Alex asked in Science & MathematicsChemistry · 10 months ago

# How many atoms of carbon are in a piece of .7mm lead?

My chemistry teacher is making us do this in honor of mole day but the only problem is I don’t know how to set it up. It would be much appreciated if I could get help! <3

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• Dr W
Lv 7
10 months ago

let's set this up with dimensional analysis

let's assume the lead is 100% carbon in graphite form

let's assume the density of that graphite is 2.27 g/cm3

let's assume that 0.7mm is the diameter of the lead

and then

.. (pi * (0.7mm/2 * 100cm/1000mm)² * 1cm)... 2.27g.. 1 mol.. .. 6.022x10^23 atoms

---- ---- ---- ---- ---- ---- --- ----- ---- ---- ---- ---- x --- --- x ---- --- x ---- ---- ----- ----- ----- =

.. .. ... ... ... .. ... . 1 cm.. ... ... .. ... ... ... ... ... ... 1 cm³.... 12g.. ... .. 1 mol of atoms

... = 4x10^20 carbon atoms / cm of "pencil lead"

• 10 months ago

The 0.7 mm is presumably the diameter of the pencil lead, but you don't say how long the pencil is, so there is no way of getting the answer.

If I suppose the length of the lead is 10 cm, then the volume of the lead would be

pi * (0.035 cm)^2 * (10 cm) = 0.0385 cm^3.

The density of graphite is 2.26 g/cm^3, so the mass of the pencil lead would be 0.087 g. The mass of 1 mole of carbon atoms is 12 g, so the lead contains 0.00725 moles, which would translate into 4.4 x 10^21 atoms.

• 10 months ago

Lead is one element, carbon is another. No matter how much pure lead you have, there are no carbon atoms in it. Do you mean perhaps a piece of pencil "lead"? Those are really graphite (mostly) mixed with clay. The graphite is carbon, with 6.022 x10^23 atoms (1 mole) per 12.01 grams. How much mass is that .7 mm lead? And what fraction of it is graphite, and how much is clay?

• Bill
Lv 6
10 months ago

lead is a complete element and does't contain any lead unless it is impure

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• 10 months ago

What???

LOL.... do you mean pencil "lead", as in graphite. Because otherwise, lead (Pb) and carbon (C) are two different elements. The 0.7mm "lead" isn't even all graphite. It contains a polymer binder. Perhaps you were given some additional data that you did not share. You would need to know more about the lead to answer the question.  Like how long it is.  The percentage of carbon in the "lead." The mass or density of the "lead."

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