Q48P - Chemistry: Molecular Nature Of Matter And Change

Question

Copper can be drawn into thin wires. How many meters of 34-gauge wire (diameter = 6.304ᵡ10^-3 in) can be produced from the copper in 5.01 lb of covellite, an ore of copper that is 66% copper by mass? (Hint: Treat the wire as a cylinder: V of cylinder = πr² h; d of copper = 8.95 g/cm³.)

Step-by-Step Solution

Answer

Copper wire can be drawn into wire, this property is known as ductility. Metals show this property. For calculating length first calculate the amount of copper present in covellite and then calculate volume. Using volume data, length of wire comes out to be 8338.973 meter.

Step 1: Calculating the amount of copper present in covellite in g

As, 1 lb = 453.59237 g

$\begin{array}{rcl}Mass of covelite& =& 5.01 Ib\\ & =& 5.01\times 453.59237g\\ & =& 2272.5g\end{array}$

Given that covellite has 66% of copper. So, Amount of copper present in covelite=$2272.5g\times \frac{66}{100}=1499.85g$

Step 2: Calculating volume of wire

$\begin{array}{rcl}Volume& =& \frac{Mass}{Density}\\ & =& \frac{1499.85g}{8.95g/c{m}^3}\\ & =& 167.58c{m}^3\end{array}$

Thus volume of the wire = 167.58cm³

Step 3: Calculating radius in cm

Diameter of the wire = 6.304ᵡ10^-3 in

$\begin{array}{rcl}Radius& =& \frac{Diameter}{2}\\ & =& \frac{6.304\times {10}^{-3}}{2}\\ & =& 3.152\times {10}^{-3}in\end{array}$

1 inch = 2.54 cm

Radius in cm = Radius in inch ᵡ conversion factor  

                      = $3.152\times {10}^{-3}in\times \frac{2.54cm}{1in}=8\times {10}^{-3}cm$

Step 4: Calculating length of copper wire

As given, V of cylinder = πr² h

$h=\frac{volume of cylinder}{\pi r^2}=\frac{167.58c{m}^3}{3.14\times {(8\times {10}^{-3}cm)}^2}=833897.3cm$

Hence, length of wire = 8338.973 meter