Starting with 649.09 g of C8H18, let's calculate the molar mass so we can find the equivalent number of moles of the octane:
(From the Periodic Table)
C: 12.011 g/mol x 8 = 96.088 g.mol
H: 1.008 g/mol x 18 = 18.144 g/mol
96.088 g.mol + 18.144 g/mol = 114.232 g/mol
And now calculating the number of moles: 649.09/114.232 = 5.6822 moles of octane (C8H18).
Using the balanced chemical reaction equation, we see that there is a molar ratio of 16 moles of CO2 produced for every 2 moles of C8H18 reacted. So if there are 5.6822 moles of octane (C8H18) reacted, then there are 5.6822(16/2) = 45.4577 moles of CO2 produced.
The ideal gas law says PV = nRT or, since we are looking for V (volume), then:
V = nRT/P
n = 45.4577 moles
T = 150.89°C + 273.15° = 424.04 K (must use Kelvin in this equation, not ˆC)
P = 1.46 atm
R = 0.08205746 L•atm/K/mol (look this constant up in a book or on Google)
So V = (45.4577)(0.08205746)(424.04)/1.46
V = 1083.38 L