How many atoms are in 5.86 mg of silicon?

2 Answers
May 25, 2017

Answer:

#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")#

May 25, 2017

Answer:

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=??#