We are asked to calculate the volume of fuel you should bring.

Calculate heat of combustion fo fuel:

C_{7}H_{16(g)} + 11 O_{2(g) }→ 7 CO_{2(g)} + 8 H_{2}O_{(g)}

$\overline{){\mathbf{\Delta H}}{{\mathbf{\xb0}}}_{{\mathbf{rxn}}}{\mathbf{=}}{\mathbf{\Delta H}}{{\mathbf{\xb0}}}_{\mathbf{f}\mathbf{,}\mathbf{}\mathbf{prod}}{\mathbf{-}}{\mathbf{\Delta H}}{{\mathbf{\xb0}}}_{\mathbf{f}\mathbf{,}\mathbf{}\mathbf{react}}}$

Note that we need to *multiply each ΔH˚ _{f} by the stoichiometric coefficient* since ΔH˚

Also, note that ΔH˚_{f} for elements in their standard state is 0.

$\mathbf{\Delta H}{\mathbf{\xb0}}_{\mathbf{rxn}}\mathbf{=}\mathbf{\Delta H}{\mathbf{\xb0}}_{\mathbf{f}\mathbf{,}\mathbf{}\mathbf{prod}}\mathbf{-}\mathbf{\Delta H}{\mathbf{\xb0}}_{\mathbf{f}\mathbf{,}\mathbf{}\mathbf{react}}\phantom{\rule{0ex}{0ex}}\mathbf{\Delta H}{\mathbf{\xb0}}_{\mathbf{rxn}}\mathbf{=}\mathbf{\left(}\mathbf{7}\mathbf{(}\mathbf{-}\mathbf{393}\mathbf{.}\mathbf{51}\mathbf{}\mathbf{kJ}\mathbf{)}\mathbf{+}\mathbf{8}\mathbf{\right(}\mathbf{-}\mathbf{241}\mathbf{.}\mathbf{82}\mathbf{}\mathbf{kJ}\mathbf{\left)}\mathbf{\right)}\mathbf{-}\mathbf{(}\mathbf{(}\mathbf{\u2013}\mathbf{224}\mathbf{.}\mathbf{4}\mathbf{}\mathbf{kJ}\mathbf{)}\mathbf{+}\mathbf{11}\mathbf{(}\mathbf{0}\mathbf{}\mathbf{kJ}\mathbf{)}\mathbf{)}$

**ΔH° _{rxn} = -4464.73 kJ **

Calculate heat needed to boil per g:

${\mathbf{q}}_{\mathbf{1}}\mathbf{}\mathbf{=}\mathbf{C}\mathbf{\u2206}\mathbf{T}\mathbf{=}(4.184J/g\overline{)\xb0C})(100\overline{)\xb0C}-25\overline{)\xb0C})\mathbf{}\mathbf{=}\mathbf{}\mathbf{313}\mathbf{.}\mathbf{8}\mathbf{}\mathbf{J}\phantom{\rule{0ex}{0ex}}{\mathbf{q}}_{\mathbf{2}}\mathbf{}\mathbf{=}\mathbf{\u2206}{\mathbf{H}}_{\mathbf{vap}}\mathbf{=}\mathbf{2260}\mathbf{}\mathbf{J}\mathbf{/}\mathbf{g}\mathbf{}\phantom{\rule{0ex}{0ex}}{\mathbf{q}}_{\mathbf{total}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{2573}\mathbf{.}\mathbf{8}\mathbf{}\mathbf{}\mathbf{J}\mathbf{/}\mathbf{g}$

When backpacking in the wilderness, hikers often boil water to sterilize it for drinking. Suppose that you are planning a backpacking trip and will need to boil 36 L of water for your group. What volume of fuel should you bring? Assume each of the following: the fuel has an average formula of C_{7}H_{16}; 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 ^{o}C; and the standard enthalpy of formation of C_{7}H_{16} is –224.4 kJ/mol.

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