My chem teacher gave us this problem
Twelve-gauge copper wire,like the kind commonly used in residential electrical systems, is roughly cylindrical and has a diameter of approximately .1040in. Copper's density is 8.92g/cubic cm and copper atoms have an approximate atomic radius of 135 pm.
a.Calculate the number of atoms it would take to span the thickness, that is, diameter, of one of these wires. Express this value as a number of atoms and a number of moles to atoms.
b.calculate the mass,in grams, of a 100ft piece of copper wire.
c.How many moles of copper atoms would be found in a piece of this wire that is exactly 100ft long? How many atoms?
I tried to convert pm to meters and converting .1040 and then dividing but I don't know if I did it right---Please Help me!!!!!
It would be far simpler for you to show your calculations and let us check them than for us to work the problems, take the time to post, and let you check our work.
please i cant solve it
Sure, I'd be happy to help you with these calculations! Let's tackle each part one by one:
a. To calculate the number of atoms it would take to span the diameter of the wire, we need to find the length of the wire that corresponds to the diameter. The diameter of the wire is given as approximately 0.1040 inches, which is equivalent to 0.1040 * 2.54 = 0.26416 cm.
If we assume the wire is a perfect cylinder, the length would be equal to the diameter. Therefore, the length of wire required to span the diameter is also 0.26416 cm.
To convert this length to moles and atoms, we need to find the volume of the cylinder. The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height (length).
Since the wire is cylindrical, the radius is half the diameter, which is 0.26416/2 = 0.13208 cm. The height is equal to the diameter, which is 0.26416 cm.
Using the formula, we get V = 3.14159 * (0.13208)^2 * 0.26416 = 0.018310829 cm^3.
Now, we can calculate the number of moles of copper atoms using the density of copper. The density is 8.92 g/cm^3. Since we know the volume in cm^3, we can multiply it by the density to get the mass in grams:
Mass = Volume * Density = 0.018310829 cm^3 * 8.92 g/cm^3 ≈ 0.163 g
Next, we need to convert grams to moles. The molar mass of copper (Cu) is 63.55 g/mol. Using this, we can calculate the number of moles:
Number of moles = Mass / Molar mass = 0.163 g / 63.55 g/mol ≈ 0.003 mols
Finally, to find the number of atoms, we need to use Avogadro's number, which is approximately 6.022 x 10^23 atoms/mol:
Number of atoms = Number of moles * Avogadro's number ≈ 0.003 mols * 6.022 x 10^23 atoms/mol ≈ 1.8066 x 10^21 atoms
So, the number of atoms it would take to span the diameter of the wire is approximately 1.8066 x 10^21 atoms, and the number of moles to atoms is approximately 0.003 mols.
b. To find the mass of a 100ft piece of copper wire, we need to use the information that the density of copper is 8.92 g/cm^3. First, let's convert 100ft to centimeters:
1 ft = 30.48 cm
100 ft = 100 * 30.48 cm = 3048 cm
Now, we need to find the volume of the wire. Since the wire is cylindrical, we can use the formula for the volume of a cylinder:
Volume = πr^2h
Given that the diameter is approximately 0.1040 inches, we can find the radius by dividing the diameter by 2:
Radius = 0.1040 inches / 2 = 0.0520 inches
To convert inches to centimeters, we multiply by 2.54:
Radius = 0.0520 inches * 2.54 cm/inch ≈ 0.13208 cm
Since the height is equal to the length of the wire, we have:
Volume = π * (0.13208 cm)^2 * 3048 cm ≈ 1635.22 cm^3
Now, we can find the mass by multiplying the volume by the density:
Mass = Volume * Density = 1635.22 cm^3 * 8.92 g/cm^3 ≈ 14590.15 g
Therefore, the mass of a 100ft piece of copper wire is approximately 14590.15 grams.
c. To find the number of moles and atoms in a 100ft piece of copper wire, we can use the mass we calculated in part b and the molar mass of copper (Cu), which is 63.55 g/mol:
Number of moles = Mass / Molar mass = 14590.15 g / 63.55 g/mol ≈ 229.78 mols
To find the number of atoms, we once again use Avogadro's number:
Number of atoms = Number of moles * Avogadro's number ≈ 229.78 mols * 6.022 x 10^23 atoms/mol ≈ 1.382 x 10^26 atoms
So, there are approximately 229.78 moles of copper atoms in a 100ft piece of copper wire, which is equivalent to approximately 1.382 x 10^26 atoms.
I hope this helps! Let me know if you have any more questions or need further clarification.
Sure! Let's break down the problem step by step.
a. To calculate the number of atoms it would take to span the diameter of the wire, we can assume that the wire is a perfect cylinder.
1. First, we need to find the length of the wire that corresponds to the diameter of the wire.
The diameter is given as approximately 0.1040 inches. To convert this to cm, we can use the conversion factor: 1 inch = 2.54 cm.
