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chemistry
physical chemistry

College Physics 7th edition Jerry D. Wilson, Anthony J. Buffa, Bo Lou - Solutions

Which of the indicators in Fig. could be used for doing the titrations in Exercises 66 and 68?Fig
When a diprotic acid, H2A, is titrated with NaOH, the protons on the diprotic acid are generally removed one at a time, resulting in a pH curve that has the following generic shape:a. Notice that the plot has essentially two titration curves. If the first equivalence point occurs at 100.0 mL NaOH
Consider the titration of 100.0 mL of 0.100 M H3A (Ka1 = 5.0 × 10-4, Ka2 = 1.0 × 10–8, Ka3 = 1.0 × 10-11) with 0.0500 M NaOH. a. Calculate the pH after 100.0 mL of 0.0500 M NaOH has been added. b. What total volume of 0.0500 M NaOH is required to reach a pH of 8.67?
The titration of Na2CO3 with HCl has the following qualitative profile:
For which of the following is the Ksp value of the ionic compound the largest? The smallest? Explain your answer.
Ag2S(s) has a larger molar solubility than CuS even though Ag2S has the smaller Ksp value. Explain how this is possible.
Calculate the solubility of each of the following compounds in moles per liter and grams per liter. (Ignore any acid–base properties.) a. Ag3PO4, Ksp = 1.8 × 10-18 b. CaCO3, Ksp = 8.7 × 10-9
Calculate the solubility of each of the following com-pounds in moles per liter. Ignore any acid– base properties. a. PbI2, Ksp = 1.4 × 10–8 b. CdCO3, Ksp = 5.2 × 10–12 c. Sr3(PO4)2, Ksp = 1 × 10-31
Use the following data to calculate the Ksp value for each solid. a. The solubility of CaC2O4 is 6.1 × 10–3 g/ L. b. The solubility of BiI3 is 1.32 × 10–5 mol/ L.
The solubility of the ionic compound M2X3, having a molar mass of 288 g/ mol, is 3.60 × 10-7 g/ L. Calculate the Ksp of the compound.
For each of the following pairs of solids, determine which solid has the smallest molar solubility. a. CaF2(s), Ksp = 4.0 × 10-11 or BaF2(s), Ksp = 2.4 × 10-5 b. Ca3(PO4) 2(s), Ksp = 1.3 × 10-32 or FePO4(s), Ksp = 1.0 × 10-22
The Ksp for silver sulfate (Ag2SO4) is 1.2 × 10-5. Calculate the solubility of silver sulfate in each of the following. a. Water b. 0.10 M AgNO3 c. 0.20 M K2SO4
Calculate the solubility (in mol/ L) of Fe(OH) × (Ksp = 4 × 10-38) in each of the following. a. water (assume pH is 7.0 and constant)
What mass of ZnS (Ksp = 2.5 × 10-22) will dissolve in 300.0 mL of 0.050 M Zn(NO3)2? Ignore the basic properties of S2-.
The concentration of Mg2+ in seawater is 0.052 M. At what pH will 99% of the Mg2+ be precipitated as the hydroxide salt? [Ksp for Mg(OH)2 = 8.9 × 10-12.]
Explain the following phenomenon:
For which salt in each of the following groups will the solubility depend on pH? a. AgF, AgCl, AgBr b. Pb(OH)2, PbCl2 c. Sr(NO3)2, Sr(NO2)2 d. Ni(NO3)2, Ni(CN)2
Describe how you could separate the ions in each of the following groups by selective precipitation. a. Ag+, Mg2+, Cu2+ b. Pb2+, Ca2+, Fe2+ c. Cl-, Br-, I- d. Pb2+, Bi3+
Nanotechnology has become an important field, with applications ranging from high-density data storage to the design of €œnano machines.€ One common building block of nanostructured architectures is manganese oxide nanoparticles. The particles can be formed from manganese
When aqueous KI is added gradually to mercury(II) nitrate, an orange precipitate forms. Continued addition of KI causes the precipitate to dissolve. Write balanced equations to explain these observations. (Hint: Hg2+ reacts with I2 to form HgI42-.)
