1. A chromoly (a 41xx series steel) steel ball bearing weighs 4.516 grams. It co
ID: 883994 • Letter: 1
Question
1. A chromoly (a 41xx series steel) steel ball bearing weighs 4.516 grams. It contains the following components by weight 0.040% Sulfur 0.20% Silicon 0.035% Phosphorus 0.50% Manganese 0.30% Carbon 0.20% Molybdenum 0.95% Chromium 97.775% Iron Determine how many atoms are in the ball bearing. 2. Assume the alloy in problem 1 has an even distribution of all of the alloying elements. If we created a new ball bearing by removing 10 sextillion atoms from the original ball bearing (a) how much would fling chromium in the new ball bearing weigh? (b) how much would the new ball bearing
Explanation / Answer
mass of ball = 4.516 grams
amount of sulfur = 0.040%
mass of sulfur = 0.040/100 * 4.516
= 0.00180 grams
atoms of sulfur = 0.00180 / 32 * 6.023x1023
= 3.387x1019
amount of silicon = 0.20%
mass of silicon = 0.20/100 * 4.516
= 0.009032 grams
atoms of silicon = 0.009032 / 28.085 * 6.023x1023
= 1.936x1020
amount of phosphorous = 0.035%
mass of phosphorous = 0.035 / 100 * 4.516
= 0.00158 grams
atoms of phosphorous = 0.00158 / 30.97 * 6.023x1023
= 3.072x1019
amount of manganese = 0.50%
mass of manganese = 0.50 / 100 * 4.516
= 0.02258 grams
atoms of manganese = 0.02258 / 54.938 * 6.023x1023
= 2.475x1020
amount of carbon = 0.30%
mass of carbon = 0.30 / 100 * 4.516
=0.0135 grams
atoms of carbon = 0.0135 / 12 * 6.023x1023
= 6.775x1020
amount of molybdenum = 0.20%
mass of molybdenum = 0.20 / 100 * 4.516
= 0.009032 grams
atoms of molybdenum = 0.009032 / 95.94 * 6.023x1023
= 5.67x1019
amount of chromium = 0.95%
mass of chromium = 0.95 / 100 * 4.516
= 0.0429 grams
atoms of chromium = 0.0429 / 51.99 * 6.023x1023
= 4.969x1020
amount of iron = 97.775%
mass of iron = 97.775 / 100 * 4.516
= 4.4155 grams
atoms of iron = 4.4155 / 55.845 * 6.023x1023
= 4.762x1022
Total number of atoms in ball bearing = 3.387x1019 + 1.936x1020 + 3.072x1019 + 2.475x1020 + 6.775x1020 + 5.67x1019 + 4.969x1020 + 4.762x1022
= 4.935x1022 atoms
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