Question

Calculate the mass, in nanograms, of 6.74 x 10^21 atoms of fluorine using unit conversions.

Answer 1

To find the mass of 6.74 x 10^21 atoms of fluorine, divide the number of atoms by Avogadro's number to get the moles, multiply by fluorine's atomic mass to convert moles to grams, and multiply by 10^9 to convert grams to nanograms. The final mass is 212,800,000 nanograms.

Step-by-step explanation:

To calculate the mass, in nanograms, of 6.74 x 10^21 atoms of fluorine using unit conversions, we need to use the atomic mass of fluorine and Avogadro's number. The atomic mass of fluorine (F) is approximately 19 amu (atomic mass units), which is equivalent to 19 grams per mole because one mole of any element contains exactly Avogadro's number of atoms, which is 6.022 x 10^23. We can set up a proportion to find the mass of the fluorine atoms using the following steps:

1. Determine the number of moles of fluorine atoms by dividing the given number of atoms by Avogadro's number: (6.74 x 10^21 atoms) ÷ (6.022 x 10^23 atoms/mol).
2. Convert the number of moles to grams using the atomic mass of fluorine: Number of moles x 19 g/mol.
3. Finally, convert the mass from grams to nanograms by multiplying by 10^9, because there are 1 billion nanograms in a gram.

Step-by-step, the calculation would look like this:

1. (6.74 x 10^21 atoms) ÷ (6.022 x 10^23 atoms/mol) = 0.0112 moles
2. 0.0112 mol x 19 g/mol = 0.2128 g
3. 0.2128 g x 10^9 ng/g = 212,800,000 ng

The mass of 6.74 x 10^21 atoms of fluorine is 212,800,000 nanograms (ng).