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? (1 point)
0.34 grams, because (2.04 ⋅ 1.67) ⋅ (1023 ⋅ 10−24) = 3.4068 ⋅ 10−1
0.37 grams, because (2.04 + 1.67) ⋅ (1023 ⋅ 10−24) = 3.71 ⋅ 10−1
3.41 grams, because (2.04 ⋅ 1.67) ⋅ (1023 ⋅ 10−24) = 3.4068
3.71 grams, because (2.04 + 1.67) ⋅ (1023 ⋅ 10−24) = 3.71
The correct answer is:
0.34 grams, because (2.04 ⋅ 1.67) ⋅ (1023 ⋅ 10−24) = 3.4068 ⋅ 10−1
To find the total mass of all the atoms in the container, we need to multiply the number of atoms by the mass of each atom.
The number of atoms is given as 2.04 ⋅ 1023.
The mass of each atom is given as 1.67 ⋅ 10−24 grams.
Multiplying these values together gives us (2.04 ⋅ 1.67) ⋅ (1023 ⋅ 10−24) = 3.4068 ⋅ 10−1 grams.
Therefore, the approximate total mass of all the atoms in the container is 0.34 grams.
The mass of a single atom is given as 1.67 ⋅ 10^-24 grams. To find the total mass of all the atoms in the container, we multiply this value by the number of atoms, which is 2.04 ⋅ 10^23. Using scientific notation, the calculation would be:
(2.04 ⋅ 10^23) * (1.67 ⋅ 10^-24) = (2.04 * 1.67) * (10^23 * 10^-24) = 3.4068 * 10^-1
Therefore, the approximate total mass of all the atoms of the gas in the container is 0.34 grams.
The correct answer is:
0.34 grams, because (2.04 ⋅ 1.67) ⋅ (10^23 ⋅ 10^-24) = 3.4068 ⋅ 10^-1
To find the approximate total mass of all the atoms of the gas in the container, we need to multiply the number of atoms by the weight of each atom.
Given that the container has 2.04 ⋅ 10^23 atoms of the gas, and each atom weighs 1.67 ⋅ 10^(-24) grams, we can calculate the total mass as follows:
Total mass = Number of atoms × Weight of each atom
Total mass = (2.04 ⋅ 10^23) × (1.67 ⋅ 10^(-24)) grams
Now we can simplify the expression:
Total mass ≈ 3.4068 ⋅ 10^(-1) grams
So, the approximate total mass of all the atoms of the gas in the container is approximately 0.34 grams.
Therefore, the correct answer is 0.34 grams, as given in option:
0.34 grams, because (2.04 ⋅ 1.67) ⋅ (10^23 ⋅ 10^(-24)) = 3.4068 ⋅ 10^(-1)