maximum shear stress developed in segments AB and BC. 2 ft 2 in. 2 in. 4 ft 70 4...

The 2-m-long tube is made of an elastic perfectly plastic material as shown. Determine the applied torque T, which subjects the material at the tube's outer edge to a shear strain of max = 0.006...

The solid shaft is made of an elastic perfectly plastic material. Determine the torque T needed to form an elastic core in the shaft having a radius of Ï Y = 20 mm. If the shaft is 3 m long,...

The crane is used to support the engine, which has a weight of 1200 lb. Draw the shear and moment diagrams of the boom ABC when it is in the horizontal position. - 3 ft -5 ft- 4 ft

Draw the shear and moment diagrams for the beam. 300 Ib 300 lb 200 lb/ft 4 ft 6 ft 4 ft

Draw the shear and moment diagrams for the beam. Mo Mo L/2- -L/2