# If 1.000g of tin metal reacts with 0.640g of fluorine gas, what is the empirical formula of the product?

Aug 7, 2016

${\text{SnF}}_{4}$

#### Explanation:

The empirical formula of a given compound tells you the smallest whole number ratio in which its constituent elements combine to form said compound.

In your case, an unknown compound is said to contain tin, $\text{Sn}$, and fluorine, $\text{F}$. This compound is synthesized by reacting tin metal with fluorine gas, ${\text{F}}_{2}$.

It's important to realize that fluorine gas exists as diatomic molecules, and so its molar mass will be twice as big as the molar mass of fluorine, $\text{F}$.

Grab a periodic table and look for tin and fluorine. Their molar masses are

M_("M Sn") = "118.72 g mol"^(-1)

M_("M F") = "18.998 g mol"^(-1)

The molar mass of fluorine gas will thus be

${M}_{\text{M F"_ 2) = 2 xx M_("M F}}$

M_("M F"_ 2) = 2 xx "18.998 g mol"^(-1) = "37.996 g mol"^(-1)

This means that your sample of fluorine gas contained

0.640 color(red)(cancel(color(black)("g"))) * "1 mole F"_2/(37.996color(red)(cancel(color(black)("g")))) = "0.016844 moles F"_2

Since every molecule of ${\text{F}}_{2}$ contains $2$ atoms of $\text{F}$

you know that your unknown compound will contain

0.016844 color(red)(cancel(color(black)("moles F"_2))) * "2 moles F"/(1color(red)(cancel(color(black)("mole F"_2)))) = "0.033688 moles F"

The sample will also contain

1.000 color(red)(cancel(color(black)("g"))) * "1 mole Sn"/(118.72 color(red)(cancel(color(black)("g")))) = "0.0084232 moles Sn"

To find the mole ratio that exists between the two elements in the unknown compound, divide both values by the smallest one

"For Sn: " (0.0084232 color(red)(cancel(color(black)("moles"))))/(0.0084232color(red)(cancel(color(black)("moles")))) = 1

"For F: " (0.033688color(red)(cancel(color(black)("moles"))))/(0.0084232color(red)(cancel(color(black)("moles")))) = 3.999 ~~ 4

Since $1 : 4$ is already the smallest whole number ratio that can exist here, you can say that this compound has the empirical formula

"Sn"_1"F"_4 implies color(green)(|bar(ul(color(white)(a/a)color(black)("SnF"_4)color(white)(a/a)|)))