Question

Using the Mole: Empirical Formulas, Molecular Formulas, % Composition5. Potassium persulfate was used in photography to remove the last traces of hypo from photographic papers and plates, A 0,8162 g sample was found to contain 0,2361 g of potassium, 0.1936 g of sulfur, and the rest was oxygen. The formula weight of this compound was measured to be 270. What are the empirical and molecular formulas of this compound?

Answer 1

Molecular formula = KSO4.

Empirical formula = K2S2O4.

Step-by-step explanation:

What is given?

Mass of K (potassium) = 0.2361 g.

Mass of S (sulfur) = 0.1936 g.

Mass of O (oxygen) = 0.8162 g - 0.2361 g - 0.1936 g = 0.3865 g.

Molar mass of K = 39.1 g/mol.

Molar mass of S = 32 g/mol.

Molar mass of O = 16 g/mol.

Weight of compound = 270 g/mol.

Step-by-step solution:

Remember that empirical formulas show the simplest whole-number ratio of atoms in a compound, and molecular formulas show the number of each type of atom in a molecule. So first, let's see what would be the molecular formula:

Let's find the number of moles of each element using its molar mass:

`\begin{gathered} 0.2361\text{ g K}\cdot\frac{1\text{ mol K}}{39.1\text{ g K}}=0.006038\text{ moles K,} \\ 0.1936\text{ g S}\cdot\frac{1\text{ mol S}}{32\text{g S}}=0.006050\text{ moles S,} \\ 0.3865\text{ g O}\cdot\frac{1\text{ mol O}}{16\text{ g O}}=0.02416\text{ moles O.} \end{gathered}`

The next step is to divide each number of moles obtained by the least number of moles, in this case, the least number is 0.006038:

`\begin{gathered} 0.006038\text{ moles K/0.006038=1 mol K,} \\ 0.006050\text{ moles S/0.006038 =}1.001\text{ moles S}\approx1\text{ mol S,} \\ 0.02416\text{ moles O/0.006038=4.001 moles O}\approx\text{4 moles O.} \end{gathered}`

Our molecular formula would contain 1 mol of K, 1 mol of S, and 4 moles of O, so it would be KSO4.

But remember that we need to find the empirical formula too, based on the molecular weight. In the statement, they're telling us that the molecular weight is 270 g/mol, but the molecular weight of KSO4 is 135 g/mol (you can calculate it using the given molar masses and by doing an algebraic sum). So, to obtain the empirical formula with 270 g/mol as molecular weight, we have to multiply by two each number of moles of the compound (135 g/mol * 2 = 270 g/mol):

`\begin{gathered} 1\text{ mol K}\cdot2=2\text{ moles K,} \\ 1\text{ mol S}\cdot2=2\text{ moles S,} \\ 4\text{ moles O }\cdot2=8\text{ moles O.} \end{gathered}`

So, you can realize that K2S2O4 would be the empirical formula because its molecular weight would be 270 g/mol.

Molecular formula = KSO4.

Empirical formula = K2S2O4.