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 $=2.04\times10^{23}$

Weight of one atom$=1.67\times10^{-24}$

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

$=2.04\times10^{23}\times1.67\times10^{-24}$

$(2.04\times1.67)(\times10^{23-24})$

$=3.40\times10^{-1}=0.34068\ grams$

Thus A is the right option.