Methane, CH4 is the main component of natural gas which is used for cooking in many homes. The molar heat of combustion of methane is -890kj/mol. A cook wants to boil some water on a gas stove. If the stove burns 5.00g of methane to heat 2575 ml of water, what is the temperature rise of the water?
mols CH4 = grams/molar mass.
Then q produced = 890 kJ/mol x ? mols from above = ?
Then q produced = mass H2O x specific heat H2O x (Tfinal-Tinitial)
To find the temperature rise of the water, we need to calculate the amount of heat energy released by burning 5.00g of methane and then use it to raise the temperature of the water.
First, let's calculate the number of moles of methane burned:
1 mole of methane (CH4) has a molar mass of 16.04 g
So, 5.00g of methane is (5.00 g) / (16.04 g/mol) = 0.311 moles of methane.
Now, we can calculate the amount of heat released during the combustion of methane using its molar heat of combustion:
Heat energy released = Number of moles of methane * Molar heat of combustion
Heat energy released = 0.311 mol * (-890 kJ/mol)
Heat energy released = -276.79 kJ
Next, we need to convert the volume of water from ml to liters because the heat capacity of water is given in J/(g·°C), and we want to have the units consistent in the calculations.
2575 ml = 2.575 L
Now, we need to know the heat capacity of water. It is 4.18 J/(g·°C), meaning that it takes 4.18 Joules of energy to raise the temperature of 1 gram of water by 1 degree Celsius.
Now, let's calculate the temperature rise of the water:
Temperature rise = Heat energy released / (Mass of water * Heat capacity of water)
Temperature rise = -276.79 kJ / (2.575 kg * 4.18 J/(g·°C))
Temperature rise = -276790 J / (2.575 kg * 4.18 J/(g·°C))
Temperature rise = -276790 J / (10.735 g·°C)
Temperature rise = -25745.48 °C / (g·°C)
Temperature rise ≈ -2399.85 °C
Since the temperature rise is negative, it means that the water would actually decrease in temperature rather than rise. However, it is important to note that this result is unrealistic, as such a large negative temperature rise is not physically possible.
It is possible that there was an error in the calculation or the given data. It is also worth considering other factors, such as heat losses to the surroundings, inaccuracy in measuring the mass of methane burned, or inaccuracies in the assumed heat capacity of water.