An average hot water tank will hold 300.0 L of water needs to be kept at 65.0OC in order to kill any bacteria in the water. If you are filling a new tank with water at a starting temperature of 12.5OC, what mass of natural gas (methane) must be burned in a complete combustion reaction in order bring your tank up to the correct temperature?
How much heat do you need?Assuming density of H2O is 1.0 g/mL, then That's
q = mass H2O x specific heat H2O x (Tfinal-Tinitial)
q = 300,000 g 4.194 J/g*C x (65.00 - 12.50) = ? J
Then CH4 + 2O2 ==> CO2 + 2H2O
Look up the heat of combustion for CH4. It will be listed in J/mol or kJ/mol or something like that.
Then heat combustion x (q from above/16) = CH4 needed
Keep the units straight. My guess is that your question has specific heat and heat of combustion listed and it would have been nice for you to include them in the post. I don't remember all of those numbers. Post your work if you get stuck.
Thank you DrBob222, really appreciate it!
I apparently we have to use formation to find the combustion of methane
heat of combustion CH4 on Google is 890.6 kJ/mol = 890,6 kJ/16 g
To calculate the mass of natural gas (methane) required to bring the water in the tank to the desired temperature, we need to consider the specific heat capacity of water, the temperature change, and the energy released during the combustion of methane.
1. Calculate the temperature change:
The initial temperature of the water is 12.5OC, and it needs to be heated to 65.0OC. So, the temperature change is:
ΔT = final temperature - initial temperature
ΔT = 65.0OC - 12.5OC
2. Calculate the energy required:
The energy required to heat the water can be calculated using the specific heat capacity (c) of water, which is approximately 4.18 J/g·°C.
The formula to calculate energy is:
Energy (Q) = mass (m) * specific heat capacity (c) * temperature change (ΔT)
3. Convert liters of water to grams:
The volume of water in the tank is given in liters, but we need to convert it to grams since the specific heat capacity is given in terms of grams. The conversion factor is approximately 1 gram = 1 milliliter.
So, the mass of water (m) in grams can be calculated as:
mass (m) = volume (V) * density (ρ) = volume (V) * 1 g/mL
Now that we have the necessary information, let's calculate the mass of natural gas required:
1. Calculate the temperature change:
ΔT = 65.0OC - 12.5OC = 52.5OC
2. Convert liters of water to grams:
mass (m) = 300.0 L * 1 g/mL = 300.0 g
3. Calculate the energy:
Energy (Q) = mass (m) * specific heat capacity (c) * temperature change (ΔT)
Q = 300.0 g * 4.18 J/g·°C * 52.5OC
4. Convert energy to joules:
Since the energy released during the combustion of methane is typically given in kilojoules (kJ), we need to convert the energy from joules to kilojoules by dividing it by 1000:
Energy (Q) = (300.0 g * 4.18 J/g·°C * 52.5OC) / 1000 kJ
5. Calculate the energy released during methane combustion:
The combustion of methane releases approximately 55.5 kJ of energy per gram.
So, the mass of methane required is:
mass of methane = Energy (Q) / 55.5 kJ/g
Now you can substitute the values into the equations and calculate the mass of methane required to bring your tank up to the correct temperature.