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.

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.

I can help explain the concept of atomic mass units (amu) and how they relate to ratios to better understand the given examples.

Atomic mass units (amu) are used to express the relative masses of atoms. The atomic mass of an element is the average mass of all its naturally occurring isotopes, taking into account their relative abundances.

Now, let's look at the example you provided.

Question: 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. Atomic weight is a weighted average of the masses of different isotopes of an element. The atomic weight of carbon is 12.01.

To find the mass of iron that contains the same number of atoms as 1 gram of carbon, we need to compare their atomic weights using a ratio. The ratio is determined by dividing the atomic weight of iron by the atomic weight of carbon:

Iron-to-Carbon ratio = (55.85 g Fe) / (12.01 g C)

This ratio gives us a measure of how many times heavier iron is compared to carbon.

In this case, the ratio is roughly 4.65. This means that 1 gram of carbon is about 4.65 times lighter than 1 gram of iron. Therefore, to have the same number of iron atoms as in 1 gram of carbon, we need to weigh out approximately 4.65 grams of iron (4.65 g Fe).

Now, let's move on to the second example:

Question: 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?

In this case, the atomic mass of oxygen-16 is taken as a reference point or standard. The atomic mass of potassium-39 is measured relative to the oxygen-16 standard.

The atomic mass of potassium-39 is found by comparing the masses of potassium-39 and oxygen-16 using the ratio:

Potassium-to-Oxygen ratio = (x g K) / (16 g O) = (39 g K) / (x g O)

By cross-multiplying, we get:

x g K = (16 g O) * (39 g K)

Dividing both sides by 16 g O, we find:

x g K = (16 g O) * (39 g K) / (16 g O)

Simplifying the equation, we get:

x g K = 39 g K

Therefore, the atomic mass of potassium-39, when using oxygen-16 as the standard, is 39 atomic mass units (39 amu).

To summarize, atomic mass units (amu) are used to express the relative masses of atoms. Ratios of atomic weights are used to compare the masses of different elements or isotopes. By understanding how to use these ratios, you can determine the relative masses of elements and solve problems like the ones you provided.