# 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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• 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"

• 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.

• 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?

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