Final answer:
To find the molecular formula for dichloroethane, calculate the moles of carbon, hydrogen, and chlorine. The empirical formula is CH2Cl, and after determining the empirical formula mass, the molar mass reveals that the molecule contains twice as many of each atom, resulting in the molecular formula C2H4Cl2.
Step-by-step explanation:
To find the molecular formula of dichloroethane, analyze it by using the percentages of carbon, hydrogen, and chlorine given. You also know the molar mass of the compound is 99 g/mol.
Let's start with 100 grams of the compound to make the calculations straightforward. According to the percentage composition by mass, we have 24.3 grams of carbon, 4.1 grams of hydrogen, and the rest is chlorine. Knowing the atomic masses of each (C = 12 g/mol, H = 1 g/mol, Cl = 35.5 g/mol), let's compute the moles of each element in the sample:
- Carbon: 24.3 g ÷ 12 g/mol = 2.025 moles
- Hydrogen: 4.1 g ÷ 1 g/mol = 4.1 moles
To find the moles of chlorine, subtract the mass of carbon and hydrogen from the total 100 grams:
Mass of chlorine = 100 g - (24.3 g + 4.1 g) = 71.6 g
Now, to find moles of chlorine:
- Chlorine: 71.6 g ÷ 35.5 g/mol = 2.017 moles
To determine the empirical formula, divide the moles of each element by the smallest number of moles calculated:
Empirical formula = CH2Cl
Next, we determine the empirical formula mass:
Empirical formula mass = (12 g/mol * 1) + (1 g/mol * 2) + (35.5 g/mol * 1) = 49.5 g/mol
The ratio of the molar mass to the empirical formula mass is:
99 g/mol ÷ 49.5 g/mol = 2
Multiply the subscripts in the empirical formula by this ratio to get the molecular formula:
Molecular formula = C2H4Cl2
Therefore, the molecular formula for dichloroethane is option (a) C2H4Cl2.