Answer:
[tex]\boxed {\boxed {\sf 1.393 *10^{24} \ atoms \ B}}[/tex]
Explanation:
1. Convert Grams to Moles
Use the molar mass (found on the Periodic Table) to convert from grams to moles.
Use this value as a ratio.
[tex]\frac {10.81 \ g \ B }{1 \ mol \ B}[/tex]
Multiply by the given number of grams.
[tex]25.00 \ g \ B *\frac {10.81 \ g \ B }{1 \ mol \ B}[/tex]
Flip the ratio so the grams of boron cancel out.
[tex]25.00 \ g \ B *\frac {1 \ mol \ B }{10.81 \ g \ B}[/tex]
[tex]25.00 *\frac {1 \ mol \ B }{10.81 }[/tex]
[tex]\frac {25.00 \ mol \ B }{10.81 }=2.312673451 \ mol \ B[/tex]
2. Convert Moles to Atoms
We use Avogadro's Number, 6.02*10²³: the number of particles (atoms, molecules, etc.) in 1 mole of a substance. In this case, the particles are atoms of boron.
[tex]\frac {6.02*10^{23} \ atoms \ B} {1 \ mol \ B}[/tex]
Multiply by the number of moles we calculated.
[tex]2.312673451 \ mol \ B *\frac {6.02*10^{23} \ atoms \ B} {1 \ mol \ B}[/tex]
The moles of boron cancel.
[tex]2.312673451 *\frac {6.02*10^{23} \ atoms \ B} {1 }[/tex]
[tex]2.312673451 *6.02*10^{23} \ atoms \ B} =1.39269195*10^{24} \ atoms \ B[/tex]
The original value of grams has 4 significant figures, so our answer should have the same. For the number we calculated, that is the thousandth place.
[tex]1.392\underline69195*10^{24} \ atoms \ B[/tex]
The 6 tells us to round the 2 to a 3.
[tex]1.393 *10^{24} \ atoms \ B[/tex]
25.00 grams of boron is equal to 1.393*10²⁴ atoms.
