On your wedding day your lover gives you a gold ring of mass 3.78 g. 50 years later its mass is 3.16 g. On the average how many atoms were abrated from the ring during each second of your marriage? The atomic mass of gold is 197 u
The ring lost 0.62 g in 50 years. That is 0.62/197 = 3.15*10^-3 moles. Multiply by Avogadro's number for the number of atoms lost: 1.90*10^21.
Next, divide that by 50 years, in seconds.
I get about 3*10^13 atoms/second
To determine the average number of atoms abraded from the gold ring during each second of the marriage, we need to calculate the number of atoms lost during the 50 years.
First, let's calculate the mass lost by the gold ring:
Mass lost = Initial mass - Final mass
Mass lost = 3.78 g - 3.16 g
Mass lost = 0.62 g
Next, let's convert the mass lost to the number of moles of gold:
Number of moles = Mass lost / Atomic mass of gold
Number of moles = 0.62 g / 197 g/mol
Number of moles ≈ 0.00315 mol
Now, we need to find the number of atoms in 0.00315 mol of gold. One mole of any substance contains Avogadro's number of atoms (6.022 x 10^23 atoms/mol).
Number of atoms = Number of moles x Avogadro's number
Number of atoms = 0.00315 mol x 6.022 x 10^23 atoms/mol
Number of atoms ≈ 1.894 x 10^21 atoms
Finally, we divide the number of atoms lost over 50 years by the number of seconds in 50 years (assuming there are 365.25 days in a year and 24 hours in a day) to find the average number of atoms abraded per second:
Average number of atoms abraded per second = Number of atoms lost / (50 years x 365.25 days/year x 24 hours/day x 60 minutes/hour x 60 seconds/minute)
Average number of atoms abraded per second ≈ 1.894 x 10^21 atoms / (50 x 365.25 x 24 x 60 x 60)
Average number of atoms abraded per second ≈ 1.198 x 10^12 atoms/second
Therefore, on average, approximately 1.198 x 10^12 atoms were abraded from the ring every second during the 50 years of marriage.