To determine the empirical formula of oil of wintergreen (methyl salicylate), you need to follow these steps:
Step 1: Convert the given masses to moles.
To do this, use the molar masses of the compounds involved. The molar masses are as follows:
Molar mass of CO2 = 44.01 g/mol
Molar mass of H2O = 18.02 g/mol
Calculate the number of moles of CO2:
moles of CO2 = mass of CO2 / molar mass of CO2
moles of CO2 = 12.24 g / 44.01 g/mol
Calculate the number of moles of H2O:
moles of H2O = mass of H2O / molar mass of H2O
moles of H2O = 2.522 g / 18.02 g/mol
Step 2: Find the molar ratios.
Divide both moles of CO2 and H2O by the smaller of the two values to obtain a whole number ratio.
moles of CO2 / smaller value = 12.24 g / 44.01 g/mol / (smaller value / smaller value)
moles of CO2 / smaller value = 12.24 g / 44.01 g/mol / 0.140476
moles of H2O / smaller value = 2.522 g / 18.02 g/mol / (smaller value / smaller value)
moles of H2O / smaller value = 2.522 g / 18.02 g/mol / 0.140476
The smaller value is 0.140476, so dividing both by this value gives:
moles of CO2 = 87.1
moles of H2O = 18.0
Step 3: Convert the moles to the smallest whole-number ratio.
Divide both values by the smallest one to obtain the simplest whole-number ratio.
moles of CO2 / 18 = 87.1 / 18 ≈ 4.84 ≈ 5
moles of H2O / 18 = 18.0 / 18 = 1
The ratio becomes:
CO2: 5
H2O: 1
Step 4: Write the empirical formula.
Finally, write the empirical formula using the ratios:
C5H2O
However, to simplify the formula further, we can multiply all the subscripts by 2:
C5H2O × 2 = C10H4O2
Therefore, the empirical formula for oil of wintergreen (methyl salicylate) is C10H4O2.