Step-by-step explanation:
To find the empirical formula of a compound, you need to determine the ratio of the different elements in the compound. In this case, you have the masses of carbon (from carbon dioxide) and hydrogen (from water) that were formed when methyl salicylate was burned. Here's how you can calculate the empirical formula:
1. Calculate the moles of carbon, hydrogen, and oxygen in the given compounds:
- Moles of carbon = mass of carbon dioxide / molar mass of carbon dioxide
- Moles of hydrogen = mass of water / molar mass of water
- Moles of oxygen = moles of carbon + moles of hydrogen (because the compound's molecular formula accounts for the rest of the mass)
2. Find the smallest ratio of moles among carbon, hydrogen, and oxygen.
3. Divide the moles of each element by the smallest number of moles to get the simple ratio.
4. Use the ratio to write the empirical formula.
Let's calculate it step by step:
1. Calculate moles:
- Moles of carbon = 12.24 g / 44.01 g/mol (molar mass of CO2) ≈ 0.278 mol
- Moles of hydrogen = 2.522 g / 18.015 g/mol (molar mass of H2O) ≈ 0.140 mol
- Moles of oxygen = 0.278 mol + 0.140 mol ≈ 0.418 mol
2. Find the smallest ratio of moles, which is 0.140 mol (moles of hydrogen).
3. Divide moles by the smallest ratio:
- Carbon: 0.278 mol / 0.140 mol ≈ 1.986
- Hydrogen: 0.140 mol / 0.140 mol = 1
- Oxygen: 0.418 mol / 0.140 mol ≈ 2.986
4. Write the empirical formula using the ratios:
- Carbon: 2 (approximately)
- Hydrogen: 1
- Oxygen: 3 (approximately)
So, the empirical formula is approximately **C2H1O3**. However, empirical formulas are usually written with the smallest whole-number ratios, so you can multiply all the subscripts by 2 to get the simplest whole-number ratio:
Empirical formula: **C4H2O6**
Please note that the molecular formula of methyl salicylate is **C8H8O3**, but the empirical formula represents the simplest whole-number ratio of the elements in the compound.