Webassign 4 -- Atomic Structure and Isotopes

1. Hydrogen sulfide is composed of two elements: hydrogen and sulfur. In an experiment, 4.965 g of hydrogen sulfide is fully decomposed into its elements.

• a) If 0.278 g of hydrogen are obtained in this experiment, how many grams of sulfur must be obtained?
• In accordance to the law of conservation of mass, 0.278 g H2 + (x) g S = 4.965 g H2S. Solve for x. The answer is 4.687 g S (to 2 significant figures).
• b) What fundamental law does this experiment demonstrate?     (Answer: The Law of Conservation of Mass)
• c) How is this law explained by Dalton's atomic theory?     (Answer: Atoms are neither created nor destroyed in a chemical reaction).

2. In a series of experiments, a chemist prepared three different compounds that contain only iodine and fluorine and determined the mass of each element in each compound.

compound	mass of iodine (g)	mass of fluorine (g)
1	4.75	3.56
2	7.64	3.43
3	9.41	9.86

• a) Calculate the mass of fluorine per gram of iodine in each compound. 
• compound 1
•  (3.56 g F) / (4.75 g I) = 0.749 / g (to 3 significant figures)
• compound 2
•  (3.43 g F) / (7.64 g I) = 0.449 / g (to 3 significant figures)
• compound 3
•  (9.86 g F) / (9.41 g I) = 1.05 / g (to 3 significant figures)
• How do the numbers in part (a) support the atomic theory?      (Answer: 5:3:7, they satisfy the law of multiple proportions). 

3. A negatively charged particle is caused to move between two electrically charged plates, as illustrated below.

• a) Why does the path of the charged particle bend?     (Answer: its charge and the charges on the plates)
• b) As the charge on the plates is increased, would you expect the bending to increase, decrease, or stay the same?     (Answer: increase)
• c) As the mass of the particle is increased while the speed of the particles remains the same, would you expect the bending to increase, decrease, or stay the same?      (Answer: decrease)
• d) An unknown particle is sent through the apparatus. Its path is deflected in the opposite direction from the negatively charged particle, and it is deflected by a smaller magnitude. What can you conclude about this unknown particle? (Select all that apply.)     (Answers: The particle has greater mass than the electron AND The particle is positively charged)

4. The radius of the rubidium (Rb) atom is about 2.1 .

• a) Express this distance in nanometers (nm). 
• (2.1 A / 1) * (1.0e-10 m / 1 A) * (1.0e9 nm / 1 m) = 0.21 nm (to 2 significant figures)
• b) Express this distance in picometers (pm).
• (2.1 A / 1) * (1.0e-10 m / 1 A) * (1,000,000,000,000 pm / 1 m) = 210 pm (to 2 significant figures)
• c) How many rubidium (Rb) atoms would have to be lined up to span 1.0 mm?
• The radius of the rubidium atom is 2.1 A, so its diameter is 4.2 A.
• (1.0 mm / 1) * (1 m / 1000 mm) * (1 A / 1.0e-10 m) * (1 atom / 4.2 A) = 2.4e6 Rb atoms (to 2 significant figures)
• d) If the atom is assumed to be a sphere, what is the volume in cm³ of a single rubidium (Rb) atom?
• The volume of a sphere is (4/3)π*r³. Calculate the volume in angstroms:
• v = (4/3)π*(2.1 A)³ = 38.7924 A³
• Now convert the volume in angstroms to cubic centimeters:
•  (38.7924 A³ / 1) * (1.0e-10 m / 1 A)³ * (100 cm / 1 m)³ = 3.9e-23 cm³ (to 2 significant figures)

5.

• a) Give the mass number of a tungsten atom with 110 neutrons.
• Mass number = protons + neutrons = 74 protons + 110 neutrons = 184
• b) Give the mass number of an iron atom with 30 neutrons. 
• Mass number = protons + neutrons = 26 protons + 30 neutrons = 56
• c) Give the mass number of an americium atom with 148 neutrons.
• Mass number = protons + neutrons = 95 protons + 148 neutrons = 243

6. Radioactive americium-241 is used in household smoke detectors and in bone mineral analysis. Give the number of electrons, protons, and neutrons in an atom of americium-241.

