Suppose that you are planning a backpacking trip and will need to boil 40 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 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 0.78g/mL; the initial temperature of the water is 25.0C; and the standard enthalpy of formation of C7H16 is -224.4kJ/mol. Express your answer using two significant figures.

To determine the volume of fuel you need to bring, you first need to calculate the amount of heat required to boil the water. Then, you can calculate the amount of fuel required to generate that amount of heat.

Step 1: Calculate the amount of heat needed to boil the water.

The heat required to raise the temperature of water from its initial temperature to its boiling point is given by the equation:

Q = m * C * ΔT,

Where:
- Q is the heat (in joules),
- m is the mass of water (in grams),
- C is the specific heat capacity of water (4.18 J/g°C), and
- ΔT is the change in temperature (in degrees Celsius).

First, convert the volume of water to mass using the density:

m = V * density.

m = 40 L * 1000 mL/L * 0.78 g/mL = 31,200 g

Next, calculate the change in temperature:

ΔT = 100°C - 25.0°C = 75°C

Now, calculate the heat required:

Q = 31,200 g * 4.18 J/g°C * 75°C = 9,296,800 J.

Step 2: Calculate the heat generated by the fuel.

Now, you need to calculate the amount of heat generated by burning the fuel. Combustion reactions typically release the heat equal to the standard enthalpy of formation (ΔH°f) of the fuel compound.

Given that the standard enthalpy of formation of C7H16 is -224.4 kJ/mol, you need to convert this to joules/mol:

ΔH°f = -224.4 kJ/mol * 1000 J/kJ = -224,400 J/mol.

However, you need to account for the fact that only 15% of the heat generated from combustion goes to heat the water, so:

Heat generated by the fuel = Q / 0.15 = 9,296,800 J / 0.15 = 61,978,667 J.

Step 3: Calculate the amount of fuel needed.

Finally, calculate the amount of fuel needed by converting the heat generated by the fuel to moles of C7H16:

moles of C7H16 = heat generated by the fuel / ΔH°f.

moles of C7H16 = 61,978,667 J / -224,400 J/mol = -276.1 mol.

Since the molar mass of C7H16 is approximately 100 g/mol, you can convert moles of C7H16 to grams of fuel:

grams of fuel = moles of C7H16 * molar mass.

grams of fuel = -276.1 mol * 100 g/mol = -27,610 g.

Note that the negative sign indicates that the amount is actually the amount of fuel required to generate the given heat, not the amount of fuel that needs to be brought.

However, you are asked to express the answer with two significant figures. Therefore, the volume of fuel you need to bring is approximately 2.8 * 10^4 g or 28,000 g.