Answer:
[tex]\boxed {\boxed {\sf About \ 37.1 \ grams \ of \ iodine }}[/tex]
Explanation:
To convert from atoms to grams, you must first convert atoms to moles, then moles to grams.
1. Convert Atoms to Moles
To convert atoms to grams, Avogadro's number must be used.
[tex]6.022*10^{23}[/tex]
This number tells us the number of particles (atoms, molecules, ions, etc.) in 1 mole. In this case, the particles are atoms of iodine.
[tex]\frac{6.022*10^{23} \ atoms \ I }{1 \ mol \ I}[/tex]
Multiply the given number of atoms by Avogadro's number.
[tex]1.76*10^{23} \ atoms \ I*\frac{6.022*10^{23} \ atoms \ I }{1 \ mol \ I}[/tex]
Flip the fraction so the atoms of iodine will cancel out.
[tex]1.76*10^{23} \ atoms \ I*\frac{ 1 \ mol \ I}{6.022*10^{23} \ atoms \ I}[/tex]
[tex]1.76*10^{23}* \frac{1 \ mol \ I}{6.022*10^{23} }[/tex]
Multiply so the problem condenses into 1 fraction.
[tex]\frac{1.76*10^{23} \ mol \ I}{6.022*10^{23} }[/tex]
[tex]0.2922617071 \ mol \ I[/tex]
2. Convert Moles to Grams
Now we must use the molar mass of iodine, which is found on the Periodic Table.
- Iodine Molar Mass: 126.9045 g/mol
Use this mass as a fraction.
[tex]\frac{ 126.9045 \ g\ I }{ 1 \ mol \ I}[/tex]
Multiply this fraction by the number of moles found above.
[tex]0.2922617071 \ mol \ I*\frac{ 126.9045 \ g\ I }{ 1 \ mol \ I}[/tex]
Multiply. The moles of iodine will cancel.
[tex]0.2922617071 *\frac{ 126.9045 \ g\ I }{ 1 }[/tex]
The 1 as a denominator is insignificant.
[tex]0.2922617071 *{ 126.9045 \ g\ I }[/tex]
[tex]37.08932581 \ g \ I[/tex]
3. Round
The original measurement of 1.76*10^23 has 3 significant figures (1, 7, and 6). Therefore we must round our answer to 3 sig figs. For this answer, that is the tenths place.
[tex]37.08932581 \ g \ I[/tex]
The 8 in the hundredth place tells us to round the 0 up to a 1.
[tex]\approx 37.1\ g \ I[/tex]
There is about 37.1 grams of iodine in 1.76*10^23 atoms.
