Question

If a mass of `"16.26 mg"` contains `1.66 xx 10^20` atoms, what is the molar mass of that atom? If you have `"1 million"` silver atoms constituting a total of `1.79 xx 10^(-16) "g"`, what is the molar mass? `"1 amu"` `=` `1.660599 xx 10^(-24) "g"`.

Answer 1

Both questions ask the same thing in opposite ways.

One gives you `"16.26 mg"` containing `1.66xx10^20` `"atoms"`. That gives you a mass and a quantity, which is enough to convert to the atomic units of `"g/mol"`.

`("16.26" cancel"mg")/(1.66xx10^20 cancel"atoms") xx "1 g"/("1000" cancel"mg") xx (6.0221413xx10^23 cancel"atoms")/"mol"`

`=` `color(blue)("58.988 g/mol")`,

which is close enough to cobalt, whose accepted value is `"58.933 g/mol"`, and our value is off by only `0.093%`.

The other gives you `"1 million"` silver atoms weighing `1.79xx10^(-16) "g"`. That gives you a quantity and a mass, which is enough to convert to the atomic units of `"g/mol"`, again.

`(1.79xx10^(-16) "g")/(10^6 cancel"Ag atoms")xx(6.0221413xx10^23 cancel"atoms")/"mol"`

`=` `color(green)("107.796 g/mol")`

which is close enough to the accepted value of `"107.868 g/mol"` (`0.066%` difference).

In either case you still get `\mathbf("g/mol")`.

WHAT IS AMU?

You are not required to use the conversion

`"1 g"/(6.0221413xx10^(23) "atoms") = "1 amu"`

`= 1.660599xx10^(-24) "g",`

unless you want to. It just depends on whether you are talking about `"1 mol"` of atoms or `"1 atom"`, and you need to choose which one is more convenient for you.

CONVERTING BETWEEN G/MOL and AMU

You can still interconvert between `"g/mol"` and `"amu"`...

`(58.988 cancel"g")/cancel"mol"xxcancel"1 mol"/(6.0221413xx10^23 cancel"atoms") xx "1 amu"/(1.660599xx10^(-24) cancel"g")xxcancel("1 atom")`

`~~ color(blue)(58.988)` `color(blue)("amu for one atom")`

i.e. The experimental atomic mass of `"1 atom"` of cobalt according to the given information is `"58.988 amu"`, while the molar mass calculated at the top of the answer is `"58.988 g/mol"`.

So, `"amu"` is just a way of giving the mass of one atom in atomic units (`"1 amu"` `ne` `"1 g"`), while `"g/mol"` gives you the mass of `\mathbf("1 mol")` of atoms.