An average hot water tank will hold 300.0 L of water needs to be kept at 65.0C in order to kill any bacteria in the water. If you are filling a new tank with water at a starting temperature of 12.5C, what mass of natural gas
(methane) must be burned in a complete combustion reaction in order to bring your tank up to the correct temperature?
I think I mostly need help with identifying the equation needed to solve this but if anyone is able to fully explain it, it would be greatly appreciated
You have three problems here.
1. First you need to determine how much heat is needed to raise the temperature of 300.0 L of water at 12.5 C to a final temperature of 65 C.
2. Then you need to write the equation for the combustion of methane and calculate how much heat 1 gram of methane (or some other quantity) produces. Then you can calculate how many grams of methane are needed to produce what you need in #1.
3. You DON'T have the heat produced from the combustion of methane. I don't know if you didn't have that in the problem or if you just didn't type it in. I assume also that the specific heat of water is given or you know it and that you know the density of water at that temperature is 1.00 g/mL.
#1. q = heat needed = mass H2O x specific heat H2O x (Tfinal - Tinitial)
q = 300,000 g x 4.184 J/g*C x (65.0 - 12.5) = approximately 66,000,000 J or 66,000 kJ. You should confirm this.
#2. CH4 + 2O2 ==> CO2 + 2H2O
I looked up the heat of combustion for CH4 on th web and found 889 kJ/mol CH4. You should use the value in your text/notes/discussions in class. So 889 kJ/mol is 889 kJ/16 g CH4. You want 66,000 kJ from part 1 and you have reaction in part 2 that will produce 889 kJ/16 g. So
16 g CH4 x 66,000 kJ/889 kJ = ? g CH4.
Hope this helps. Post your work if you get stuck.
Thank you DrBob222, really appreciate it!
Well, well, well, looks like we have a hot water tank in need of some hot gas action! But don't worry, I'm here to clown-around and help you out!
To solve this problem, we need to figure out how much natural gas (methane) needs to be burned to heat the water in the tank. We can start by identifying the equation for the combustion reaction of methane.
The combustion of methane can be represented by the following balanced equation:
CH4 + 2O2 → CO2 + 2H2O
According to this equation, one mole of methane (CH4) will produce one mole of CO2 and two moles of H2O.
Now, let's break it down step by step:
Step 1: Calculate the moles of water needed to be heated.
Since we know the volume of water in the tank (300.0 L) and the density of water (1 g/mL), we can determine the mass of water in grams using the equation: mass = volume x density. Then, we can convert the mass to moles using the molar mass of water (18.015 g/mol).
Step 2: Calculate the change in temperature.
The temperature needs to increase from 12.5°C to 65.0°C. The change in temperature (∆T) can be calculated as the final temperature minus the initial temperature.
Step 3: Calculate the heat required to raise the temperature of the water.
The heat required can be determined using the equation: Q = mc∆T, where Q is the heat, m is the mass of water in grams, c is the specific heat capacity of water (4.18 J/g°C), and ∆T is the change in temperature.
Step 4: Calculate the moles of methane needed.
Since the combustion of methane is a 1:1 ratio with CO2 and a 1:2 ratio with H2O, we just need to consider the moles of water. Divide the heat obtained in step 3 by the heat of combustion of water (286 kJ/mol) to get the moles of water. Then, multiply by the mole ratio (1 mole of CH4 for 2 moles of H2O) to find the moles of methane needed.
Step 5: Calculate the mass of methane needed.
Multiply the moles of methane needed by the molar mass of methane (16.04 g/mol) to get the mass of methane required.
And voila! You've got the mass of natural gas (methane) needed to bring your tank up to the correct temperature. Just remember, it's all about heating things up with some fiery chemistry!
To solve this problem, we can use the heat transfer equation:
Q = mcΔT
Where:
Q is the heat transferred,
m is the mass of the water being heated,
c is the specific heat capacity of water, and
ΔT is the change in temperature.
First, let's calculate the heat required to raise the temperature of 300.0 L of water from 12.5°C to 65.0°C.
