2.7: End of Chapter Problems

Exercises

1. In the following drawing, the green spheres represent atoms of a certain element. The purple spheres represent atoms of another element. If the spheres of different elements touch, they are part of a single unit of a compound. The following chemical change represented by these spheres may violate one of the ideas of Dalton’s atomic theory. Which one?

   

2. Which postulate of Dalton’s theory is consistent with the following observation concerning the weights of reactants and products? When 100 grams of solid calcium carbonate is heated, 44 grams of carbon dioxide and 56 grams of calcium oxide are produced.
3. Identify the postulate of Dalton’s theory that is violated by the following observations: 59.95% of one sample of titanium dioxide is titanium; 60.10% of a different sample of titanium dioxide is titanium.
4. Samples of compound X, Y, and Z are analyzed, with results shown here. Do these data provide example(s) of the law of definite proportions, the law of multiple proportions, neither, or both? What do these data tell you about compounds X, Y, and Z?

Compound	Description	Mass of Carbon	Mass of Hydrogen
X	clear, colorless, liquid with strong odor	1.776 g	0.148 g
Y	clear, colorless, liquid with strong odor	1.974 g	0.329 g
Z	clear, colorless, liquid with strong odor	7.812 g	0.651 g

5. The existence of isotopes violates one of the original ideas of Dalton’s atomic theory. Which one?

Answer

Dalton originally thought that all atoms of a particular element had identical properties, including mass. Thus, the concept of isotopes, in which an element has different masses, was a violation of the original idea. To account for the existence of isotopes, the second postulate of his atomic theory was modified to state that atoms of the same element must have identical chemical properties.

6. How are electrons and protons similar? How are they different?

Answer

Both are subatomic particles that reside in an atom’s nucleus. Both have approximately the same mass. Protons are positively charged, whereas neutrons are uncharged.

7. How are protons and neutrons similar? How are they different?

Answer

Both are subatomic particles that reside in an atom’s nucleus. Both have approximately the same mass. Protons are positively charged, whereas neutrons are uncharged.

8. Predict and test the behavior of α particles fired at a “plum pudding” model atom.
   1. Predict the paths taken by α particles that are fired at atoms with a Thomson’s plum pudding model structure. Explain why you expect the α particles to take these paths.
   2. If α particles of higher energy than those in (a) are fired at plum pudding atoms, predict how their paths will differ from the lower-energy α particle paths. Explain your reasoning.
   3. Now test your predictions from (a) and (b). Open the Rutherford Scattering simulation and select the “Plum Pudding Atom” tab. Set “Alpha Particles Energy” to “min,” and select “show traces.” Click on the gun to start firing α particles. Does this match your prediction from (a)? If not, explain why the actual path would be that shown in the simulation. Hit the pause button, or “Reset All.” Set “Alpha Particles Energy” to “max,” and start firing α particles. Does this match your prediction from (b)? If not, explain the effect of increased energy on the actual paths as shown in the simulation.

Answer

a.The plum pudding model indicates that the positive charge is spread uniformly throughout the atom, so we expect the α particles to (perhaps) be slowed somewhat by the positive-positive repulsion, but to follow straight-line paths (i.e., not to be deflected) as they pass through the atoms. b. Higher-energy α particles will be traveling faster (and perhaps slowed less) and will also follow straight-line paths through the atoms. c. The α particles followed straight-line paths through the plum pudding atom. There was no apparent slowing of the α particles as they passed through the atoms.

9. Predict and test the behavior of α particles fired at a Rutherford atom model.
   1. Predict the paths taken by α particles that are fired at atoms with a Rutherford atom model structure. Explain why you expect the α particles to take these paths.
   2. If α particles of higher energy than those in (a) are fired at Rutherford atoms, predict how their paths will differ from the lower-energy α particle paths. Explain your reasoning.
   3. Predict how the paths taken by the α particles will differ if they are fired at Rutherford atoms of elements other than gold. What factor do you expect to cause this difference in paths, and why?
   4. Now test your predictions from (a), (b), and (c). Open the Rutherford Scattering simulation and select the “Rutherford Atom” tab. Due to the scale of the simulation, it is best to start with a small nucleus, so select “20” for both protons and neutrons, “min” for energy, show traces, and then start firing α particles. Does this match your prediction from (a)? If not, explain why the actual path would be that shown in the simulation. Pause or reset, set energy to “max,” and start firing α particles. Does this match your prediction from (b)? If not, explain the effect of increased energy on the actual path as shown in the simulation. Pause or reset, select “40” for both protons and neutrons, “min” for energy, show traces, and fire away. Does this match your prediction from (c)? If not, explain why the actual path would be that shown in the simulation. Repeat this with larger numbers of protons and neutrons. What generalization can you make regarding the type of atom and effect on the path of α particles? Be clear and specific.

