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 35 L of water for your group. What volume of fuel should you bring? Assume that the fuel has an average formula of C7 H16 , 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 C7 H 16 is -224.4 kJ>mol.

2.104 L fuel

Explanation:

Given that:

Volume of water = 35 L = 35 × 10³ mL

initial temperature of water = 25.0 ° C

The amount of heat needed to boil water at this temperature can be calculated by using the formula:

where

specific heat   of water c= 4.18 J/g° C

Also; Assume that the fuel has an average formula of C7 H16 and 15% of the heat generated from combustion goes to heat the water;

thus the heat of combustion can be determined via the expression

For heptane; the equation for its combustion reaction can be written as:

The standard enthalpies of the  products and the reactants are:

Therefore; the standard enthalpy for this combustion reaction is:

This simply implies that the amount of heat released from 1 mol of C7H16 = 4466.1 kJ

However the number of moles of fuel required to burn heat released is:

Since number of moles = mass/molar mass

The  mass of the fuel is:

Given that the density of the fuel is = 0.78 g/mL

and we know that :

density = mass/volume

therefore making volume the subject of the formula in order to determine the volume of the fuel ; we have

volume of the fuel = mass of the fuel / density of the fuel

volume of the fuel =

volume of the fuel  = 2.104 L fuel

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