What is mass of atom in KG?

Avogadro's number is one of the most important constants used in chemistry. It is the number of particles in a single mole of a material, based on the number of atoms in exactly 12 grams of the isotope carbon-12. Although this number is a constant, it contains too many significant figures to work with, so we use a rounded value of 6.022 x 1023. So, you know how many atoms are in a mole. Here's how to use the information to determine the mass of a single atom.

• Avogadro's number is the number of particles in one mole of anything. In this context, it is the number of atoms in one mole of an element.
• It's easy to find the mass of a single atom using Avogadro's number. Simply divide the relative atomic mass of the element by Avogadro's number to get the answer in grams.
• The same process works for finding the mass of one molecule. In this case, add up all the atomic masses in the chemical formula and divide by Avogadro's number.

Question: Calculate the mass in grams of a single carbon (C) atom.

Solution

To calculate the mass of a single atom, first look up the atomic mass of carbon from the periodic table. This number, 12.01, is the mass in grams of one mole of carbon. One mole of carbon is 6.022 x 1023 atoms of carbon (Avogadro's number). This relation is then used to 'convert' a carbon atom to grams by the ratio:

mass of 1 atom / 1 atom = mass of a mole of atoms / 6.022 x 1023 atoms

Plug in the atomic mass of carbon to solve for the mass of 1 atom:

mass of 1 atom = mass of a mole of atoms / 6.022 x 1023

mass of 1 C atom = 12.01 g / 6.022 x 1023 C atoms
mass of 1 C atom = 1.994 x 10-23 g

Answer

The mass of a single carbon atom is 1.994 x 10-23 g.

The mass of a single atom is an extremely small number! This is why chemists use Avogadro's number. It makes working with atoms easier because we work with moles rather than individual atoms.

Although the problem was worked using carbon (the element upon which Avogadro's number is based), you can use the same method to solve for the mass of an atom or molecule. If you're finding the mass of an atom of a different element, just use that element's atomic mass.

If you want to use the relation to solve for the mass of a single molecule, there's an extra step. You need to add up the masses of all of the atoms in that one molecule and use them instead.

Let's say, for example, you want to know the mass of a single atom of water. From the formula (H2O), you know there are two hydrogen atoms and one oxygen atom. You use the periodic table to look up the mass of each atom (H is 1.01 and O is 16.00). Forming a water molecule gives you a mass of:

1.01 + 1.01 + 16.00 = 18.02 grams per mole of water

and you solve with:

mass of 1 molecule = mass of one mole of molecules / 6.022 x 1023

mass of 1 water molecule = 18.02 grams per mole / 6.022 x 1023 molecules per mole

mass of 1 water molecule = 2.992 x 10-23 grams

• Born, Max (1969): Atomic Physics (8th ed.). Dover edition, reprinted by Courier in 2013. ISBN 9780486318585
• Bureau International des Poids et Mesures (2019). The International System of Units (SI) (9th ed.). English version.
• International Union of Pure and Applied Chemistry (1980). "Atomic Weights of the Elements 1979". Pure Appl. Chem. 52 (10): 2349–84. doi:10.1351/pac198052102349
• International Union of Pure and Applied Chemistry (1993). Quantities, Units and Symbols in Physical Chemistry (2nd ed.). Oxford: Blackwell Science. ISBN 0-632-03583-8. 
• National Institute of Standards and Technology (NIST). "Avogadro constant". Fundamental Physical Constants.

We are perfectly used to the determination of the mass of a macroscopic object. Commonly, we use scales for this type of measurement. Strictly speaking, a pair of scales measures the weight of an object as the result of being subjected to the Earth’s gravitation.

Mass is a physical quantity that is independent of local gravitation. We all know the examples of astronauts on Moon where they experience just 1/6 of their weight on Earth. However, their mass is still the same independent of where they are.
The unit of mass is the kilogram (kg).

The masses of atoms and molecules are extremely small, by far beyond our imagination. The amount of 12.0 g of carbon corresponds to the amount of substance we define as one mole (1 mol). The mole is defined as a number of particles, 6.022 ´ 1023 particles to be accurate.

To calculate the mass of a single atom of carbon, we just need to divide the molar mass of 12.0 g (0,012 kg) by the number of particles per mole (Avogadro’s number). Doing so yields 1.99 ´ 10–26 kg as the mass of a carbon atom. Large molecules, in particular macromolecules are composed of many atoms. Still, even a large molecule like insulin, C254H377N65O75S6, has a mass of just 9.53 ´ 10–24 kg or 9.53 ´ 10–21 g.

To illustrate the tiny size of a molecule, one may compare the proportions of a molecule of ascorbinic acid (vitamin C, ca. 1 nm) to those of a grapefruit (ca. 10 cm) containing vitamin C. We find that ratio is about 1: 100.000.000. Now, the proportion of this grapefruit to Earth is also about 1:100.000.000.

Thus, weighing is no more feasible. Even the most sensitive laboratory scales, capable of weighing down to about 1 µg (microgram, one millionth of a g or 10–6 g) are far away from measuring the mass of a molecule. So let us go down by several orders of magnitude: 1 ng (nanogram, one billionth of a g or 10–9 g), 1 pg (10–12 g), 1 fg (femtogram, 10–15 g), 1 ag (attogram, 10–18 g). And even the attogram is roughly by a factor of 1000 larger than the mass of a single molecule of insulin. Clearly, weighing isn’t anymore an option.

The so-called unified atomic mass (unit symbol u) serves to quantify atomic and molecular mass. The unified atomic mass is defined as 1/12 of the mass of one atom of the nuclide 12C. (The nuclide 12C represents the most abundant type of carbon atoms, about 99%, the others are 13C, and in traces the radioactive 14C). In analogy to our above calculation we obtain
1 u = 1.67 ´ 10–27 kg.

Provided we know the mass number of an atom, its mass can be calculated quite accurately by multiplying this mass number by 1 u. It may appear disappointing to some degree that this simple calculation does not yield the exact mass, but this may even be exploited to our advantage for formula determination based on measuring accurate mass.

So one carbon atom 12C possesses a mass of 12 u or 1.99 ´ 10–26 kg, one molecule of insulin has 5734 u or 9.53 ´ 10–24 kg. Clearly, using atomic mass units comes in more handy than using kilograms. They are nonetheless far beyond our imagination and it definitely requires some completely different approach for their accurate measurement: mass spectrometry!

A note concerning gigantic and minuscule numbers in science. Nature comprises enormous orders of magnitude. Factors of billions are common in natural sciences. Atmospheric pressure, for example, is 1000 mbar while high vacuum is 10–6 mbar, one billionth of atmospheric pressure. Due to the formula C12H22O11, a sugar molecule (saccharose) has a mass of 342.3 u or 5.72 ´ 10–25 kg; a grain of sugar of 0,05 mg thus corresponds to 1.46 ´ 10–5 mol or 88 trillion molecules. Anything outside our daily reality may appear as something very special or even unreal. Just accept these orders of magnitude as something natural.