How many individual H atoms are in a sample of C2H4Cl2 that also contains 12.1 grams of chlorine?

Question

I really need help with this question. I have no clue how to put it into a formula that I can solve to get the answer.

Answer 1

first you want to convert the given mass of Cl into moles by dividing by the molar mass

12.1 g / (35.45 g/mol) = 0.3413 moles of Cl

then you can divide by 2 because there are 2 chlorines atoms for every 1 molecule of the compound

moles of C2H4Cl2 = moles of Cl / 2 = 0.3413 / 2 = 0.1707 moles of C2H4Cl2

the next step then is multiplying by 4 to convert over to moles of hydrogen atoms

0.1707 moles C2H4Cl2 x 4 = 0.6828 moles of H

finally then you can multiply by Avogadro's number to find the total number of atoms

0.6828 x (6.022 x 10^23) = 4.11 x 10^23 atoms

Answer 2

You don't really "put it into a formula", but rather you work it out knowing certain facts.

1 mol of C₂H₄Cl₂ contains 2 mols of C atoms, 4 mols of H atoms and 2 mols of Cl atoms.

But we have 12.1 grams of Cl. Let us first convert that to moles of Cl:

12.1 g Cl x 1 mol Cl / 35.5 g = 0.3408 mols of Cl

Now, we can determine the moles of H because there are 4 moles of H for every 2 moles of Cl:

0.3408 mols Cl x 4 mols H / 2 mols Cl = 0.6816 moles of H

Now, we use Avogadro's number to convert moles to individual number of atoms:

0.6816 mol H x 6.02x10²³ atoms / mol = 4.10 x10²³ atoms of H

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You could do this another way by using dimensional analysis and knowing the above facts. Maybe you'll find this easier.

12.1 g Cl x 1 mol Cl/35.5 g x 1 mol C₂H₄Cl₂ / 2 mol Cl x 4 mol H / mol C₂H₄Cl₂ x 6.02x1023 H atoms / mol = 4.10x1023 H atoms