A closed container has 3.06 ⋅ 1023 atoms of a gas. Each atom of the gas weighs 1.67 ⋅ 10−24 grams.

Question

Which of the following shows and explains the approximate total mass, in grams, of all the atoms of the gas in the container?

Group of answer choices

0.47 grams, because (3.06 + 1.67) ⋅ (1023⋅ 10−24) = 4.73 ⋅ 10−1

0.51 grams, because (3.06 ⋅ 1.67) ⋅(1023⋅ 10−24) = 5.1102 ⋅ 10−1

4.73 grams, because (3.06 + 1.67) ⋅ (1023⋅ 10−24) = 4.73

5.11 grams, because (3.06 ⋅ 1.67) ⋅ (1023⋅ 10−24) = 5.1102

Answer 1

To calculate the total mass of the gas in the container, you can use the formula:

\[ \text{Total mass} = \text{number of atoms} \times \text{mass of each atom} \]

Given:

• Number of atoms = \(3.06 \times 10^{23}\)
• Mass of each atom = \(1.67 \times 10^{-24}\) grams

Now, substituting the values:

\[ \text{Total mass} = (3.06 \times 10^{23}) \times (1.67 \times 10^{-24}) \]

To perform the multiplication, you multiply the coefficients and add the exponents:

1. Multiply the coefficients: \(3.06 \times 1.67 = 5.1102\).
2. Add the exponents: \(10^{23} \times 10^{-24} = 10^{(23 - 24)} = 10^{-1}\).

So,

\[ \text{Total mass} = 5.1102 \times 10^{-1} \text{ grams} = 0.51102 \text{ grams} \approx 0.51 \text{ grams} \]

Thus, the correct choice is:

0.51 grams, because (3.06 ⋅ 1.67) ⋅(1023 ⋅ 10−24) = 5.1102 ⋅ 10−1.