Question

How many carbon atoms are there in a 1.3-carat diamond? diamonds are a form of pure carbon. (1 carat?

Answer 1

How many carbon atoms are there in a 1.3-carat diamond? Answer: 1.3 x 10^22 C atoms...
If a 1 carat = 0.20 g ... then 0.3 carat = 0.20 / 0.3 = 0.06 g
Thus, 1.3 carat = 0.26g
Find the moles first:
Moles= Grams / Mm of C
0.26 / 12.011 = 0.0216 mols of C
Atoms = Moles * Avogadro's number (6.022*10^23)
0.0216 * 6.022*10^23 = 1.3*10^22 C atoms

Hope this helps! :)

Answer 2

$\boxed{ \ 1,3 \times 10^{22} \ carbon \ atoms \ }$

Further explanation

Diamond is 100% pure elemental carbon, compressed to its crystal form, under extreme heat and pressure deep within the Earth. The symbol for carbon is C.

Step-1: convert carat to grams

The carat represent the unit of weight for diamonds and other gemstones. From several sources, it is known that 1-carat = 0.2 grams of carbon atoms.

Converting 1.3-carat to several grams of carbon atoms

$\boxed{ \ 1.3-carat \times \frac{0.2 \ grams}{1 \ carat} = 0.26 \ grams \ }$

So 1.3-carat diamonds are equal to 0.26 grams of carbon atoms.

Step-2: convert grams to moles

From the periodic table of elements, we know that the atomic mass of carbon is 12 g/mol. The relationship between mole, gram, and atomic mass is

$\boxed{ \ moles = \frac{grams}{atomic \ mass}}$

Converting 0.26 grams to moles

$\boxed{ \ moles = \frac{0.26 \ grams}{12 \ g/mol}}$

We obtain 0.0217 moles of carbon atoms.

Final step: convert mole to atoms

The relationship between mole, the number of atoms (N), and Avogadro's number is

$\boxed{\ moles = \frac{N}{6.022 \times 10^{23}} \rightarrow N = moles \times 6.022 \times 10^{23} \ }$

$N = 0.0217 \times 6.022 \times 10^{23}$

Rounding to 2 decimal places to produce $0.13 \times 10^{23}$ and in the form of scientific notation is $\boxed{\ 1.3 \times 10^{22} \ carbon \ atoms}$

So there is $\boxed{\ 1.3 \times 10^{22} \ carbon \ atoms}$ are there in a 1.3-carat diamond.

Quick way

$\boxed{\ \frac{N}{6.022 \times 10^{23}} = \frac{grams}{atomic \ mass} \ }$

Rearrange it

$\boxed{\ N = 6.022 \times 10^{23} \times \frac{grams}{atomic \ mass} \ }$

$N = 6.022 \times 10^{23} \times \frac{1.3 \times 0.2}{12} \ }$

$\boxed{\ N = 1.3 \times 10^{22} \ carbon \ atoms}$

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Keywords: how many, carbon atoms, in a 1.3-carat diamond, a form of pure carbon, elemental, 100%, 1-carat = 0.2 grams, moles, atomic mass, avogadro's number, converting