Question:Dimethylhydrazine, the
fuel used in the Apollo lunar descentmodule, has a molar mass of
60.10 g/mol. It is made up of carbon,hydrogen, and nitrogen atoms.
The combustion of 2.859g of the fuelin excess oxygen yields 4.190g
of carbon dioxideand 3.428g ofwater. What are the simplest and
molecular formulas fordimethylhydrazine?

The empirical formula of a compound is its simplest formula. The molecular formula is the actual formula of the compound showing the proportions of the atoms.

We can derive the empirical formula of a compound from its molecular formula and vice versa.

Here, we have to work from empirical formula to molecular formula.

Solving

We know that the compound contains C, H and N atoms. We need to first find the masses of these atoms in the compound

For Carbon, we can determine the mass from the amount of carbon dioxide produced:

mass of carbon in compound = [tex]\frac{12}{44}[/tex] x 4.19g = 1.14g

For Hydrogen, we can determine the mass from the amount of water produced:

mass of hydrogen in compound = [tex]\frac{2}{18}[/tex] x 3.428g = 0.38g

To determine the mass of N in the compound:

mass of compound = mass of C + mass of H + mass of N

mass of N = mass of compound - (mass of C + mass of H)

mass of N = 2.859g - (1.14g + 0.38g) = 1.34g

2. we now proceed to find the empirical formula using the process below:

Elements C H N

mass of the

elements 1.14 0.38 1.34

Atomic mass

of elements 12 1 14

Number of

moles 1.14/12 0.38/1 1.34/14

0.095 0.38 0.095

Dividing by

the smallest 0.095/0.095 0.38/0.095 0.095/0.095

1 4 1

The empirical formula of the compound is CH₄N

To obtain the molecular formula, we need to find the number of times the empirical formula must have repeated itself in the original form.

Molar mass of CH₄N = 12 + 4 + 14 = 30g/mol

Ratio = [tex]\frac{molar mass of molecular formula}{molar mass of empirical formula}[/tex] = [tex]\frac{60.1}{30}[/tex] = 2

Molecular formula = 2(CH₄N) = C₂H₈N₂