According to the periodic table , a single carbon has a mass of 12.011 amu. what is the mass of a single carbon atom in grams?

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Nam D. Share
Mar 9, 2018

Well, no carbon atom has exactly a mass of $12.011 \setminus \text{amu}$...

Explanation:

The periodic table gives the average mass of all the elements, that is, taking the average mass of all the elements' isotopes, and then taking their abundance on Earth into account as well.

For instance, carbon does not only exist as ""^12C, but can also exist as ""^13C and ""^14C. However, the latter isotopes are not as common as ""^12C, and so the mass of carbon on average would be a little bit over $12$, i.e. $12.011$.

If you still want to know what will the average mass of a carbon atom in grams, we can find that out as follows.

We know that $1 \setminus \text{amu"=1.66*10^-24 \ "g}$.

So, the mass of a carbon atom in grams will be

$12.011 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{amu"*(1.66*10^-24 \ "g")/(1color(red)cancelcolor(black)"amu")~~2*10^-23 \ "g}}}}$

So, the average mass of a carbon atom will be approximately $2 \cdot {10}^{-} 23$ grams.

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Mar 9, 2018

There is no single carbon atom with that mass of 12.011 units.

Explanation:

Natural carbon is formed by 98.93% of isotope C-12 with mass 12.000000 units, and 1.07% of isotope C-13 with mass 13.003355 units.
If you take the average of ten thousand atoms, you get the following weighed average mass of carbon atoms:

$\text{average mass} = \frac{12.000000 \cdot 9893 + 13.003355 \cdot 107}{10000} =$
$= \frac{118716 + 1391}{10000} = \frac{120107}{10000} = 12.0107 \approx 12.011 \text{ units}$

Now, if we are interested to know the masses of actual carbon atoms in grams, we should take the most abundant isotope, C-12.

Its mass is exactly 12 u because of the definition of the "unified atomic mass unit" or u as one-twelfth of that isotope carbon.

That mass corresponds to $1.660539040 \cdot {10}^{-} 24 g$, thus the mass in grams of a single atom of isotope 12 is $12.000000 \cdot 1.660539040 \cdot {10}^{-} 24 g = 19 , 926468 \cdot {10}^{-} 24 g r a m s$.

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