What will be the mass of 100 atoms of hydrogen? A. 100 g B. 1.66 × 10^-22 g C. 6.023 × 10^23 g D. 100 × 6.023 × 10^23 g
The Correct Answer and Explanation is:
Correct Answer: B. 1.66 × 10⁻²² g
To determine the mass of 100 atoms of hydrogen, begin by recalling that the mass of one hydrogen atom is approximately 1.66 × 10⁻²⁴ grams. This value originates from dividing the molar mass of hydrogen (1.008 g/mol) by Avogadro’s number, which is 6.022 × 10²³ atoms/mol. Mass of one hydrogen atom≈1.008 g/mol6.022×1023 atoms/mol≈1.66×10−24 g\text{Mass of one hydrogen atom} ≈ \frac{1.008\ \text{g/mol}}{6.022 × 10^{23}\ \text{atoms/mol}} ≈ 1.66 × 10^{-24}\ \text{g}Mass of one hydrogen atom≈6.022×1023 atoms/mol1.008 g/mol≈1.66×10−24 g
To find the mass of 100 hydrogen atoms, multiply the mass of one atom by 100: Mass of 100 H atoms=100×1.66×10−24 g=1.66×10−22 g\text{Mass of 100 H atoms} = 100 × 1.66 × 10^{-24}\ \text{g} = 1.66 × 10^{-22}\ \text{g}Mass of 100 H atoms=100×1.66×10−24 g=1.66×10−22 g
Thus, the correct answer is option B.
The other options are incorrect for the following reasons:
- Option A (100 g): This represents the approximate mass of 100 moles of hydrogen atoms, not 100 individual atoms. One mole contains 6.022 × 10²³ atoms, far more than 100.
- Option C (6.023 × 10²³ g): This is a misrepresentation; it implies that the mass of one mole of hydrogen atoms is 6.023 × 10²³ grams, which is incorrect. The mass of one mole of hydrogen atoms is only about 1 gram.
- Option D (100 × 6.023 × 10²³ g): This equals 6.023 × 10²⁵ g, which suggests an enormous and unrealistic quantity of hydrogen. This does not match the problem’s scale of just 100 atoms.
By careful use of atomic mass and Avogadro’s number, the true mass of 100 hydrogen atoms is best represented by 1.66 × 10⁻²² grams.
