Answer to Question #84630 in General Chemistry for Morgan D Laughlin

Question

Copper can be drawn into thin wires. How many meters of 34−gauge wire (diameter = 6.304 × 10−3 in) can be produced from the copper in 6.40 lb of covellite, an ore of copper that is 66.0% copper by mass?

(Hint: Treat the wire as a cylinder: V of cylinder = πr2h; d of copper = 8.95 g/cm3)

Answer 1

Find volume of copper in ore:

V= m(pure Cu)/d

m(pure Cu)= m(ore)*w(Cu) = 6.40 lb *0.66 = 4.224 lb

As 1lb = 453.592 g then m(Cu) = 4.224 lb *453.592 g/lb = 1915.972 g

V(Cu) = 1915.972 g / 8.95 g/cm³ = 214.075 cm³

Find length of a wire:

as we consider a wire as a cylinder then V (Cylinder) = πr²h

h = V/πr²

r = diameter/2 = 6.304*10^-3 in/2 = 3.152*10^-3 in

As 1 in = 2.54 cm then r = 3.152*10^-3 in * 2.54 cm/in = 8.006*10^-3 cm

h = 214.075 cm³/ (3.1415*(8.006*10^-3)²) = 1063136.52 cm = 10631.36 m

Answer: 10631.36 m