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Numerade Educator



Problem 98 Hard Difficulty

The first sulfur-nitrogen compound was prepared in 1835 and has been used to synthesize many others. In the early 1980 $\mathrm{s}$ researchers made another such compound that conducts electricity
like a metal. Mass spectrometry of the compound shows a molar mass of 184.27 $\mathrm{g} / \mathrm{mol}$ , and analysis shows it to contain 2.288 $\mathrm{g}$ of S for every 1.000 $\mathrm{g}$ of $\mathrm{N}$ . What is its molecular formula?


molecular formula: $\mathrm{S}_{4} \mathrm{N}_{4}$


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Video Transcript

The molecular formula is always a multiple of the empirical formula. No, and typically we find with this multiple is by using the molar mass of the compound. So to find the empirical formula given grams of elements present the first convert the grams to moles. And then we find the simplest whole number ratio of moles, which allows us to write the empirical formula. So if, for example, we have a compound that we know has 2.288 grams of sulfur and one gram of nitrogen. To find the empirical formula, we changed two moles. So we do that by dividing each by its Moeller Mass just found in the periodic table, we're 0.715 bowls of sulfur. If I take one gram of nitrogen and divide by its Moeller math, which is 14.0, I see that's equivalent to point 0714 moles of nitrogen. So in this compound I have 0.715 moles of sulfur in 0.714 moles of nitrogen. To find the simplest whole number ratio. I divide each number by the smallest one. So I take the top number and divided by 0.714 Divide bottom number by 0.714 Find that my ratio is one to one. So in my compound and my empirical formula for every nitrogen, there's one sulfur. So the empirical formula this compound s and we can find the molar mass of sm simply adding up the atomic masses of each element. So 32.0 plus 14.0 is 46 grams per mole. To find the empirical, the molecular formula, we divide the given Moller Mass by the molar mass of the empirical formula, or 184 0.27 grams per mole, divided by 46 grams per mole, which equals four. And so what that means is ready to find the molecular formula. We multiply each element present by four. So the molecular formula is s for end for