<u>Answer:</u> The length of copper wire that can be produced is 40.2 m
<u>Explanation:</u>
We are given:
Mass of chalcocite = 5.23 lb = 2374.42 g (Conversion factor: 1 lb = 454 g)
79.8 % (m/m) of copper
This means that 79.8 grams of copper is present in 100 grams of chalcocite
Applying unitary method:
In 100 grams of chalcocite, the mass of copper present is 79.8 grams
So, in 2374.42 grams of chalcocite, the mass of copper present will be = ![\frac{79.8}{100}\times 2374.42=1873.42g](https://tex.z-dn.net/?f=%5Cfrac%7B79.8%7D%7B100%7D%5Ctimes%202374.42%3D1873.42g)
To calculate volume of a substance, we use the equation:
![\text{Density of substance}=\frac{\text{Mass of substance}}{\text{Volume of substance}}](https://tex.z-dn.net/?f=%5Ctext%7BDensity%20of%20substance%7D%3D%5Cfrac%7B%5Ctext%7BMass%20of%20substance%7D%7D%7B%5Ctext%7BVolume%20of%20substance%7D%7D)
Density of copper = ![8.96g/cm^3](https://tex.z-dn.net/?f=8.96g%2Fcm%5E3)
Mass of copper = 1873.42 g
Putting values in above equation, we get:
![8.96g/cm^3=\frac{1873.42g}{\text{Volume of copper}}\\\\\text{Volume of copper}=\frac{1873.42g}{8.96g/cm^3}=209.08cm^3](https://tex.z-dn.net/?f=8.96g%2Fcm%5E3%3D%5Cfrac%7B1873.42g%7D%7B%5Ctext%7BVolume%20of%20copper%7D%7D%5C%5C%5C%5C%5Ctext%7BVolume%20of%20copper%7D%3D%5Cfrac%7B1873.42g%7D%7B8.96g%2Fcm%5E3%7D%3D209.08cm%5E3)
To calculate the length of the wire, we use the equation:
![V=\pi r^2h](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E2h)
where,
V = volume of copper wire =
(Conversion factor:
)
r = radius of the copper wire =
(Conversion factor: 1 in = 0.0254 m)
h = length/ height of the copper wire = ?
Putting values in above equation, we get:
![209.08\times 10^{-6}m^3=(3.14)\times (1.29\times 10^{-3})^2\times h\\\\h=\frac{209.08\times 10^{-6}}{3.14\times (1.29\times 10^{-3})^2}=40.2m](https://tex.z-dn.net/?f=209.08%5Ctimes%2010%5E%7B-6%7Dm%5E3%3D%283.14%29%5Ctimes%20%281.29%5Ctimes%2010%5E%7B-3%7D%29%5E2%5Ctimes%20h%5C%5C%5C%5Ch%3D%5Cfrac%7B209.08%5Ctimes%2010%5E%7B-6%7D%7D%7B3.14%5Ctimes%20%281.29%5Ctimes%2010%5E%7B-3%7D%29%5E2%7D%3D40.2m)
Hence, the length of copper wire that can be produced is 40.2 m