# 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".

Apr 16, 2016

Both questions ask the same thing in opposite ways.

One gives you $\text{16.26 mg}$ containing $1.66 \times {10}^{20}$ $\text{atoms}$. That gives you a mass and a quantity, which is enough to convert to the atomic units of $\text{g/mol}$.

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

$=$ $\textcolor{b l u e}{\text{58.988 g/mol}}$,

which is close enough to cobalt, whose accepted value is $\text{58.933 g/mol}$, and our value is off by only 0.093%.

The other gives you $\text{1 million}$ silver atoms weighing $1.79 \times {10}^{- 16} \text{g}$. That gives you a quantity and a mass, which is enough to convert to the atomic units of $\text{g/mol}$, again.

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

$=$ $\textcolor{g r e e n}{\text{107.796 g/mol}}$

which is close enough to the accepted value of $\text{107.868 g/mol}$ (0.066% difference).

In either case you still get $\setminus m a t h b f \left(\text{g/mol}\right)$.

WHAT IS AMU?

You are not required to use the conversion

$\text{1 g"/(6.0221413xx10^(23) "atoms") = "1 amu}$

$= 1.660599 \times {10}^{- 24} \text{g} ,$

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

CONVERTING BETWEEN G/MOL and AMU

You can still interconvert between $\text{g/mol}$ and $\text{amu}$...

$\left(58.988 \cancel{\text{g")/cancel"mol"xxcancel"1 mol"/(6.0221413xx10^23 cancel"atoms") xx "1 amu"/(1.660599xx10^(-24) cancel"g")xxcancel("1 atom}}\right)$

$\approx \textcolor{b l u e}{58.988}$ $\textcolor{b l u e}{\text{amu for one atom}}$

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

So, $\text{amu}$ is just a way of giving the mass of one atom in atomic units ($\text{1 amu}$ $\ne$ $\text{1 g}$), while $\text{g/mol}$ gives you the mass of $\setminus m a t h b f \left(\text{1 mol}\right)$ of atoms.