Question

What is the mass of `9.75xx10^26` `"lithium atoms"`?

Answer 1

`1.12*10^4g`

Explanation:

Well first, we need to convert `9.75*10^26` atoms of lithium into moles of lithium. Note that, `1mol=6.02*10^23` atoms.

`:.` There are `(9.75*10^26)/(6.02*10^23)=1619.6~~1620` moles of lithium.

Now to find the mass, we can use the molar mass of lithium and multiply it by the number of moles.

`"mass"="molar mass"*"moles"`

Lithium has a molar mass of `6.941g"/"mol`.

`:.` Its mass would be `1620cancel(mol)*6.941g"/"cancel(mol)=11244.42g`

We now need to round to three significant figures.

`:.=1.12*10^4g`

Answer 2

The mass of `9.75xx"10"^26"` atoms of lithium is `color(blue)(1.12xx"10"^4" g Li")`.

Explanation:

You need to convert atoms Li to moles Li by multiplying by `("1 mol Li )/(6.022"xx"10"^23" atoms Li")`. This gives you moles Li. Then multiply moles Li by the molar mass of Li `("6.94 g/mol" -"from the periodic table")`.

Moles Li

`9.75xx10^26color(red)cancel(color(black)("atoms Li"))xx(1"mol Li")/(6.022xx10^23color(red)cancel(color(black)("atoms Li")))=1.619xx"10"^3" mol Li"`

Mass Li

`1.619xx10^3color(red)cancel(color(black)("mol Li"))xx(6.94"g Li")/(1color(red)cancel(color(black)("mol Li")))=1.12xx"10"^4" g Li"` rounded to three significant figures

You can combine the two steps into one equation.

`9.75xx10^26color(red)cancel(color(black)("atoms Li"))xx(1color(red)cancel(color(black)("mol Li")))/(6.022xx10^23color(red)cancel(color(black)("atoms Li")))xx(6.94"g Li")/(1color(red)cancel(color(black)("mol Li")))=1.12xx"10"^4" g Li"`