Answer:
ΔH o rxn = -2.23 x 10⁶ kJ
Explanation:
The reaction of combustion for isooctane is
C₈H₁₈ (l) + 9/2 O₂ (g) ----------------------- 8 CO₂ (g) + 9 H₂O (g)
with an enthalpy change of -5.44 x 10³ kJ/mol
So what we need is to calculate the number of moles that are the 17.9 gal to solve this question.
1 gal = 3.785 L ∴ 17.9 gal x 3.785 L/ gal = 67.75 L = 67.5 x 1000 mL/L
= 6.78 x 10³ mL
d= m/ v ∴ m= d x v = 0.692 g/mL x 6.78 x 10⁴ g/1000 mL = 4.69 x 10⁴ g
Molecular Weight Isooctane is equal to 114.22 g/mol therefore moles
n = 4.69 x 10 ⁴ g / 114.22 g/mol = 4.10 x 10² mol
and the heat of combustion for this number of moles will be given by
-5.44 x 10³ kJ/mol x 4.10 x 10² mol = -2.23 x 10⁶ kJ
-2.24 × 10^6 KJ is evolved when 17.9 gal of isooctane is burnt.
We have to convert the volume to millilitres before we can solve;
Since 1 gal = 3.8 L
17.9 gal = 17.9 gal × 3.8 L/1 gal
= 68.02 L or 68020 mL
The mass of Isooctane is obtained from its density as follows;
Density = mass/volume
Mass = Density × volume
Mass = 0.692 g/mL × 68020 mL
Mass = 47070 g
Number of moles of isooctane is obtained from;
Number of moles = mass/molar mass
Molar mass of isooctane = 114 g/mol
Number of moles = 47070 g/114 g/mol = 413 moles
If 1 mole of isooctane produces −5.44 × 103 kJ of heat
413 moles of isooctane yields 413 moles × −5.44 × 103 kJ / 1 mole
= -2.24 × 10^6 KJ
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