1. Convert liters of water to kilograms:
1 L of water is equal to 1 kg.
So, 300.0 L of water = 300.0 kg of water.
2. Calculate the heat required using the heat transfer equation:
Q = mcΔT
Q = 300.0 kg * 4.18 J/g°C * (65.0°C - 12.5°C)
Notice that we convert the specific heat capacity of water from J/g°C to J/kg°C.
3. Now, solve for Q to get the heat required.
Next, let's calculate the heat produced by burning methane.
The combustion reaction of methane is as follows:
CH4 + 2O2 -> CO2 + 2H2O
From the balanced chemical equation, the molar ratio between CH4 and H2O is 1:2.
This means that for every mole of CH4 burned, 2 moles of H2O are produced.
4. Convert the calculated heat (Q) from J to moles of water using the molar heat of vaporization of water.
The molar heat of vaporization of water is 40.7 kJ/mol.
5. Determine the moles of CH4 required to produce the calculated moles of water.
From the balanced equation, the molar ratio between CH4 and H2O is 1:2.
6. Convert the moles of CH4 to grams of CH4 using the molar mass of CH4.
The molar mass of CH4 is 16.04 g/mol.
Finally, you can use the mass of CH4 found in step 6 to determine the amount of natural gas (methane) that needs to be burned in a complete combustion reaction in order to bring the water in the tank up to the correct temperature.
To solve this problem, we first need to understand the concepts involved.
1. Heat transfer: Heat is transferred from a higher temperature to a lower temperature until thermal equilibrium is reached. In this case, heat will be transferred from the burned natural gas to the water in the tank.
2. Specific heat capacity: The specific heat capacity of a substance is the amount of heat energy required to raise the temperature of one kilogram of the substance by one degree Celsius. The specific heat capacity of water is approximately 4.18 J/g°C or 4.18 kJ/kg°C.
3. Enthalpy of combustion: The enthalpy of combustion (∆Hc) is the heat produced when one mole of a substance is completely burned in excess oxygen. The enthalpy of combustion for methane (CH4) is -890.3 kJ/mol.
Now let's break down the steps to solve the problem:
Step 1: Calculate the temperature difference
The temperature difference (∆T) is the difference between the final and initial temperatures of the water.
∆T = 65.0°C - 12.5°C = 52.5°C
Step 2: Calculate the mass of water in the tank
Given that the tank holds 300.0 L of water, we need to convert it to mass using the density of water.
Density of water = 1 g/cm³ = 1000 kg/m³
Mass of water = volume × density = 300.0 L × 1000 kg/m³ = 300,000 g = 300 kg
Step 3: Calculate the heat energy required
The heat energy required can be calculated using the equation:
Heat energy (Q) = mass × specific heat capacity × temperature difference
Q = 300 kg × 4.18 kJ/kg°C × 52.5°C = 65,925 kJ
Step 4: Convert heat energy to moles of methane
We can use the enthalpy of combustion for methane to find the number of moles of methane required to produce the necessary heat energy.
Number of moles of methane = Heat energy / enthalpy of combustion
Number of moles of methane = 65,925 kJ / (-890.3 kJ/mol) ≈ -74.06 mol
Note: The negative sign indicates that the reaction is exothermic.
Step 5: Calculate the mass of methane
The molar mass of methane (CH4) is:
1 atom of carbon (C) = 12.01 g/mol
4 atoms of hydrogen (H) = (1.01 g/mol) × 4 = 4.04 g/mol
Molar mass of methane = 12.01 g/mol + 4.04 g/mol = 16.05 g/mol
Mass of methane = Number of moles of methane × molar mass of methane
Mass of methane = -74.06 mol × 16.05 g/mol ≈ -1,187.03 g
Note: The negative sign indicates that the mass of methane must be burned to produce the required heat.
Therefore, approximately 1,187 grams of natural gas (methane) must be burned in a complete combustion reaction to bring the water in the tank to the correct temperature.