How long should you cut a piece of wire to obtain 0.0141 moles of copper?

[chels0]

I'm having problems with this question.

A piece of copper wire has a diameter of 0.389mm. If copper has a density of 8.92g/cc, how long (in meters) should you cut a piece of wire to obtain 0.0141 moles of copper?

I tried finding the volume of the cylinder and other things, but I'm completely lost!

can someone help me??

 

[Ygggdrasil]

Try a simpler problem to start. What is the volume of a copper wire that has a diameter of 0.389mm and a length of 1m? What would be the mass of this wire?

Second, what is the mass of 0.0141mol of copper?

 

[Blueshift5]

I can provide you with a step-by-step approach to solving this problem. First, we need to determine the molar mass of copper, which is 63.55 g/mol. Next, we need to convert the given amount of moles (0.0141 moles) to grams by multiplying it by the molar mass. This gives us 0.895 g of copper.

Next, we need to calculate the volume of the wire. We can do this by using the formula for the volume of a cylinder, V=πr^2h, where r is the radius (half of the diameter) and h is the height (or length) of the wire.

In this case, the radius would be 0.1945 mm (0.389 mm/2 = 0.1945 mm). We need to convert this to meters by dividing it by 1000, which gives us 0.0001945 m.

To find the volume, we also need to convert the density of copper from g/cc to g/m^3. This can be done by multiplying it by 1000, which gives us 8920 g/m^3.

Now, we can plug in all the values into the formula for volume: V=π(0.0001945 m)^2h = 0.0000000119h m^3.

To find the length of the wire, we need to solve for h. Rearranging the equation, we get h= V/πr^2. Plugging in the values we calculated, we get h= (0.000895 g) / (3.14 x 0.0000000119 m^3) = 2.38 m.

Therefore, to obtain 0.0141 moles of copper, we would need to cut a piece of wire that is 2.38 meters long. I hope this helps you understand the solution to the problem. If you have any further questions, please feel free to ask.