Question

How many atoms are present in 80 gm of oxygen.

Answer 1

Hey there!

There are two formulas you need to use. They are:

$n=\dfrac{m}{M}$, where

       $n=$ no. of moles

       $m=$ given mass

       $M=$ Gram Atomic Mass of Oxygen

and $n=\dfrac{N}{N_{A}}$, where

       $n=$ no. of moles

       $N=$ number of atoms

       $N_{A}=$ Avogadro's constant, which is $6.022 \times 10^{23}$

We can see that the Left Hand Side of both the formulas are equal, so we can equate each of their Right Hand Side, as shown below:

$\dfrac{m}{M}=\dfrac{N}{N_{A}}$

We will use this formula later. Let's first get the values of the variables.

• $m$ is equal to the given mass, which is $80g$, as in the question.
• $M$ is equal to the Atomic Mass. Here, they asked the number of atoms, so we must calculate the mass of $O$ (not $O_{2}$). So $M=16g$
• $N_{A}$ is equal to $6.022 \times 10^{23}$.

Now put these values in the equation.

$\dfrac{m}{M}=\dfrac{N}{N_{A}}$

$\dfrac{80g}{16g}=\dfrac{N}{6.022 \times 10^{23}}$

$5=\dfrac{N}{6.022 \times 10^{23}}$

Taking the denominator to the Left Hand Side, we get:

$5 \times 6.022 \times 10^{23}=N$

$30.11 \times 10^{23}=N$

$N=30.11 \times 10^{23}$

Therefore, 80 grams of Oxygen has $30.11 \times 10^{23}$ atoms of Oxygen.

Important points/concepts to remember:

1. Formula of calculating given mass, no. of moles, Gram Atomic Mass
2. Formula of calculating number of atoms/molecules, no. of moles.
3. Application of the correct formulas to get the result.
4. Substitution of all known values into the equation and solve for the unknown variable.