Please type clear. (1) During the calculation of 1 mole volume of carbon atoms,
ID: 1035435 • Letter: P
Question
Please type clear.
(1) During the calculation of 1 mole volume of carbon atoms, why we use density of diamond rather than that of graphite? (2) Avogadro's number is a conversion factor between moles and number of molecules Molar mass is a conversion factor between moles and mass of molecules. Assume a person counted the number of gold atoms, one atom per a second for 80 years Did he/she count the number of gold atoms that can be measured by usual balance? (molar mass of gold is 197.0 g/mol) Explain.Explanation / Answer
[1] In diamond carbon atoms atoms are closely packed in face-centered cubic structure. It is a 3-D netwrok of tetrahedrally bonded carbond atoms.
While, graphite has a layered structure. And the distance between the layers is 0.335 nm. It has honeycomb structure with the separation between carbon atoms around 0.142 nm. Which means the density (or amount of carbon) is not same in all direction (more carbon atom in the layer, and less along the perpendicular direction).
So, that is why one uses the density of allotrope (diamond) which has equal distribution of material (carbon atom) in space.
[2] Firstly we will calculate the number of carbon atom counted by the person in 80 years, at a rate of 1 atom per second.
For simplicity we will consider 1 year =365 day (not considering leap year!)
1 hour = 3600 s
1 day = 24 hours
therefore, 80 years = 3600 * 24 * 365 * 80 s = 2.5228 * 109 s
So, Number of Gold atoms counted = rate of counting * time = 1 atom/s * 2.5228 * 109 s = 2.5228 * 109 atoms.
Now, 1 mole (6.022 *1023 atom) of Gold weight = 197.0 g
so, 2.5228 * 109 atom of Gold weight = (197.0 g) * (2.5228 * 109 atoms) / 6.022 *1023 atoms = 8.2532 * 10-13 g
It means the person has counted * 10-13 g of Gold.
And, this amount is too small to be measured by normal balance (even the sophisticated one can measure only of the order of 10-6 g).
So, the answer is no, the person has not counted enough gold atoms to be measured by usual balance.