Problem Set 4

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105

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Chemistry

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Jan 9, 2024

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Problem Set 04 – Moles and Mass Chem 105 1. (a) Naturally occurring sulfur consists of four isotopes: 32 S (31.9721 amu, 95.04%); 33 S (32.9715 amu, 0.75%); 34 S (33.9679 amu, 4.20%); and 36 S (35.9671 amu, 0.01%). Use this information to calculate the average atomic mass of sulfur. amu=64.1557 (b) Calculate the atomic weight of nickel t o the correct number of significant figures using the following data: 58 Ni, 68.075%, 57.9353429 amu 60 Ni, 26.221%, 59.9307864 amu 61 Ni, 1.1399%, 60.9310560 amu 62 Ni, 3.637%, 61.9283451 amu 64 Ni, 0.9271%, 63.9279660 amu 120amu 2. (a) Naturally occurring Mg has three stable isotopes, 24 Mg, 25 Mg, and 26 Mg. This means that there are three forms of Mg atoms, each with a unique atomic weight. This appears to be contrary to the idea that atomic weight is the defining property of an element. Explain (in 3 sentences or less) why all three of these types of atoms are indeed the same element. Though this seems contrary to the defining property they are indeed the same element because an element isn’t defined by its atomic weight and instead defined by its atomic number. The atomic number is the number of protons in the nucleus which is what quantifies an element. (b) Chemical analyses conducted by the first Mars rover robotic vehicle in its 1997 mission produced the magnesium isotope data shown in the table below. Is the average atomic mass of magnesium in this Martian sample the same as on Earth (24.305 amu)? (use the correct number of sig figs): Martian Magnesium amu=24.31 it does have the same amu as earth magnesium. 3. The following elements all have two stable isotopes. Which isotope in each of the following pairs of stable isotopes is more abundant? Explain how you know. a) 10 B or 11 B; 11 B is more abundant because the atomic mass of boron is closer to 11 than it is to 12. b) 6 Li or 7 Li; 7 Li is more abundant because the atomic mass of boron is closer to 7 than it is to 6 c) 14 N or 15 N 7 N is more abundant because the atomic mass of boron is closer to 15 than it is Isotop e Mass (amu) Natural Abundance (%) 24 Mg 23.9850 78.70 25 Mg 24.9858 10.13 26 Mg 25.9826 11.17

to 15 d) 20 Ne or 22 Ne 20 Ne is more abundant because the atomic mass of boron is closer to 20 than it is to 21 e) 35 Cl or 37 Cl 35 Cl is more abundant because the atomic mass of boron is closer to 35 than it is to 36 4. Which of the highlighted elements below form monatomic ions with a charge of (a) 1+, None (b) 2+, Red (c) 3+, Purple (d) 1– Blue and (e) 2– Grey 5. Describe how the charges of the monatomic ions that elements form change as group number increases in a particular row of the periodic table and how ion charges change as the row number increases in a particular group. As you go across the periodic table to the right from the left the elements become more likely to lose electrons until you get to the column containing carbon and then the elements become more likely to gain and electron, increasing until you get to the noble gasses at the leftmost section of the periodic table which aren’t reactive. As you go down the periods the elements become more and more reactive. 6. (a) Define the mole using 1-3 sentences. Mole, also spelled mol, in chemistry, a standard scientific unit for measuring large quantities of very small entities such as atoms, molecules, or other specified particles. (b) In principle, we could use the more familiar unit dozen in place of the mole when expressing the quantities of particles (atoms, ions, or molecules). What would be the disadvantage in doing so? The disadvantage would be the lack of accuracy, the mole helps to highlight the exacting number of moles in a sample. 7. (a) If you had 1 mole of M&M’s, how big would the box need to be to hold all of them? Assume the volume of a single M&M® candy is about 2.2 cm 3 , and calculate the volume of the box in km 3 . 1.3e23 cm^3 (b) Assuming the box from part (a) is a cube with all sides of equal length, is the side of the box closest

in length to the diameter of the Sun (1,400,000 km), the diameter of the Earth (13,000 km), the length of the state of Texas (1200 km), the length of Utah Lake (39 km) or the width of the BYU Marriott Center (120 m)? It is closest in length to the diameter of the sun. 8. (a) Calculate the molar masses of the following common flavors in food. a. vanillin, C 8 H 8 O 3 =152.15 b. oil of cloves, C 10 H 12 O 2 =164.20 c. anise oil, C 10 H 12 O =148.20 d. oil of cinnamon, C 9 H 8 O = 132.16 (b) Calculate the molar masses of the following common sweeteners. e. Sucrose (table sugar), C 12 H 22 O 11 =342.29 f. Saccharin (1 st artificial sweetener), C 7 H 5 O 3 NS =183.19 g. aspartame (NutraSweet), C 14 H 18 N 2 O 5 =294.331 h. fructose (sugar in fruit), C 6 H 12 O 6 =180.15 (c) If you had 1.5 moles of each substance listed in a–h, calculate how many moles of oxygen each would contain. Which contains the most moles of oxygen? Sucrose would have the most mole of oxygen. 9. (a) Suppose pairs of balloons are filled with 10.0 g of the following pairs of gases. Which balloon in each pair has the greater number of molecules (or atoms in the case of Ar)? Explain how you know. (a) CO 2 or NO (b) CO 2 or SO 2 (c) O 2 or Ar B would have the greatest number of molecules because there are more atomic components in CO 2 or SO 2 (b) If you had equal masses of the substances in the following pairs of compounds, which of the two would contain the greater number of ions? (a) NaBr or KCl (b) NaCl or MgCl 2 (c) CrCl 3 or Na 2 S 10. Although they are not too common, there are US one-dollar coins. These are the so-called “golden dollars” which bear the likeness of Sacagawea or past US presidents. The composition of these “golden” coins as given by the US government is 6.0% zinc, 3.5% manganese, 2.0% nickel, and 88.5% copper. How many atoms of manganese are there in a Sacagawea dollar coin that weighs 8.100 g? 1.7e23 11. (a) A common gem size used in wedding rings is about ½ carat. The white diamond in my wedding ring is 0.536 carats. Given that the density of white diamond (a pure form of carbon) is 3.50 g/cm 3 and 1 carat = 200. mg, how many C atoms are in my ring? 5.374e21 How many moles of C is this? 0.008925 (b) The Cullinan diamond (3106.75 carats) is the largest gem quality rough white diamond ever found. How many diamonds like the one in part (a) could the Cullinan diamond have been used to make? 5796 12. (a) Two inorganic blue pigments are Han blue (BaCuSi 4 O 10 ) and Egyptian blue (CaCuSi 4 O 10 ) . Which has a higher molar mass and by how much (include 4 significant figures)? Han blue is heavier by 97.25 amu (b) If you had a 10.0 g chunk of each pigment, one in your right hand and one in your left, which sample would contain more Cu atoms? Egyptian blue would have more Cu because there is less weight so a greater density of the atom would be needed to equal the weight. How many more Cu atoms would it contain? About 123.67 moles.

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