Car engine combustion question

Question

A car engine it is powered by the burning of octane (C8H18) with oxygen (O2). The combustion reaction forms carbon dioxide (CO2) and water (H2O).



a) write a balanced chemical equation for this combustion reaction.

b) Assuming a reaction starts with 1 mole of octane, which burns at 220°C, and is at a pressure of 1 atm, what volume will the products occupy upon reaction completion?

Answer 1

a) 2 C₈H₁₈(l) + 25 O₂(g) ==> 16 CO₂(g) + 18 H₂O(g) ... balanced equation

b) PV = nRT

P = pressure = 1 atm

V = volume in liters = ?

n = moles of gas = 17 (2 mols C8H18 -> 16 mols CO2(g) + 18 mols H2O(g), so 1 mol -> 8 + 9 = 18 mols gas)

R = gas constant = 0.0821 Latm/Kmol

T = temperature in K = 220ºC + 273 = 493 K

Solving for V we have...

V = nRT/P = (17)(0.0821)(493) / (1)

V = 688 L