Question

A closed container has 4.02 ⋅ 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?

6.71 grams, because (4.02 ⋅ 1.67) ⋅ (10^23 ⋅ 10^−24) = 6.7134

5.69 grams, because (4.02 + 1.67) ⋅ (10^23 ⋅ 10^−24) = 5.69

0.67 grams, because (4.02 ⋅ 1.67) ⋅ (10^23 ⋅ 10^−24) = 6.7134 ⋅ 10^−1

0.57 grams, because (4.02 + 1.67) ⋅ (10^23 ⋅ 10^−24) = 5.69 ⋅ 10^−1

Answer 1

Total mass of the atoms=number of atoms * weight of an atom
Total mass of the atoms=(4.02*10²³)*(1.67*10⁻²⁴)=(4.02*1.67)*(10²³⁻²⁴)=
=6.7134*10⁻¹

Answer: 0.67 grams, because (4.02*1.67)*(10²³*10⁻²⁴)=6.7134*10⁻¹

Answer 2

Answer: 0.67 grams, because
`(4.02\cdot1.67)(10^(23)\cdot10^(-24))=6.7134\cdot10^(-1)`

Explanation:

Given : The number of atoms in a closed container =
`4.02\cdot10^(23)\ atoms`

The weight of each atom of the gas =
`1.67\cdot10^(-24)\ grams`

We know that the total mass of atoms of the gas in the container

`=\text{number of atoms in the container}*\text{weight of each atoms}\\=4.02\cdot10^(23)*1.67\cdot10^(-24)\\=(4.02\cdot1.67)(10^(23)\cdot10^(-24))\\=6.7134\cdot(10^(23-24))\\=6.7134\cdot10^(-1)=0.67134\approx=0.67\ grams`

Hence, the approximate total mass of all the atoms of the gas in the container =0.67 grams