• a) electrons
• The number of electrons of a neutrally charged atom is the same as its number of protons. The answer is 95.
• b) protons
• The number of protons is equal to the atomic number found on the periodic table. The answer is 95.
• c) neutrons
• The mass number = protons + neutrons. 241 = 95 protons + x neutrons. The answer is 146.

7. Strontium has four stable isotopes. Strontium-84 has a very low natural abundance, but ⁸⁶Sr, ⁸⁷Sr, and ⁸⁸Sr are all reasonably abundant. Knowing that the atomic weight of strontium is 87.62, which of the more abundant isotopes predominates?    

• (The atomic weight will be closest to the isotope with the greatest abundance. The answer is ⁸⁸Sr, since 87.62 is closest to 88).

8. Magnesium has three naturally occurring isotopes. ²⁴Mg (23.985 amu) with 78.99% abundance, ²⁵Mg (24.986 amu) with 10.00% abundance, and a third with 11.01% abundance. Look up the atomic mass of magnesium, and then calculate the mass of the third isotope.

• The atomic weight is a weighted average of each of an element's isotopes.
• (23.985 amu * 0.7899) + (24.986 amu * 0.1) + (x amu * 0.1101) = Atomic weight
• (23.985 amu * 0.7899) + (24.986 amu * 0.1) + (x amu * 0.1101) = 24.3050
• Solve for x. The answer is 26 amu (to 2 significant figures)

9.

• a) What particle did James Chadwick's experiments discover?      (Answer: Neutron)
• b) In what part of the atom is this particle located?     (Answer: Nucleus)

10.

• a) Which scientist's experiment indicated that the atom is mostly empty space and rejected the 'plum pudding' atomic model? Enter only the last name.     (Answer: Rutherford)
• b) What metal did he use in the experiment?     (Answer: Gold)

11. Complete the table.

Isotope	% Natural Abundance	Atomic Mass (amu)	Average Atomic Mass (amu)
copper-63	69.17	62.929599
copper-65	30.83	64.927793

•  Atomic mass is a weighted average of the abundance of the isotopes of an element multiplied by the atomic masses of the isotopes.
• (69.17 amu * 0.62929599) + (30.83 * 0.64927793) = 63.55 amu (to 4 significant figures)

12. How many protons, neutrons, and electrons are there in ³⁺?

• a) protons
• The number of protons is equal to the atomic number found on the periodic table. The answer is 31.
• b) neutrons
• The mass number = protons + neutrons. 69 = 31 protons + x neutrons. The answer is 38.
• c) electrons
• The number of electrons of an ion with a +3 charge is equal to the number of electrons in a neutral atom minus 3, as the plus indicates negative charge has been lost. 31 electrons - 3 = 28 electrons.

13. How many protons, neutrons, and electrons are there in ^2-?

• a) protons
• The number of protons is equal to the atomic number found on the periodic table. The answer is 16.
• b) neutrons
• The mass number = protons + neutrons. 32 = 16 protons + x neutrons. The answer is 16.
• c) electrons
• The number of electrons of an ion with a -2 charge is equal to the number of electrons in a neutral atom plus 2, as the minus indicates negative charge has been gained. 16 electrons + 2 = 18 electrons.

14. How many protons, neutrons, and electrons are there in ^1-?

• a) protons
• The number of protons is equal to the atomic number found on the periodic table. The answer is 85.
• b) neutrons
• The mass number = protons + neutrons. 215 = 85 protons + x neutrons. The answer is 130.
• c) electrons
• The number of electrons of an ion with a -1 charge is equal to the number of electrons in a neutral atom plus 1, as the minus indicates negative charge has been gained. 85 electrons + 1 = 86 electrons.