Washing soda is a hydrate of sodium carbonate. Elemental analysis of a sample of washing soda gave 4.20% C and 7.05% H. What is the formula for washing soda?

Na₂CO₃ · 10H₂O

Explanation:

The formula for sodium carbonate hydrate is:

Na₂CO₃ · xH₂O

The unknown "x" is the number of water molecules contained in the hydrate.

To find "x" we have to use the hydrogen percentage in the sample, 7.05 % H.

First we calculate the molecular weight of Na₂CO₃ · xH₂O:

molecular weight of Na₂CO₃ · xH₂O = 23 * 2 + 12 + 16 * 3 + 18x

molecular weight of Na₂CO₃ · xH₂O = 106 + 18x g/mole

Now we devise the fallowing reasoning tanking in account 1 mole of Na₂CO₃ · xH₂O:

if in 106 + 18x grams of Na₂CO₃ · xH₂O we have 2x grams of hydrogen

then in 100 grams of Na₂CO₃ · xH₂O we have 7.05 grams of hydrogen

106 + 18x = (100 * 2x) / 7.05

106 + 18x = 28.4x

106 = 28.4x - 18x

106 = 10.4x

x = 106 / 10.4

x = 10.2 ≈ 10

The formula for the washing soda is Na₂CO₃ · 10H₂O.