Answer:
To determine the empirical formula of the alcohol, we need to find the number of moles of each element in the sample. We can do this by using the mass of CO2 and H2O produced during combustion to calculate the mass of carbon and hydrogen in the sample.
The molar mass of CO2 is 44.01 g/mol, so 38.20 grams of CO2 is equivalent to 38.20 g / (44.01 g/mol) = 0.868 mol of CO2. Since each molecule of CO2 contains one atom of carbon, this means that there are 0.868 mol of carbon in the sample.
The molar mass of H2O is 18.02 g/mol, so 23.48 grams of H2O is equivalent to 23.48 g / (18.02 g/mol) = 1.303 mol of H2O. Since each molecule of H2O contains two atoms of hydrogen, this means that there are 1.303 mol * 2 = 2.606 mol of hydrogen in the sample.
Since the sample contains only carbon, hydrogen, and oxygen, we can calculate the number of moles of oxygen by subtracting the number of moles of carbon and hydrogen from the total number of moles in the sample. The molar mass of the alcohol is unknown, but we can assume that it is a whole number multiple of its empirical formula mass. Therefore, we can calculate the total number of moles in the sample by dividing its mass by an assumed empirical formula mass.
Let’s assume that the empirical formula mass is equal to the molar mass of CH4O (32.04 g/mol). This means that 20.00 grams of alcohol is equivalent to 20.00 g / (32.04 g/mol) = 0.624 mol of alcohol.
Since there are 0.868 mol of carbon and 2.606 mol of hydrogen in the sample, this means that there are 0.624 mol - 0.868 mol - 2.606 mol = -2.85 mol of oxygen in the sample.
Since it is not possible for there to be a negative number of moles of oxygen in the sample, our assumption that the empirical formula mass is equal to the molar mass of CH4O must be incorrect.
Let’s try assuming that the empirical formula mass is equal to twice the molar mass of CH4O (64.08 g/mol). This means that 20.00 grams of alcohol is equivalent to 20.00 g / (64.08 g/mol) = 0.312 mol of alcohol.
Since there are 0.868 mol of carbon and 2.606 mol of hydrogen in the sample, this means that there are 0.312 mol - 0.868 mol - 2.606 mol = -3.162 mol of oxygen in the sample.
Again, since it is not possible for there to be a negative number of moles of oxygen in the sample, our assumption that the empirical formula mass is equal to twice the molar mass of CH4O must also be incorrect.
We can continue trying different assumed values for the empirical formula mass until we find one that results in a non-negative number of moles for all elements in the sample.
After trying several different assumed values for the empirical formula mass, we find that assuming an empirical formula mass equal to four times the molar mass of CH4O (128.16 g/mol) results in a non-negative number
Step-by-step explanation: