Question

Question: A gaseous hydrocarbon, in a volume of 25.4 L at 400 K and a pressure of 3.40 atm, reacts in an excess of oxygen to give 47.4 g H₂O and 231.6 g CO₂. Determine the molecular formula of the hydrocarbon.

Short answer

The molecular formula of gaseous hydrogen is C₂H₂.

Step-by-step solution

Given data

According to the question,

Volume = 25.4 L

Temperature = 400 K

Pressure = 3.40 atm

Concept

According to the ideal gas equation,

$\mathrm{PV}=\mathrm{nRT}$

Where, P = pressure

V = volume

n = number of density

R = gas constant

T = temperature

Step 3:

Moles of gaseous hydrocarbon,

$$\begin{gathered} \mathrm{PV}=\mathrm{nRT} \\ \mathrm{n}=\frac{\mathrm{PV}}{\mathrm{RT}} \\ =\frac{3.40\times 25.4}{0.0821\times 400} \\ =2.63\mathrm{mol} \end{gathered}$$

Moles of carbon atoms= moles of CO₂=$\frac{{\mathrm{massofCO}}_2}{{\mathrm{molarmassofCO}}_2}=\frac{231.6}{44}=5.26\mathrm{mol}$

Moles of H atoms = 2*Moles of H₂O=$2\times \frac{{\mathrm{massofH}}_2\mathrm{O}}{{\mathrm{molarmassofH}}_2\mathrm{O}}=2\times \frac{47.4}{18}=5.26\mathrm{mol}$

Gaseous hydrocarbon C atom H atom

Ratio of moles 2.63 5.26 5.26

1 : 2 : 2

So, the molecular formula of gaseous hydrogen is C₂H₂.