The overall formation constant for HgI42- is 1.0 Ã— 1030. That is,
Kf for the complex ion Ag(NH3)2+ is 1.7 × 107. Ksp for AgCl is 1.6 × 10-10. Calculate the molar solubility of AgCl in 1.0 M NH3.
a. Using the Ksp for Cu(OH)2 (1.6 × 10-19) and the overall formation constant for Cu(NH3)42+ (1.0 × 1013), calculate a value for the equilibrium constant for the reaction Cu(OH)2(s) + 4NH3(aq) ⇌ Cu(NH3) 42+(aq) + 2OH–(aq) b. Use the value of the equilibrium constant you calculated in part a
The copper(I) ion forms a chloride salt that has Ksp = 1.2 × 10-6. Copper(I) also forms a complex ion with Cl2: Cu+(aq) + 2Cl-(aq) ⇌ CuCl2-(aq) K = 8.7 × 104 a. Calculate the solubility of copper(I) chloride in pure water. (Ignore CuCl2- formation for part a.) b. Calculate the solubility of
a. Calculate the molar solubility of AgI in pure water. Ksp for AgI is 1.5 × 10-16. b. Calculate the molar solubility of AgI in 3.0 M NH3. The overall formation constant for Ag(NH3)2+ is 1.7 × 107. c. Compare the calculated solubilities from parts a and b. Explain any differences.
Will a precipitate of Cd(OH)2 form if 1.0 mL of 1.0 M Cd(NO3)2 is added to 1.0 L of 5.0 M NH3? Cd2+(aq) + 4NH3(aq) ⇌ Cd(NH3)42+(aq) K = 1.0 × 107 Cd(OH)2(s) ⇌ Cd2+(aq) + 2OH-(aq) Ksp = 5.9 × 10-15
Tris(hydroxymethyl)aminomethane, commonly called TRIS or Trizma, is often used as a buffer in biochemical studies. Its buffering range is from pH 7 to 9, and Kb is 1.19 Ã— 10-6 for the reactiona. What is the optimum pH for TRIS buffers? b. Calculate the ratio [TRIS]/[TRISH+] at pH =
The salts in Table 8.5, with the possible exception of the hydroxide salts, have one of the following mathematical relationships between the Ksp value and the molar solubility s.i. Ksp = s2ii. Ksp = 4s3iii. Ksp = 27s4iv. Ksp = 108s5For each mathematical relationship, give an example of a salt in
You have the following reagents on hand:What combinations of reagents would you use to prepare buffers at the following pH values? a. 3.0 b. 4.0 c. 5.0 d. 7.0 e. 9.0
Another way to treat data from a pH titration is to graph the absolute value of the change in pH per change in milliliters added versus milliliters added (ΔpH/ ΔmL versus mL added). Make this graph using your results from Exercise 65. What advantage might this method have over the traditional
The equilibrium constant for the following reaction is 1.0 Ã— 10-3:
Calculate the concentration of Pb2+ in each of the following.
The active ingredient in aspirin is acetylsalicylic acid. A 2.51-g sample of acetylsalicylic acid required 27.36 mL of 0.5106 M NaOH for complete reaction. Addition of 15.44 mL of 0.4524 M HCl to the flask containing the aspirin and the sodium hydroxide produced a mixture with pH = 3.48. Find the
Consider the following two acids: pKa1 = 2.98; pKa2 = 13.40HO2CCH2CH2CH2CH2CO2H Adipic acid pKa1 = 4.41; pKa2 = 5.28 In two separate experiments, the pH was measured during the titration of 5.00 mmol of each acid with 0.200 M NaOH. Each experiment showed only one stoichiometric point when the data
The copper(I) ion forms a complex ion with CN- according to the following equation: Cu+(aq) + 3CN-(aq) ⇌ Cu(CN)32-(aq) Kf = 1.0 × 1011 a. Calculate the solubility of CuBr(s) (Ksp = 1.0 × 10-5) in 1.0 L of 1.0 M NaCN. b. Calculate the concentration of Br- at equilibrium. c. Calculate the
a. Calculate the molar solubility of SrF2 in water, ignoring the basic properties of F-. (For SrF2, Ksp = 7.9 × 10-10) b. Would the measured molar solubility of SrF2 be greater than or less than the value calculated in part a? Explain.
What is the maximum possible concentration of Ni2+ ion in water at 25oC that is saturated with 0.10 M H2S and maintained at pH 3.0 with HCl?
A mixture contains 1.0 × 10-3 M Cu2+ and 1.0 × 10-3 M Mn2+ and is saturated with 0.10 M H2S. Determine a pH where CuS precipitates but MnS does not precipitate. Ksp for CuS = 8.5 × 10-45 and Ksp for MnS = 2.3 × 10-13.
