We can start by determining the number of moles of carbon and hydrogen in the given mass of cumene (47.6 mg).
Step 1: Calculate the number of moles of CO2 and H2O
From the combustion reaction, we know that 47.6 mg of cumene produces 42.8 mg of water.
The molar mass of CO2 is 44.01 g/mol, and the molar mass of H2O is 18.02 g/mol.
Number of moles of CO2 = (42.8 mg) / (44.01 g/mol) = 0.000972 mol
Number of moles of H2O = (47.6 mg) / (18.02 g/mol) = 0.00264 mol
Step 2: Determine the moles of C and H
Since each molecule of CO2 contains one carbon atom, the number of moles of carbon is equal to the number of moles of CO2.
Moles of C = Number of moles of CO2 = 0.000972 mol
Each molecule of H2O contains two hydrogen atoms, so the number of moles of hydrogen is twice the number of moles of H2O.
Moles of H = 2 x Number of moles of H2O = 2 x 0.00264 mol = 0.00528 mol
Step 3: Find the simplest whole number ratio
To find the simplest whole number ratio, we need to divide both the number of carbon and hydrogen moles by the smallest number of moles. In this case, the smallest number of moles is 0.000972 mol (moles of carbon).
Moles of C / 0.000972 mol = 0.000972 / 0.000972 = 1
Moles of H / 0.000972 mol = 0.00528 / 0.000972 = 5.5
Step 4: Write the empirical formula
The empirical formula is written using the whole-number ratio obtained in Step 3.
C:H = 1:5.5
Since empirical formulas are always written in the simplest whole-number ratio, we need to multiply the ratio by 2 to obtain the most straightforward formula.
C:H = 2:11
Therefore, the empirical formula for cumene is C2H11.
