Question

1. For each of the following, you’ll need to perform dimensional analyses. Show your work, use significant figures and show all conversion factors you use. You may need to use some of the conversion factors or equations below and you many need to look some up.

1 mole = 6.02x10²³ atoms

mass of a gold atom = 3.27 x 10^-22 g

radius of a gold atom = 174 picometers

density of gold = 19.3 g/mL

volume of a sphere = 4/3πr³

Hint: for some of these questions, think about radius vs diameter

1. The moon is 238,900 miles away. If you could string together atoms of gold, how many gold atoms would it take to stretch reach the moon and come back? (5 pts)
2. How many mL of gold is that (5 pts)?
3. You have 0.0126 L of a solution that has gold dissolved into at a concentration of 1 mg/mL. If you could get all of the gold out of that solution and turn it into a string, how many times could it reach between earth and the moon? (just the distance between, not the distance of a round trip) (7 pts).

Answer 1

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AMUTLUN SITLUL II 'W 1 mile= to 600km 1.609x10 m = 160gm.edi > Amar NOO-VO distance moon to from earth from a 160gm. 1609 meters. for a round trip - 2x1609 - 3218 m. Sozco Я əрос 710-0 U = 174 picometer .. Gold atom radius = 174 pecon 717 4X102m. - diameter of gold atom=28=2(174X10 6 . - 348 x1ől?m. Alo of gold atoms teeded to reach moon and come back = 2x1609 th 3218x102 / 19.24x102 no. of atoms 348x1012 h 348 12 Ans IT mass of gold atom = 3.27 x1029gm. -) 1 atom of gold - 3.27 810 22 gm @ 924 xió? atoms of gold = 9.24 xıb? x 3.27x10 - 30-21 x 7oºgm. densilõ of gold = 193 g/ me. => 1903 gm of gold: I me -) 30.21 Xiólºgm 3021 x1ő me 19.3 = 11.56 xiolo me Ans Solution = 0.0126 L = 12.6 mL concentration - 1 mg/me ex 1 mL solution: 1mg gold =7 12.6 mL solution = 12.6 mg gold. = 0.0126 gon of geld from equation ③ 3.27 X1022 qm = 1 atom of you 0.0126 gm - 1.26x10 gm = 61-26 X102.0385x1020 3-27 X1022 - 3.85 x 10h no of golatoms- 19

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Additional Sheet- I from equation ③ diameter of gold atom = 34681012m. => 1 gold atom = 348x10 tam distance - 3.85 x10 no. of gold atom = 3.85x109 x 348x1022 = 1339.8 x 187 from equation - 1.3398 xldºmi ④ earth to moon distance = 1609 meters. No. of times it factof earth - moon Distance – 1.3398810 m covered 16096 - 0.83.36X197 = 1832.6100 times ] 1832.6x100 times ), Ans