What volume of 0.0100 M NaOH must be added to 1.00 L of 0.0500 M HOCl to achieve a pH of 8.00?
Consider the titration of 100.0 mL of 0.10 M phosphoric acid with 0.10 M NaOH.a. Determine the pH at the third half- equivalence point by assuming it is a €œspecial point€ (see Fig.).b. Calculate the pH at the third equivalence point.c. Why must the answer to part a be
Consider the titration curve in Exercise 89 for the titration of Na2CO3 with HCl. a. If a mixture of NaHCO3 and Na2CO3 was titrated, what would be the relative sizes of V1 and V2? b. If a mixture of NaOH and Na2CO3 was titrated, what would be the relative sizes of V1 and V2? c. A sample contains a
Two cylinders of equal mass sitting on a horizontal surface are made from materials with different densities. (a) Which cylinder will have the greater moment of inertia about an axis passing horizontally through the center? (b) Which cylinder will have the greater moment of inertia about an axis
Here is an interesting experiment you can try for your-self at home. Prepare a hard- boiled egg and have a raw egg available. Set them both spinning on the kitchen table. Stop both eggs quickly, and the release both. You will notice the hard- boiled one remains at rest, whereas the raw one starts
Why does jerking a paper towel from a roll cause the paper to tear more easily than pulling it smoothly? Will the amount of paper on the roll affect the results?
A solid cylinder and an annular cylinder of equal mass are rolling on the floor with the same speed. (a) If the solid cylinder’s radius is equal to the annular cylinder’s inner radius, which cylinder would be harder to stop? Explain. (b) Would it make any stopping difference if the solid
Cats usually land on their feet when they fall, even if held upside down when dropped ( Fig. 8.35). While a cat is falling, there is no external torque and its center of mass falls as a particle. How can cats turn themselves over while falling?
Two ice skaters that weigh the same skate toward each other with the same mass and same speed on parallel paths. As they pass each other, they link arms. (a) What is the velocity of their center of mass after they link arms? (b) What happens to their initial, translational kinetic energies?
If the top of your automobile tire is moving with a speed of v, what is the reading of your speedometer?
In cutting large trees, loggers first notch or make a V- cut on the side of the tree in the desired direction of fall and then cut from the other side. Why is this? Is there any danger for the logger to be on the opposite side of the tree of the direction of fall?
A yo-yo is thrown downward with a rotational spin. Reaching the bottom of the string, it climbs back upward. Is the rotational direction reversed at the bottom? Explain.
The drain plug on a car’s engine has been tightened to a torque of 25 m ∙ N. If a 0.15-m-long wrench is used to change the oil, what is the minimum force needed to loosen the plug?
In Exercise 10, due to limited work space, you must crawl under the car. The force thus cannot be applied perpendicularly to the length of the wrench. If the applied force makes a 30o angle with the length of the wrench, what is the force required to loosen the drain plug? In Exercise The drain
Two children are sitting on opposite ends of a uniform seesaw of negligible mass. (a) Can the seesaw be balanced if the masses of the children are different? How? (b) If a 35-kg child is 2.0 m from the pivot point (or fulcrum), how far from the pivot point will her 30-kg playmate have to sit on
A uniform meter stick pivoted at its center, as in Example 8.5, has a 100-g mass suspended at the 25.0-cm position. (a) At what position should a 75.0-g mass be suspended to put the system in equilibrium? (b) What mass would have to be suspended at the 90.0-cm position for the system to be in
A worker applies a horizontal force to the top edge of a crate to get it to tip forward (Fig. 8.36). If the create has a mass of 100 kg and is 1.6 m tall and 0.80 m in depth and width, what is the minimum force needed to make the crate start tipping? (Assume the center of mass of the crate is at
Show that the balanced meterstick in Example 8.5 is in static rotational equilibrium about a horizontal axis through the 100-cm end of the stick.
Telephone and electrical lines are allowed to sag between poles so that the tension will not be too great when something hits or sits on the line. (a) Is it possible to have the lines perfectly horizontal? Why or why not? (b) Suppose that a line were stretched almost perfectly horizontally
In Fig. 8.37, what is the force Fm supplied by the deltoid muscle so as to hold up the outstretched arm if the mass of the arm is 3.0 kg? (Fj is the joint force on the bone of the upper arm€”the humerus.)
