Chemistry - Relative Mass - Christopher Boo

Problem Set

Relative Mass Problem 1

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:

Relative Atomic Mass is for atom. $C, H, O, N, P$
Relative Molecular Mass is for molecule. $CO_2, H_2O, NH_3$

Some other notes:

At the beginning, scientist did not use the mass of $\frac{1}{12}$ $\text{Carbon-12}$ as the standard but $\text{Hydrogen}$ instead.
Relative Mass has no unit as it is a comparison between mass of atoms or molecules.

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Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
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`\frac{2}{3}`	$\frac{2}{3}$
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`\sum_{i=1}^3`	$\sum_{i=1}^3$
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Comments

Why is hydrogen not used now?

shuvayan ghosh dastidar - 7 years, 4 months ago

Yes, I will go through this history later.

Christopher Boo - 7 years, 4 months ago

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

Akhil Bansal - 5 years, 11 months 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?

Daniel Lim - 7 years, 4 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 $= 16$

Anish Puthuraya - 7 years, 4 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 :)

Thanks to both of you

I had already known the atomic number before this

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

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].

Mursalin Habib - 7 years, 4 months ago

Thank you

@Daniel Lim – Always glad to help!

Instructive post.

Soham Dibyachintan - 7 years, 4 months ago

GOOD THING

sachin verma - 7 years, 4 months ago

great post

fairooze waziha - 7 years, 4 months ago

Very instructive post.

Vivian Sudhir - 7 years, 4 months ago

Math	Appears 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}`	$\boxed{123}$