Question

A closed container has 6.08 ⋅ 1023 atoms of a gas. Each atom of the gas weighs 1.67 ⋅ 10–24 grams. Which of the following shows and explains the approximate total mass, in grams, of all the atoms of the gas in the container?

Answer 1

Total mass = 6.08 x 10^23 * 1.67 x 10^-24 = 1.01536

Answer 2

Answer:

$10.1536\times  10^{-1}\approx 1.02$ grams.

Step-by-step explanation:

We have been given that a closed container has $6.08\times 10^{23}$ atoms of a gas. Each atom of the gas weighs $1.67\times 10^{-24}$ grams.

To find the total mass, in grams, of all the atoms of the gas in the container, we will multiply number of atoms with mass of each atom.

$\text{Total mass}=6.08\times 10^{23}\times 1.67\times 10^{-24}$

Using exponent property $a^b\times a^c=a^{b+c}$, we will get:

$\text{Total mass}=6.08\times 1.67\times  10^{23}\times 10^{-24}$

$\text{Total mass}=10.1536\times  10^{23+(-24)}$

$\text{Total mass}=10.1536\times  10^{-1}$

$\text{Total mass}=10.1536\times\frac{1}{10}$

$\text{Total mass}=1.01536$

$\text{Total mass}\approx 1.02$

Therefore, the approximate total mass, in grams, of all the atoms of the gas in the container is $10.1536\times  10^{-1}\approx 1.02$ grams.