Given :
Diameter of gold , [tex]D = 0.506\ mm = 0.0506\ cm[/tex] .
Density , [tex]d=19.3 \ g/cc[/tex] .
To Find :
How long (in meters) should you cut a piece of wire to obtain 0.0323 moles of gold .
Solution :
Molecular mass of gold , MM =197 g/mole .
Mass of gold :
[tex]m = n\times MM\\\\m=0.0323\times 197\ g\\\\m=6.3631\ g[/tex]
Volume is given by :
[tex]V=\dfrac{m}{d}\\\\V=\dfrac{6.3631}{19.3}\ cm^3\\\\V=0.33\ cm^3[/tex]
Now , volume is given by :
[tex]V=h\pi\dfrac{d^2}{4}\\\\V=h\times \pi \times \dfrac{0.0506^2}{4}\\\\V=h\times 0.002[/tex]
[tex]h\times 0.002=0.33\\\\h=\dfrac{0.33}{0.002}\ cm\\\\h=165\ cm = 1.65 \ m[/tex]
Therefore , length of wire is 1.65 m .
Hence , this is the required solution .
