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What volume of fuel should you bring? Assume each of the following: the fuel has an average formula of C7H16; 15% of the heat generated from combustion goes to heat the water (the rest is lost to the surroundings); the density of the fuel is 0.78 g/mL; the initial temperature of the water is 25.0 ∘C; and the standard enthalpy of formation of C7H16 is -224.4 kJ/mol.

Answer :

davidlcastiblanco

Answer:

The volume in L is V=2.2L

Explanation:

Supposing the water will be boiled at no great elevation, so its boiling point will be 100°C:

[tex](37 L)*(1000 \frac{g}{L})=37000L[/tex]

[tex]37000L*(4.184 \frac{J}{g*C})*(100 C - 25.0 C)=11610600 J[/tex]

[tex]\frac{11610600}{0.15}=77404000 J[/tex]

7 C(s) + 8 H2(g) → C7H16(l), ΔH = -224.4 kJ/mol C7H16

C(s) + O2(g) → CO2(g), ΔH = -393.5 kJ/mol

H2(g) + ½ O2(g) → H2O(g), ΔH = -241.82  kJ/mol

Rearranging as necessary:

C7H16(l) → 7 C(s) + 8 H2(g), ΔH = +224.4 kJ

7 C(s) + 7 O2(g) → 7 CO2(g), ΔH = -2754.5 kJ

8 H2(g) + 4 O2(g) → 8 H2O(g), ΔH =  -1934.56 kJ

Add up all three equations:

C7H16(l) + 11 O2(g) → 7 CO2(g) +  8 H2O(g), ΔH = -4464.66 kJ

V= [tex]\frac{77404kJ}{4464.66\frac{kJ}{mol}}*\frac{100.2019\frac{gC7H16}{mol}}{0.79\frac{g}{mL}} = 2227 mL = 2.2 L fuel[/tex]

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