In Figure 8.4b, determine the force exerted by the bicep muscle, assuming that the hand is holding a ball with a mass of 5.00 kg. Assume that the mass of the forearm is 8.50 kg with its center of mass located 20.0 cm away from the elbow joint (the black dot in the figure). Assume also that the
A rope goes over a circular pulley with a radius of 6.5 cm. If the pulley makes 4 revolutions without the rope slipping, what length of rope passes over the pulley?
A bowling ball (mass 7.00 kg and radius 17.0 cm) is released so fast that it skids without rotating down the lane (at least for a while). Assume the ball skids to the right and the coefficient of sliding friction between the ball and the lane surface is 0.400. (a) What is the direction of the
A variation of Russell traction (Fig. 8.38) supports the lower leg in a cast. Suppose that the patient€™s leg and cast have a combined mass of 15.0 kg and m1 is 4.50 kg.(a) What is the reaction force of the leg muscles to the traction? (b) What must m2 be to keep the leg horizontal?
In doing physical therapy for an injured knee joint, a person raises a 5.0-kg weighted boot as shown in Fig. 8.39. Compute the torque due to the boot for each position shown.
An artist wishes to construct a birds and bees mobile, as shown in Fig. 8.40. If the mass of the bee on the lower left is 0.10 kg and each vertical support string has a length of 30 cm, what are the masses of the other birds and bees? (Neglect the masses of the bars and strings.)
The location of a person€™s center of gravity relative to his or her height can be found by using the arrangement shown in Fig. 8.41. The scales are initially adjusted to zero with the board alone.(a) Would you expect the location of the center of gravity to be (1) mid-way between the
(a) How many uniform, identical textbooks of width 25.0 cm can be stacked on top of each other on a level surface without the stack falling over if each successive book is displaced 3.00 cm in width relative to the book below it? (b) If the books are 5.00 cm thick, what will be the height of the
A 10.0-kg solid uniform cube with 0.500-m sides rests on a level surface. What is the minimum amount of work necessary to put the cube into an unstable equilibrium position?
While standing on a long board resting on a scaffold, a 70-kg painter paints the side of a house, as shown in Fig. 8.43. If the mass of the board is 15 kg, how close to the end can the painter stand without tipping the board over?
A mass is suspended by two cords as shown in Fig. 8.44. What are the tensions in the cords?
A wheel rolls 5 revolutions on a horizontal surface without slipping. If the center of the wheel moves 3.2 m, what is the radius of the wheel?
If the cord attached to the vertical wall in Fig. 8.44 were horizontal (instead of at a angle), what would the tensions in the cords be?
A force is applied to a cord wrapped around a solid 2.0-kg cylinder as shown in Fig. 8.45. Assuming the cylinder rolls without slipping, what is the force of friction acting on the cylinder?
In a circus act, a uniform board (length 3.00 m, mass 35.0 kg) is suspended from a bungie-type rope at one end, and the other end rests on a concrete pillar. When a clown (mass 75.0 kg) steps out halfway onto the board, the board tilts so the rope end is from the horizontal and the rope stays
The forces acting on Einstein and the bicycle (Fig. 2 of the Insight 8.1, Stability in Action) are the total weight of Einstein and the bicycle (mg) at the center of gravity of the system, the normal force (N) exerted by the road, and the force of static friction (fs) acting on the tires due to the
A fixed 0.15-kg solid-disk pulley with a radius of 0.075 m is acted on by a net torque of 6.4 m ∙ N. What is the angular acceleration of the pulley?
What net torque is required to give a uniform 20-kg solid ball with a radius of 0.20 m an angular acceleration of 20 rad/s2?
For the system of masses shown in Fig. 8.46, find the moment of inertia about(a) The x-axis, (b) The y-axis, and (c) An axis through the origin and perpendicular to the page (z-axis). Neglect the masses of the connecting rods.
A 2000-kg Ferris wheel accelerates from rest to an angular speed of in 12 s. Approximate the Ferris wheel as a circular disk with a radius of 30 m. What is the net torque on the wheel?
