Answer to Question #158987 in Chemistry for pip

Question

100 grams of water was produced from the complete combustion of naphthalene (C10H8).

Calculate for the initial volume of the fuel in liters. Assume that it is stored in a container

under a pressure of 1 atm and a temperature of 25°C.

Answer 1

Solution:

Fuels such as petroleum and coal contain naphthalene.

The balanced chemical equation:

C₁₀H₈ + 12O₂ → 10CO₂ + 4H₂O

According to the equatione above: n(C₁₀H₈) = n(H₂O)/4

Moles of H₂O = Mass of H₂O / Molar mass of H₂O

The molar mass of H₂O is 18.015 g mol^-1.

Hence,

n(H₂O) = 100 g / 18.015 g mol^-1 = 5.55 mol

n(C₁₀H₈) = n(H₂O) / 4 = 5.55 mol / 4 = 1.3875 mol

n(C₁₀H₈) = 1.3875 mol

The Ideal Gas equation can be used:

PV = nRT

P = 1 atm

V = unknown

n = 1.3875 mol

R = 0.082 L atm K^-1 mol^-1

T = 25°C + 273.15 = 298.15 K

Thus,

V(fuel) = nRT/P

V(fuel) = (1.3875 mol × 0.082 L atm K^-1 mol^-1 × 298.15 K) / (1 atm) = 33.922 L = 33.9 L

V(fuel) = 33.9 L

Answer: The initial volume of the fuel is 33.9 liters.