So, the diameter of the wire in cm is 0.1040 inches * 2.54 cm/inch = 0.26456 cm.
2. Now, we can calculate the number of atoms that would span this length.
The atomic radius of copper is given as 135 pm (picometers), which is equal to 135 * 10^(-12) meters.
Since the diameter of the wire is twice the radius, the length per atom would be 2 * 135 * 10^(-12) meters.
3. To find the number of atoms, we divide the length of the wire by the length per atom.
Number of atoms = 0.26456 cm / (2 * 135 * 10^(-12) m) = (0.26456 cm) / (2 * 135 * 10^(-12) m) * (100 cm/m) = 9.80448 x 10^9 atoms.
4. Lastly, let's convert this number to moles. Avogadro's number tells us that 1 mole of a substance contains 6.022 x 10^23 atoms.
Number of moles = (9.80448 x 10^9 atoms) / (6.022 x 10^23 atoms/mol) ≈ 1.6276 x 10^(-14) moles.
b. To calculate the mass of a 100ft piece of copper wire, we need to know the density of copper and the volume of the wire.
1. The density of copper is given as 8.92 g/cm^3.
2. First, let's find the volume of the wire. The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
The radius is half of the diameter, so the radius of the wire is 0.26456 cm / 2 = 0.13228 cm.
The height of the wire is given as 100ft. To convert this to cm, we can use the conversion factor: 1 ft = 30.48 cm.
So, the height of the wire is 100 ft * 30.48 cm/ft = 3048 cm.
Volume of the wire = π * (0.13228 cm)^2 * 3048 cm = 1656.509 cm^3.
3. Now, we can calculate the mass of the wire using the density.
Mass of the wire = Volume of the wire * Density of copper = 1656.509 cm^3 * 8.92 g/cm^3 ≈ 14,753.3 grams.
c. To find the number of moles and atoms in a 100ft long piece of copper wire, we need to know the molar mass of copper.
1. The molar mass of copper is given as 63.55 g/mol.
2. First, let's calculate the number of moles of copper in the wire.
Number of moles = Mass of the wire / Molar mass of copper = 14,753.3 g / 63.55 g/mol ≈ 232.17 moles.
3. To find the number of atoms, we multiply the number of moles by Avogadro's number.
Number of atoms = Number of moles * Avogadro's number = 232.17 moles * 6.022 x 10^23 atoms/mol ≈ 1.397 x 10^26 atoms.
So, in summary:
a. It would take approximately 9.80448 x 10^9 atoms (or 1.6276 x 10^(-14) moles) to span the diameter of the wire.
b. The mass of a 100ft piece of copper wire is approximately 14,753.3 grams.
c. A 100ft long piece of copper wire contains approximately 232.17 moles of copper atoms (or 1.397 x 10^26 atoms).
To solve this problem, we will break it down into three parts:
a) calculating the number of atoms it would take to span the diameter of the wire,
b) calculating the mass of a 100ft piece of copper wire, and
c) determining the number of moles and atoms in the 100ft wire.
a) To calculate the number of atoms that would span the diameter of the wire, we first need to convert the diameter from inches to centimeters. Since 1 inch is equal to 2.54 centimeters, we have:
Diameter = 0.1040 in * 2.54 cm/in = 0.26416 cm
Next, we need to calculate the length of wire needed to span the diameter. The length is equal to the circumference of the wire, which can be calculated using the formula:
Circumference = π * Diameter
Using the given value for diameter, we can calculate the circumference:
Circumference = π * 0.26416 cm
Now, let's calculate the number of atoms. We know that the density of copper is 8.92 g/cm³, and the atomic radius of copper is 135 pm (picometers) = 135 * 10^(-12) cm.
The volume of a cylinder is given by the formula:
Volume = π * (Radius^2) * Length
Since the wire is cylindrical and its diameter is given, the radius (r) can be calculated as half of the diameter:
Radius = Diameter / 2 = 0.26416 cm / 2
Now, we can calculate the volume:
Volume = π * (0.26416 cm / 2)^2 * Circumference
Finally, we need to convert the volume to mass in grams using the density of copper:
Mass = Volume * Density
We can now convert the mass to moles using the molar mass of copper, which is 63.55 g/mol. To calculate the number of moles, divide the mass by the molar mass:
Number of moles = Mass / Molar mass
b) To calculate the mass of a 100ft piece of copper wire, we need to convert the length from feet to centimeters. Since 1 foot is equal to 30.48 centimeters, we have:
Length = 100 ft * 30.48 cm/ft
Now, we can follow the same steps as in (a) to calculate the mass.
c) To calculate the number of moles and atoms in the 100ft wire, we use the same calculations as in (b) and then convert the mass to moles and moles to atoms using Avogadro's number (6.022 × 10^23 atoms/mol).
I hope this explanation helps you solve the problem! Let me know if you have any further questions.