Two objects of different masses are joined by a light rod. (a) Is the moment of inertia about the center of mass the minimum or the maximum? Why? (b) If the two masses are 3.0 kg and 5.0 kg and the length of the rod is 2.0 m, find the moments of inertia of the system about an axis perpendicular
Two masses are suspended from a pulley as shown in Fig. 8.47 (the Atwood machine revisited; see Chapter 4, Exercise 55). The pulley itself has a mass of 0.20 kg, a radius of 0.15 m, and a constant torque of due to the friction between the rotating pulley and its axle.What is the magnitude of the
A bowling ball with a radius of 15.0 cm travels down the lane so that its center of mass is moving at 3.60 m/s. The bowler estimates that it makes about 7.50 complete revolutions in 2.00 seconds. Is it rolling with-out slipping? Prove your answer, assuming that the bowler’s quick observation
To start her lawn mower, Julie pulls on a cord that is wrapped around a pulley. The pulley has a moment of inertia about its central axis of and a radius of 5.00 cm. There is an equivalent frictional torque impeding her pull of τf = 0.430 m ∙ N. To accelerate the pulley at α = 4.55 rad/s2, (a)
For the system shown in Fig. 8.48, m1 = 8.0 kg, m2 = 3.0 kg, Î¸ = 30o, and the radius and mass of the pulley are 0.10 m and 0.10 kg, respectively.(a) What is the acceleration of the masses? (Neglect friction and the string€™s mass.) (b) If the pulley has a constant frictional
A meterstick pivoted about a horizontal axis through the 0-cm end is held in a horizontal position and let go. (a) What is the initial tangential acceleration of the 100-cm position? Are you surprised by this result? (b) Which position has a tangential acceleration equal to the acceleration due
Pennies are placed every 10 cm on a meterstick. One end of the stick is put on a table and the other end is held horizontally with a finger, as shown in Fig. 8.49. If the finger is pulled away, what happens to the pennies?
A uniform 2.0-kg cylinder of radius 0.15 m is suspended by two strings wrapped around it (Fig. 8.50). As the cylinder descends, the strings unwind from it. What is the acceleration of the center of mass of the cylinder? (Neglect the mass of the string.)
A planetary space probe is in the shape of a cylinder. To protect it from heat on one side (from the Sun€™s rays), operators on the Earth put it into a €œbarbecue mode,€ that is, they set it rotating about its long axis. To do this, they fire four small rockets
A ball of radius R and mass Mrolls down an incline of angle . (a) For the ball to roll without slipping, should the tangent of the maximum angle of incline be equal to (1) 3 μs/2, (2) 5 μs/2, (3) 7 μs/2, or (4) 9 μs/2? Here, is the coefficient of static friction. (b) If the ball is made of
A constant retarding torque of 12 m ∙ N stops a rolling wheel of diameter 0.80 m in a distance of 15 m. How much work is done by the torque?
A person opens a door by applying a 15-N force perpendicular to it at a distance 0.90 m from the hinges. The door is pushed wide open (to 120o) in 2.0 s. (a) How much work was done? (b) What was the average power delivered?
In Fig. 8.23, a mass m descends a vertical distance from rest. (Neglect friction and the mass of the string.)(a) From the conservation of mechanical energy, will the linear speed of the descending mass be (1) greater than, (2) equal to, or (3) less than ˆš2gh? Why? (b) If m = 1.0, and ,
A ball with a radius of 15 cm rolls on a level surface, and the translational speed of the center of mass is 0.25 m/s. What is the angular speed about the center of mass if the ball rolls without slipping?
A constant torque of is applied to the rim of a 10-kg uniform disk of radius 0.20 m. What is the angular speed of the disk about an axis through its center after it rotates 2.0 revolutions from rest?
A 2.5-kg pulley of radius 0.15 m is pivoted about an axis through its center. What constant torque is required for the pulley to reach an angular speed of after rotating 3.0 revolutions, starting from rest?
A solid ball of mass m rolls along a horizontal surface with a translational speed of v. What percent of its total kinetic energy is translational?
Estimate the ratio of the translational kinetic energy of the Earth as it orbits the Sun to the rotational kinetic energy it has about its N– S axis.
You wish to accelerate a small merry-go-round from rest to a rotational speed of one-third of a revolution per second by pushing tangentially on it. Assume the merry-go-round is a disk with a mass of 250 kg and a radius of 1.50 m. Ignoring friction, how hard do you have to push tangentially to
A pencil 18 cm long stands vertically on its point end on a horizontal table. If it falls over without slipping, with what tangential speed does the eraser end strike the table?
A uniform sphere and a uniform cylinder with the same mass and radius roll at the same velocity side by side on a level surface without slipping. If the sphere and the cylinder approach an inclined plane and roll up it without slipping, will they be at the same height on the plane when they come to
A hoop starts from rest at a height 1.2 m above the base of an inclined plane and rolls down under the influence of gravity. What is the linear speed of the hoop’s center of mass just as the hoop leaves the incline and rolls onto a horizontal surface? (Neglect friction.)

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