# Question #87cb7

##### 1 Answer

#### Explanation:

Your strategy here will be pick a sample of this compound and use the given **percent composition** to determine how many grams of each element it contains.

To make calculations easier, pick a

#22.8% -> "22.6 g Na"# #21.5% -> "21.5 g B"# #55.7% -> "55.7 g O"#

Next, use the **molar mass** of each element to determine how many **moles** of each you have in the sample

#"For Na: " 22.6 color(red)(cancel(color(black)("g"))) * "1 mole Na"/(23.0color(red)(cancel(color(black)("g")))) = "0.9826 moles Na"#

#"For B: " 21.5 color(red)(cancel(color(black)("g"))) * "1 mole B"/(10.811color(red)(cancel(color(black)("g")))) = "1.989 moles B"#

#"For O: " 55.7color(red)(cancel(color(black)("g"))) * "1 mole O"/(15.9994color(red)(cancel(color(black)("g")))) = "3.481 moles O"#

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

To do that, divide all values by the *smallest one* to get

#"For Na: " (0.9826color(red)(cancel(color(black)("moles"))))/(0.9826color(red)(cancel(color(black)("moles")))) = 1#

#"For B: " (1.989color(red)(cancel(color(black)("moles"))))/(0.9826color(red)(cancel(color(black)("moles")))) = 2.024 ~~2#

#"For O: " (3.481color(red)(cancel(color(black)("moles"))))/(0.9826color(red)(cancel(color(black)("moles")))) = 3.543#

Since you're looking for the smallest **whole number ratio**, multiply all the values by

#"For Na: " 1 xx 2 = 2#

#"For B: " 2 xx 2 = 4#

#"For O: "3.543 xx 2 = 7.09 ~~ 7#

The empirical formula for this compound will thus be

#("Na"_1"B"_2"O"_3.5)_2 = color(green)(|bar(ul(color(white)(a/a)color(black)("Na"_2"B"_4"O"_7)color(white)(a/a)|)))#