# Chemistry - Relative Mass

Problem Set

How do we express the mass of an atom? It is nearly $0kg$! By using the Mass Spectrometer, scientists can now determine the mass of atoms. For example, Oxygen atom is approximately $2.657\times10^{-26}kg$. However, do you have any idea how heavy or light $2.657\times10^{-26}kg$ is? So we can see that it is not easy to write or memorize if we use the exact mass of the atom.

So, scientists compare the mass of each atom. They use the mass of $\frac{1}{12} \text{Carbon-12}$ $(^{12}C)$ as a standard and compare it with other atoms. For example,

$\text{Mass of }\frac{1}{12} \text{Carbon-12}:\text{Mass of Oxygen atom}$

$1:16$

Then, the value $16$ is the Relative Atomic Mass of Oxygen atom.

We write it as $A_r(O)=16$.

What about the mass of a molecule? We use the same idea, but called Relative Molecular Mass. What we have to do is sum up all the relative atomic mass of each atoms in the molecule. For example,

$\text{Mass of }\frac{1}{12} \text{Carbon-12}:\text{Mass of water, }H_2O$

$1:2\times1+16$

$1:18$

Then, the value $18$ is the Relative Molecular Mass of water $H_2O$ molecule.

We write it as $M_r(H_2O)=18$.

Note that the difference are:

1. Relative Atomic Mass is for atom. $C, H, O, N, P$

2. Relative Molecular Mass is for molecule. $CO_2, H_2O, NH_3$

Some other notes:

1. At the beginning, scientist did not use the mass of $\frac{1}{12}$ $\text{Carbon-12}$ as the standard but $\text{Hydrogen}$ instead.

2. Relative Mass has no unit as it is a comparison between mass of atoms or molecules.

Note by Christopher Boo
7 years, 6 months ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
• Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

Sort by:

Why is hydrogen not used now?

- 7 years, 6 months ago

Yes, I will go through this history later.

- 7 years, 6 months ago

Bcos carbon combines with most compounds while hydrogen doesn't,that's why it becomes easy to calculate relative mass using C

- 6 years ago

Hi, Christopher I am new to chemistry and I hope that someone will reply to this comment How do you know that the value 16 is the Relative Atomic Mass of Oxygen atom? Had you already known that it is 16 or you calculated it right while you post this?

- 7 years, 6 months ago

An element is identified by the number of protons that its nucleus contains. Oxygen atom has 8 protons by definition. Similarly, Carbon is identified with 6 protons in its nucleus.

Now, for both of these atoms, in their standard isotope, the protons are accompanied by the same number of neutrons. i.e, Oxygen has 8 Protons and 8 Neutrons, while Carbon has 6 Protons, and 6 Neutrons.

The mass of a proton and a neutron is approximately same. Thus, if we define :

$1 A.M.U$ (Atomic Mass Unit) $=$ Mass of a Proton, then, clearly,

Mass of Oxygen atom (standard isotope) $= 8+8 = 16 A.M.U$, and,
Mass of Carbon atom (standard isotope) $= 6+6 = 12 A.M.U$

Now,
If we take $\frac{1}{12}$th of the mass of carbon atom $= \frac{1}{12}\times 12 = 1 A.M.U$, then this is defined as the standard Atomic Mass.

Thus, clearly,
Relative Mass of Oxygen atom $= 16$

- 7 years, 6 months ago

Thanks Anish Puthuraya for further explanation as I did not include any information about protons and neutrons.

Daniel-

If you don't know the number of protons or neutrons of an atom, you can always refer to the Periodic Table Scroll down to 9.6 until you saw a table full of elements, the value below each elements is their relative atomic mass.

For relative molecular mass, we don't have a table but it is easy too sum up all the relative atomic mass of atoms present in that molecule. For example, $NH_3$ has 1 $N$ and 3 $H$ is $14+3\times1=17$.

Hope this helps :)

- 7 years, 6 months ago

Thanks to both of you

I had already known the atomic number before this

- 7 years, 6 months ago

Is it only for $C, H, O, N, P$ and $CO_2, H_2O, NH_3$?

- 7 years, 6 months ago

No, we use the term atomic mass for atoms. There are $115$ elements as of now. So, there are $115$ atoms. And they all of atomic masses. In short, the atomic mass of an atom tells you how much massive that atom is compared to $\frac{1}{12}$ of the mass of a $C-12$ atom.

We use the term molecular mass for molecules. There are a lot of different molecules in the world, so they all have their own molecular masses [not just $CO_2, H_2O$ and $NH_3$. They were just examples].

- 7 years, 6 months ago

Thank you

- 7 years, 6 months ago

Always glad to help!

- 7 years, 6 months ago

Instructive post.

- 7 years, 6 months ago

GOOD THING

- 7 years, 6 months ago

great post

- 7 years, 6 months ago

Very instructive post.

- 7 years, 6 months ago