Answer:
Na₂S₃O₇H₇.
Step-by-step explanation:
To find the empirical formula of a substance based on its percentage composition by mass, you need to determine the ratio of the elements in the compound. Given that the substance contains sodium (Na), sulfur (S), oxygen (O), and water of crystallization, you can follow these steps:
Convert the percentages to grams:
Sodium (Na) = 18.2% of the total mass
Sulfur (S) = 12.7% of the total mass
Oxygen (O) = 19.1% of the total mass
Water of crystallization = 50% of the total mass
Assume you have 100 grams of the substance for simplicity. Then:
Sodium (Na) = 18.2 grams
Sulfur (S) = 12.7 grams
Oxygen (O) = 19.1 grams
Water of crystallization = 50 grams
Determine the moles of each element:
Moles of Na = 18.2 g / 23.0 g/mol (molar mass of Na) = 0.791 moles
Moles of S = 12.7 g / 32.1 g/mol (molar mass of S) = 0.395 moles
Moles of O = 19.1 g / 16.0 g/mol (molar mass of O) = 1.194 moles
Moles of H (from water) = 50 g / 18.0 g/mol (molar mass of H2O) = 2.778 moles
Find the simplest whole number ratio of moles:
Divide each of the moles by the smallest number of moles (which is 0.395 moles in this case):
Na: 0.791 moles / 0.395 moles = 2
S: 0.395 moles / 0.395 moles = 1
O: 1.194 moles / 0.395 moles = 3
H: 2.778 moles / 0.395 moles = 7.02 (approximately 7)
Write the empirical formula using the whole number ratios:
The empirical formula for the substance is Na₂S₃O₇H₇. However, empirical formulas are usually written with the simplest whole-number ratios, so you should simplify it further:
Divide all the subscripts by the greatest common factor, which is 1 in this case:
The simplified empirical formula is Na₂S₃O₇H₇.