A hungry backpacker needs to boil 150 mL of water to prepare a cup of Ramen Noodles. The filtered river water is at a temperature of 14.2 oC. The pressure is 760 mm Hg and he wants to eat the chicken flavored noodles. How many mL of his liquid butane camping fuel will he use to prepare his meal?
Not sure where to start? Then you have a problem. A problem involves organizing information, using formulas you know to develop a strategy, and computing small steps in developing an overall solution.
Reaction:
C4H8 (g) + 6 O2 (g) „³ 4 CO2 (g) + 4 H2O (g)
Physical Data of Butane
Density: d = 2.48 g/cm3
Heat of vaporization of liquid butane: ƒ´Hvap = 22.44 kJ/mol
Standard Enthalpy of Formation of gaseous butane: Hfo = ¡V125.6 kJ/mol
To solve this problem, we need to calculate the amount of liquid butane camping fuel required to boil 150 mL of water.
Step 1: Calculate the amount of heat needed to evaporate the water
The heat needed to evaporate water can be calculated using the formula:
q = m x ΔHvap
Where:
q = heat needed (in joules)
m = mass of water (in grams)
ΔHvap = heat of vaporization of water (in J/g)
In this case, we know the volume of water (150 mL) and the density of water (1 g/mL), so we can calculate the mass of water as follows:
m = volume x density
m = 150 mL x 1 g/mL
m = 150 g
The heat of vaporization of water is approximately 40.7 kJ/mol or 40,700 J/g.
q = 150 g x 40,700 J/g
q = 6,105,000 J
Step 2: Convert the heat needed to mol of butane
To use the reaction given, we need to convert the heat needed to moles of butane. We can use the molar mass of water to convert the mass of water to moles.
The molar mass of water (H2O) is approximately 18 g/mol.
moles of water = mass of water / molar mass of water
moles of water = 150 g / 18 g/mol
moles of water = 8.33 mol
According to the reaction equation, 6 moles of O2 react with 1 mole of butane to produce 4 moles of H2O. So we can set up a ratio to determine the moles of butane needed.
moles of butane = 1 mole / 6 moles of O2 x 4 moles of H2O x moles of water
moles of butane = 1/6 x 4 x 8.33 mol
moles of butane = 55.5 mol
Step 3: Convert moles of butane to volume of liquid butane camping fuel
To convert the moles of butane to volume, we can use the molar volume of butane at standard temperature and pressure (STP). The molar volume at STP is 22.4 L/mol.
volume of butane = moles of butane x molar volume
volume of butane = 55.5 mol x 22.4 L/mol
volume of butane = 1242 L
However, we need to convert liters to milliliters because the question asks for the volume in mL. Since there are 1000 mL in 1 L, we can multiply the volume by 1000.
volume of butane = 1242 L x 1000 mL/L
volume of butane = 1,242,000 mL
Therefore, the backpacker will use approximately 1,242,000 mL of liquid butane camping fuel to prepare his meal.
It is important to note that safety precautions should be taken when handling any flammable substances such as liquid butane camping fuel. This calculation is for educational purposes only.