# How many atoms are in 5.86 mg of silicon?

May 25, 2017

$1.26 \times {10}^{20} \text{atoms}$

#### Explanation:

In one mole of any substance there are $6.022 \times {10}^{23}$ units of that substance. (This number is called Avogadro's number, ${N}_{\text{A}}$.)

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

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 $\text{Si}$:

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:

$2.09 \times {10}^{-} 4 \cancel{\text{mol Si")((6.022 xx 10^23 "atoms Si")/(1cancel( "mol Si"))) = color(red)(1.26 xx 10^20 "atoms Si}}$

May 25, 2017

Approx. $1.3 \times {10}^{20}$ $\text{silicon atoms................}$

#### Explanation:

We need (i) to find the molar quantity, and given this (ii) we multiply by $\text{Avogadro's number}$, $6.022 \times {10}^{23} \cdot m o {l}^{-} 1$ to give the number of silicon atoms..........

$\text{Moles of silicon}$ $=$ $\frac{5.86 \times {10}^{-} 3 \cdot g}{28.1 \cdot g \cdot m o {l}^{-} 1} = 2.1 \times {10}^{-} 4 \cdot m o l$.

And number of silicon atoms,

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