Answer

a. The Rutherford atom has a small, positively charged nucleus, so most α particles will pass through empty space far from the nucleus and be undeflected. Those α particles that pass near the nucleus will be deflected from their paths due to positive-positive repulsion. The more directly toward the nucleus the α particles are headed, the larger the deflection angle will be. b. Higher-energy α particles that pass near the nucleus will still undergo deflection, but the faster they travel, the less the expected angle of deflection. c. If the nucleus is smaller, the positive charge is smaller and the expected deflections are smaller—both in terms of how closely the α particles pass by the nucleus undeflected and the angle of deflection. If the nucleus is larger, the positive charge is larger and the expected deflections are larger—more α particles will be deflected, and the deflection angles will be larger. d. The paths followed by the α particles match the predictions from (a), (b), and (c).

10. In what way are isotopes of a given element always different? In what way(s) are they always the same?
11. Write the symbol for each of the following ions:
    1. the ion with a 1+ charge, atomic number 55, and mass number 133.
    2. the ion with 54 electrons, 53 protons, and 74 neutrons
    3. the ion with atomic number 15, mass number 31, and a 3− charge
    4. the ion with 24 electrons, 30 neutrons, and a 3+ charge

Answer

a. ¹³³Cs⁺; b. ¹²⁷I⁻; c. ³¹P³⁻; d. ⁵⁷Co³⁺

12. Write the symbol for each of the following ions
    1. the ion with a 3+ charge, 28 electrons, and a mass number of 71
    2. the ion with 36 electrons, 35 protons, and 45 neutrons
    3. the ion with 86 electrons, 142 neutrons, and a 4+ charge
    4. the ion with a 2+ charge, atomic number 38, and mass number 87

13. Determine the number of protons, neutrons, and electrons in the following isotopes that are used in medical diagnoses:
    1. atomic number 9, mass number 18, charge of 1−
    2. atomic number 43, mass number 99, charge of 7+
    3. atomic number 53, atomic mass number 131, charge of 1−
    4. atomic number 81, atomic mass number 201, charge of 1+
    5. Name the elements in parts (a), (b), (c), and (d).

14. The following are properties of isotopes of two elements that are essential in our diet. Determine the number of protons, neutrons and electrons in each and name them.
    1. atomic number 26, mass number 58, charge of 2+
    2. atomic number 53, mass number 127, charge of 1−

Answer

a. Iron, 26 protons, 24 electrons, and 32 neutrons; b. iodine, 53 protons, 54 electrons, and 74 neutrons

15. Give the number of protons, electrons, and neutrons in neutral atoms of each of the following isotopes:
    1. \(\ce{^{10}_5B}\)
    2. \(\ce{^{199}_{80}Hg}\)
    3. \(\ce{^{63}_{29}Cu}\)
    4. \(\ce{^{13}_6C}\)
    5. \(\ce{^{77}_{34}Se}\)
16. Give the number of protons, electrons, and neutrons in neutral atoms of each of the following isotopes:
    1. \(\ce{^7_3Li}\)
    2. \(\ce{^{125}_{52}Te}\)
    3. \(\ce{^{109}_{47}Ag}\)
    4. \(\ce{^{15}_7N}\)
    5. \(\ce{^{31}_{15}P}\)

Answer

a. 3 protons, 3 electrons, 4 neutrons; b. 52 protons, 52 electrons, 73 neutrons; c. 47 protons, 47 electrons, 62 neutrons; d. 7 protons, 7 electrons, 8 neutrons; e. 15 protons, 15 electrons, 16 neutrons

17. Click on the site and select the “Mix Isotopes” tab, hide the “Percent Composition” and “Average Atomic Mass” boxes, and then select the element boron.
    1. atomic number 26, mass number 58, charge of 2+
    2. atomic number 53, mass number 127, charge of 1−
18. Click on the site and select the “Mix Isotopes” tab, hide the “Percent Composition” and “Average Atomic Mass” boxes, and then select the element boron.
    1. Write the symbols of the isotopes of boron that are shown as naturally occurring in significant amounts.
    2. Predict the relative amounts (percentages) of these boron isotopes found in nature. Explain the reasoning behind your choice.
    3. Add isotopes to the black box to make a mixture that matches your prediction in (b). You may drag isotopes from their bins or click on “More” and then move the sliders to the appropriate amounts.
    4. Reveal the “Percent Composition” and “Average Atomic Mass” boxes. How well does your mixture match with your prediction? If necessary, adjust the isotope amounts to match your prediction.
    5. Select “Nature’s” mix of isotopes and compare it to your prediction. How well does your prediction compare with the naturally occurring mixture? Explain. If necessary, adjust your amounts to make them match “Nature’s” amounts as closely as possible.
    6. Repeat Exercise using an element that has three naturally occurring isotopes.