Question

How many atoms are in 5.86 mg of silicon?

Answer 1

`1.26 xx 10^20 "atoms"`

Explanation:

In one mole of any substance there are `6.022 xx 10^23` units of that substance. (This number is called Avogadro's number, `N_"A"`.)

We need to convert the mass of silicon to moles using the molar mass of silicon, `28.06 "g"/"mol"`. This number means that one mole of pure silicon would have a mass of `28.06 "g"`. Our given mass, however, is in milligrams; to convert this to grams we'll use the conversion factor `(1 "g")/(10^3 "mg")`:

`5.86 cancel("mg Si")((1 "g")/(10^3 cancel("mg"))) = 0.00586 "g Si"`

Now, using silicon's molar mass, we'll convert this mass to moles of `"Si"`:

`0.00586 cancel("g Si")((1 "mol Si")/(28.06 cancel("g Si"))) = 2.09 xx 10^-4 "mol Si"`

Finally, let's use Avogadro's number to convert moles of silicon to individual unts (atoms) of silicon:

`2.09 xx 10^-4 cancel("mol Si")((6.022 xx 10^23 "atoms Si")/(1cancel( "mol Si"))) = color(red)(1.26 xx 10^20 "atoms Si")`

Answer 2

Approx. `1.3xx10^20` `"silicon atoms................"`

Explanation:

We need (i) to find the molar quantity, and given this (ii) we multiply by `"Avogadro's number"`, `6.022xx10^23*mol^-1` to give the number of silicon atoms..........

`"Moles of silicon"` `=` `(5.86xx10^-3*g)/(28.1*g*mol^-1)=2.1xx10^-4*mol`.

And number of silicon atoms,

`-=2.1xx10^-4*molxx6.022xx10^23*mol^-1=??`