Dissecting a Physics Answer Dealing with Converting to Mols

[mysticxhobo]

I'm attempting to understand what is going on in the solution to a problem. Heres the question and the answer:

Question:
On your wedding day your lover gives you a gold ring of mass 3.74 g. 53 years later its mass is 3.21 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.

Answer:
Step 1: 3.74-3.21 = 0.26 g lost
Step 2: 0.26g /197 g/mol = 0.001319797mols x 6.02214179x1023 atoms/mol = 7.948004393x1020atoms
Step 3: 53yrs x 365days/year x 24hours/day x 60min/hr x 60 sec/min =1671408000 seconds
Step 4: 7.948004393x1020 atoms/1671408000 seconds =4.75527483x1011atoms/second

I understand everything besides step two. You are given 197 as the atomic mass unit in the question. But what do you do with this number so that it can be multiplied by avagadro's number? so basically what operations lead to 0.001319797mols?

thanks,
mysticxhobo

 

[mysticxhobo]

okay i figured out what was done. the total grams of the substance was divided by the atomic mass of the substance.

.26 / 197 = .0031.. . . . .

but can someone explain why it was done this way?

thanks

 

[Borek]

If molar mass of iron is 56g/mol and you have 56g of iron, obviously you have

$$\frac {56 g}{56 \frac{g}{mol}}=1 mol$$

of iron. If you have 28g of iron, you have

$$\frac {28 g}{56 \frac{g}{mol}}=\frac 1 2 mol$$

and so on.