Question

A closed container has 2.04 ⋅ 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?

a) 0.34 grams, because (2.04 ⋅ 1.67) ⋅ (1023 ⋅ 10−24) = 3.4068 ⋅ 10−1
b) 0.37 grams, because (2.04 + 1.67) ⋅ (1023 ⋅ 10−24) = 3.71 ⋅ 10−1
c) 3.41 grams, because (2.04 ⋅ 1.67) ⋅ (1023 ⋅ 10−24) = 3.4068
d) 3.71 grams, because (2.04 + 1.67) ⋅ (1023 ⋅ 10−24) = 3.71

Answer 1

2.04 ⋅ 10^23 * 1.67 ⋅ 10^−24 =
0.34 grams, because (2.04 ⋅ 1.67) ⋅ (1023 ⋅ 10−24) = 3.4068 ⋅ 10−1

Answer 2

Answer:-a) 0.34 grams, because
`(2.04\cdot1.67)\cdot(10^(23)\cdot10^(-24))=3.4068\cdot10^(-1)\ grams.`

Explanation:-

Given:

Number of atoms in a closed container
`=2.04*10^(23)`

Weight of one atom
`=1.67*10^(-24)`

Total mass of all the atoms of the gas in the container
`=\text{Number of atoms}*\text{Weight of one atom}`

`=2.04*10^(23)*1.67*10^(-24)`

`(2.04*1.67)(*10^(23-24))`

`=3.40*10^(-1)=0.34068\ grams`

Thus A is the right option.