The empirical formula of trioxane, derived from combustion data, is C₃H₆O₃. Analysis of produced water (H₂O) and carbon dioxide (CO₂) yields a ratio of moles, resulting in the empirical formula representing the simplest whole-number ratio of carbon, hydrogen, and oxygen.
To determine the empirical formula of trioxane, we can follow these steps:
1. Find the moles of carbon and hydrogen in the given compounds (CO2 and H2O).
2. Determine the ratio of moles of carbon to moles of hydrogen.
3. Use the ratio to write the empirical formula.
Let's go through the calculations:
Step 1: Find the moles of carbon and hydrogen
The molar mass of water (H2O) is approximately 18.015 g/mol, and the molar mass of carbon dioxide (CO2) is approximately 44.01 g/mol.
Moles of H2O = Mass of H2O / Molar mass of H2O
= 10.477 g / 18.015 g/mol
≈ 0.582 moles of H2O
Moles of CO2 = Mass of CO2 / Molar mass of CO2
= 25.612 g / 44.01 g/mol
≈ 0.582 moles of CO2
Now, we need to find the moles of carbon and hydrogen in trioxane. Since trioxane is composed of only C, H, and O, we can set up equations based on the combustion reaction:
C₃H₆O₃ + aO₂ → bCO₂ + cH₂O
From the given data, we know that:
b = moles of CO2 = 0.582
c = moles of H2O = 0.582
Now, we need to find a. The molecular formula of trioxane gives us the sum of the moles of carbon and hydrogen:
a = b/3 + c/2
= 0.582/3 + 0.582/2
= 0.194 + 0.291
= 0.485
Step 3: Write the empirical formula
Now that we know the ratio of carbon to hydrogen is 0.485, we can write the empirical formula:
Empirical formula = C₃H₆O₃ (Multiply by 2 to get whole numbers: C₁.₅H₃O₃)
So, the empirical formula for trioxane is C₁.₅H₃O₃, but to express it with whole numbers, we multiply by 2 to get C₃H₆O₃.