A ball bearing has the following composition of alloying elements (the remainder

Question

A ball bearing has the following composition of alloying elements (the remainder is iron) and has a weight of 3.846g. If we removed 7 sextillion atoms from the ball bearing how much would the remaining chromium in the modified ball bearing weigh? The answer should be in grams and have 3 decimals of accuracy. Use the periodic table below.

Component Weight % Sulfur 0.031 Silicon 0.247 Phosphorus 0.036 Manganese 0.541 Carbon 0.352 Molybdenum 0.169 Chromium 0.961 MAIN-GROUP Periodic Table of the Elements ELEMENTS MAIN GROUP ELEMENTS Metals (main-group) Metals (transition) VILLA Metals (inner transition) (18) (1) Metalloids Nonmetals H ILA. IIIA IVA VA VIA VILA He 1.008 C N O F Ne Be 6.941 9.012 0,8I 12.01 16.00 TRANSITION ELEMENTS 3 Na Mig IIIB IVB VB VIB VIIB 31 33 35 Min Fe Coo Ni cu Zn Ga Ge As Se Br Kr 4 K Ca Sc 50.94 52.00 54.94 55.85 58.93 58.69 63.55 65.39 69.72 72.61 4,92 78,96 79,90 83,80 39.10 40.08 85.47 87.62 27.6 126.9 131.3 88.91 91.22 92.91 81 82 83 Pt Au Hig TI Pb Bi Po At Rn Ba 1970 2006 204.4 20.2 209.0 0209) 0210) (222) 132.9 137.3 110 88 Fr Ra Db Uuu (269) (272) (223) (226) 227) (261) (262) (266) (262) 0265) 0266) INNER TRANSITION ELEMENTS 71 62 63 64 65 66 67 Lanthanides Nd Gd Tma 157.3 158.9 167.3 168.9 175.00 140.1 152.0 164.9 173.0 102 103 Fm Md Actinides U Np Pu Am Cm Bk.

Explanation / Answer

Given-

Alloying elements weight = 3.846g.

Component       Weight %

Sulfur    0.031

Silicon   0.247

Phosphorus       0.036

Manganese        0.541

Carbon 0.352

Molybdenum    0.169

Chromium         0.961

Total weight % = 0.031 + 0.247 +0.036 + 0.541+0.352 +0.169 +0.961 = 2.337%

  Weight % of iron 100 - 2.337 = 97.663%

Weight of Cr in alloy = 3.846g x (0.961/100) = 0.036960 g

Mols of Cr in alloy = 0.036960 g/52 = 0.000710769 moles

One mole contains 6.022e23 atoms.

That means one mole contains roughly

602,200,000,000,000,000,000,000 atoms = (602 sextillion)

If we removed 7 sextillion atoms from the ball bearing

7 sextillion=7,000,000,000,000,000,000,000 atoms

7 sextillion =7,000,000,000,000,000,000,000/602,200,000,000,000,000,000,000 mols

       = 70 /6022 = 0.011624 mols

Mols of Cr removed from alloy = 0.011624 mols x (0.961/100) = 0. 00011170664 moles

The remaining chromium in the modified ball bearing weighs

= 0.000710769 moles – 0. 00011170664 moles = 0.000599062 mols

Convert mols into g-

0.000599062 x 52 = 0.031151 g

3 decimals of accuracy = 0.031g

The remaining chromium in the modified ball bearing weighs 0.031g

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