All categories

4 months ago

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

Chemistry

2 answers:

alisha [2.9K]4 months ago

8 0

To determine the number of carbon atoms in a 1.3-carat diamond: Result: 1.3 x 10^22 C atoms...
Given that 1 carat equals 0.20 g... therefore, 0.3 carat converts to 0.20 / 0.3 = 0.06 g
Thus, for a 1.3 carat = 0.26g
Calculating moles first:
Moles= Grams / Molar Mass of C
0.26 / 12.011 = 0.0216 mols of C
Atoms calculated = Moles * Avogadro's number (6.022*10^23)
0.0216 * 6.022*10^23 yields 1.3*10^22 C atoms

Hope this information is useful!:)

lions [2.9K]4 months ago

6 0

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

Further explanation

Diamonds are entirely composed of elemental carbon, structured into crystal forms due to immense pressure and temperature deep within the Earth's mantle. The chemical symbol for carbon is C.

Step-1: convert carats to grams

A carat is a weight unit used for diamonds and other gemstones. It is generally accepted that 1 carat equals 0.2 grams of carbon atoms.

Translating 1.3 carats into grams of carbon atoms:

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

Thus, a 1.3-carat diamond corresponds to 0.26 grams of carbon atoms.

Step-2: convert grams to moles

The atomic weight of carbon, as per the periodic table, is 12 g/mol. The equation linking moles, grams, and atomic weight is:

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

Transforming 0.26 grams into moles:

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

This results in 0.0217 moles of carbon atoms.

Final step: convert moles to atoms

The correlation between moles, atom count (N), and Avogadro's constant is represented as follows:

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

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

Adjusting to two decimal points gives $0.13 \times 10^{23}$ and expressed in scientific notation becomes $\boxed{\ 1.3 \times 10^{22} \ carbon \ atoms}$

This indicates that there are $\boxed{\ 1.3 \times 10^{22} \ carbon \ atoms}$ atoms present in a 1.3-carat diamond.

Quick method

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

Rearranging it

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

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

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

Learn more

General issues about types of reactions, mixtures and compounds
How many atoms of copper are present in one mole of copper?
Which unit is used for measuring atomic mass?

Keywords: number of carbon atoms, in a 1.3-carat diamond, pure carbon, elemental, 100%, 1-carat equals 0.2 grams, moles, atomic mass, Avogadro's number, converting