What is the empirical formula for the compound that has 46 grams of sodium, 64 grams of sulfur, and 48 grams of oxygen?

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What is the empirical formula for the compound that has 46 grams of sodium, 64 grams of sulfur, and 48 grams of oxygen?

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Answer 1 · 2016-08-06T19:20:44

${Na}_{2} S_{2} O_{3}$ $"Na"_2"S"_2"O"_3$

Explanation:

Your tool of choice here will be the Periodic Table of Elements.

Grab one and look for the molar mass of sodium, $Na$ $"Na"$ , sulfur, $S$ $"S"$ , and oxygen, $O$ $"O"$ . Notice that you have

$M_{M Na} \approx {23 g mol}^{- 1}$ $M_("M Na") ~~ "23 g mol"^(-1)$

$M_{M S} \approx {32 g mol}^{- 1}$ $M_("M S") ~~ "32 g mol"^(-1)$

$M_{M O} \approx {16 g mol}^{- 1}$ $M_("M O") ~~ "16 g mol"^(-1)$

This tells you that the sample given to you contains

$46 color(red)(cancel(color(black)("g"))) * "1 mole Na"/(23color(red)(cancel(color(black)("g")))) = "2 moles Na"$

$64 color(red)(cancel(color(black)("g"))) * "1 mole S"/(32color(red)(cancel(color(black)("g")))) = "2 moles S"$

$48 color(red)(cancel(color(black)("g"))) * "1 mole O"/(16color(red)(cancel(color(black)("g")))) = "3 moles O"$

Now, in order to write the empirical formula of the compound, you must find the smallest whole number ratio that exists between its constituent elements.

Since the $2:2:3$ ratio is already in its smallest whole number form, you can say that the empirical formula of the compound is

$color(green)(|bar(ul(color(white)(a/a)color(black)("Na"_2"S"_2"O"_3)color(white)(a/a)|)))$

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What is the empirical formula for the compound that has 46 grams of sodium, 64 grams of sulfur, and 48 grams of oxygen?

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