Question

A piece of gold wire has a diameter of 0.506 mm. If gold has a density of 19.3 g/cc, how long (in meters) should you cut a piece of wire to obtain 0.0323 moles of gold?

Answer 1

Given :

Diameter of gold , $D = 0.506\ mm = 0.0506\ cm$ .

Density , $d=19.3 \ g/cc$ .

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 :

$m = n\times MM\\\\m=0.0323\times 197\ g\\\\m=6.3631\ g$

Volume is given by :

$V=\dfrac{m}{d}\\\\V=\dfrac{6.3631}{19.3}\ cm^3\\\\V=0.33\ cm^3$

Now , volume is given by :

$V=h\pi\dfrac{d^2}{4}\\\\V=h\times \pi \times \dfrac{0.0506^2}{4}\\\\V=h\times 0.002$

$h\times 0.002=0.33\\\\h=\dfrac{0.33}{0.002}\ cm\\\\h=165\ cm = 1.65 \ m$

Therefore , length of wire is 1.65 m .

Hence , this is the required solution .