Question

I have trouble understanding ratios and relativity so I can't understand how to use atomic mass units. Here is an example from my book:

How many grams of iron would contain the same number of iron atoms as the number of carbon atoms contained in 1.000 g of carbon?

Solution: Iron has an atomic weight of 55.85 meaning that it is 55.85/12.01 times as heavy as carbon. If you have 1 gram of carbon, you would need to weight out:

(55.85 g Fe/ 12.01 g C) x 1.000 g C = 4.650 g Fe

I don't understand why Iron is 5.85/12.01 times as heavy as carbon.

Another related question was: Instead of carbon-12 oxygen-16 was used as the standard for atomic mass units. Using oxygen-16 as the standard what would be the atomic mass of potassium-39?

I have the answers for these questions, but I just don't understand where they come from.

Answer 1

The atomic mass of Fe is 55.85 but that is a relative number (it is relative to carbon 6C12. The relative mass of carbon is 12.015 (again relative to the 6C12 isotope of carbon). So Fe is 55.85/12.01 times heavier than C.
There are other ways to work the problem without using ratios and proportion.
How many moles of C are in 1.000 g C? That will be 1.000/12.01 = 8.33 x 10^-2.

Since 8.326 x 10^-2 moles Fe and C will contain the same number of atoms, then convert 8.326 x 10^-2 moles Fe to grams.
g = moles x molar mass = 8.326 x 10^-2 x 55.85 = 4.650 g Fe.