Question

Analysis of a sample of hydrated salt shows that it contains 4.86 g Mg, 6.20 g P, 11.20 g O, and 5.40 g H2O. What is the formula of the hydrated salt?

Answer 1

Mg₂P₂O₇ · 3 H₂O

Step-by-step explanation:

(Step 1)

First, you need to convert each mass to moles via the molar masses of each element/compound.

Molar Mass (Mg): 24.305 g/mol

4.86 grams Mg 1 mole
------------------------ x ------------------------ = 0.200 moles Mg
24.305 grams

Molar Mass (P): 30.974 g/mol

6.20 grams P 1 mole
--------------------- x ------------------------ = 0.200 moles P
30.974 grams

Molar Mass (O): 15.998 g/mol

11.20 grams O 1 mole
----------------------- x ----------------------- = 0.700 moles O
15.998 grams

Molar Mass (H₂O): 2(1.008 g/mol) + 15.998 g/mol

Molar Mass (H₂O): 18.014 g/mol

5.40 grams H₂O 1 mole
-------------------------- x ----------------------- = 0.300 moles H₂O
18.014 grams

(Step 2)

To find the amount of each element/compound in the formula, you need to divide each molar value by the smallest molar value. This allows you to determine the accurate molar ratio the hydrated salt should have. In this case, 0.200 moles is the smallest value.

0.200 moles Mg / 0.200 = 1 mole Mg

0.200 moles P / 0.200 = 1 mole P

0.700 moles O / 0.200 = 3.5 moles O

0.300 moles H₂O / 0.200 = 1.5 moles H₂O

There can only be whole number amounts of each element/compound in the formula. Therefore, you need to multiply each amount by 2.

1 mole Mg x 2 = 2 moles Mg

1 mole P x 2 = 2 moles P

3.5 moles O x 2 = 7 moles O

1.5 moles H₂O x 2 = 3 moles H₂O

(Step 3)

Now that we know the amount of each element/compound, we can build the formula. The amount of each element is represented by subscripts and the amount of each compound (H₂O) is represented by coefficients.

Mg₂P₂O₇ · 3 H₂O