A gaseous fuel mixture contains 20.9% methane (CH4), 43.2% ethane (C2H6) and the rest propane (C3H8) by volume.
Part A
When the fuel mixture contained in a 1.58 L tank, stored at 748 mmHg and 298 K, undergoes complete combustion, how much heat is emitted? (Assume that the water produced by the combustion is in the gaseous state.)
Express your answer with the appropriate units.
1. Start with 1.58 L sample. Use PV = nRT at the conditions listed and calculate n = total mols.
2. n*% each gas = mols of each gas.
3. Write equation for combustion of each gas.
4. Look up heat combustion per mole for each gas and calculate heat generated by each gas based on the moles of that gas.
5. Add heat generated by each gas for total heat generated.
Post your work if you get stuck.
Well, it seems like this fuel mixture is about to have a hot time! Let's calculate the heat emitted during combustion.
To find the heat emitted, we need to determine the moles of each gas in the mixture and then use the balanced equation for combustion to calculate the heat emitted.
First, let's find the moles of each gas in the mixture:
For methane (CH4):
0.209 x 1.58 L = 0.32962 L (convert to L)
For ethane (C2H6):
0.432 x 1.58 L = 0.68256 L (convert to L)
Since the remaining gas is propane (C3H8), the moles of propane can be found by subtracting the moles of methane and ethane from the total moles of the mixture:
Moles of propane = Total moles - Moles of methane - Moles of ethane
= 1.58 L - 0.32962 L - 0.68256 L
= 0.56782 L (convert to L)
Now, let's use the balanced equation for combustion of each gas to calculate the heat emitted:
For methane:
CH4(g) + 2O2(g) -> CO2(g) + 2H2O(g)
ΔH = -891 kJ/mol (heat of combustion)
Heat emitted by methane = Moles of methane x ΔH
= 0.32962 L x -891 kJ/mol
For ethane:
C2H6(g) + 7/2O2(g) -> 2CO2(g) + 3H2O(g)
ΔH = -1560 kJ/mol (heat of combustion)
Heat emitted by ethane = Moles of ethane x ΔH
= 0.68256 L x -1560 kJ/mol
For propane:
C3H8(g) + 5O2(g) -> 3CO2(g) + 4H2O(g)
ΔH = -2219 kJ/mol (heat of combustion)
Heat emitted by propane = Moles of propane x ΔH
= 0.56782 L x -2219 kJ/mol
Finally, let's sum up the heat emitted by each gas to find the total heat emitted:
Total heat emitted = Heat emitted by methane + Heat emitted by ethane + Heat emitted by propane
Now that we have all the necessary information, I'll let you do the math and find the answer!
To calculate the amount of heat emitted during complete combustion, we need to determine the moles of each component in the fuel mixture and use their respective enthalpy of combustion values.
Step 1: Calculate moles of each component.
To calculate the moles of each component, we need to use the ideal gas law equation:
PV = nRT
Given:
Partial pressure of methane (CH4) = 20.9% of 748 mmHg
Partial pressure of ethane (C2H6) = 43.2% of 748 mmHg
Partial pressure of propane (C3H8) = 100% - (20.9% + 43.2%) = 35.9% of 748 mmHg
Partial pressure can be converted to atm by dividing by 760 mmHg:
P_CH4 = (20.9/100) * (748 mmHg / 760 mmHg)
P_C2H6 = (43.2/100) * (748 mmHg / 760 mmHg)
P_C3H8 = (35.9/100) * (748 mmHg / 760 mmHg)
Now, rearrange the ideal gas law equation to solve for moles (n):
n = PV / RT
Where:
P = partial pressure of the component
V = volume of the tank
R = ideal gas constant (0.0821 L * atm / (mol * K))
T = temperature in Kelvin
Using the given values, we can calculate the moles for each component:
n_CH4 = P_CH4 * V / RT
n_C2H6 = P_C2H6 * V / RT
n_C3H8 = P_C3H8 * V / RT
Step 2: Determine the enthalpy of combustion values.
The enthalpy of combustion (ΔH) is the amount of heat emitted when one mole of a substance is completely burned.
The enthalpy of combustion for methane (CH4) = -882 kJ/mol
The enthalpy of combustion for ethane (C2H6) = -1560 kJ/mol
The enthalpy of combustion for propane (C3H8) = -2220 kJ/mol
Step 3: Calculate the heat emitted.
The heat emitted during complete combustion can be calculated using the equation:
ΔH_total = (ΔH_CH4 x n_CH4) + (ΔH_C2H6 x n_C2H6) + (ΔH_C3H8 x n_C3H8)
Substitute the given values:
ΔH_total = (-882 kJ/mol x n_CH4) + (-1560 kJ/mol x n_C2H6) + (-2220 kJ/mol x n_C3H8)
Finally, calculate ΔH_total using the calculated moles:
ΔH_total = (-882 kJ/mol x n_CH4) + (-1560 kJ/mol x n_C2H6) + (-2220 kJ/mol x n_C3H8)
This will give you the amount of heat emitted during complete combustion in kJ.
To find out the amount of heat emitted during the complete combustion of the fuel mixture, you need to calculate the amount of heat released by each of the components separately and then sum them up.
Here's how you can do it step by step:
Step 1: Determine the moles of each component.
To calculate the moles of each component, you need to use the given volume, pressure, and temperature along with the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
First, convert the given pressure from mmHg to atm:
1 atm = 760 mmHg
So, 748 mmHg / 760 mmHg/atm = 0.983 atm
Now, calculate the moles of each component:
For methane (CH4):
V = 1.58 L
P = 0.983 atm
R = 0.0821 L·atm/mol·K
T = 298 K
n_CH4 = PV / RT = (0.983 atm * 1.58 L) / (0.0821 L·atm/mol·K * 298 K)
Repeat the same calculation for ethane (C2H6) and propane (C3H8) to find their respective moles.
Step 2: Calculate the moles of water produced.
During the combustion of methan, ethane, and propane, water is produced. The balanced chemical equation for the combustion of each fuel is as follows:
CH4 + 2O2 -> CO2 + 2H2O (1)
C2H6 + 7/2O2 -> 2CO2 + 3H2O (2)
C3H8 + 5O2 -> 3CO2 + 4H2O (3)
By comparing the coefficients in these equations to the volume percentages, you can deduce that for every mole of methane, 2 moles of water are produced; for every mole of ethane, 3 moles of water are produced, and for every mole of propane, 4 moles of water are produced.
Multiply the respective moles of each fuel calculated in Step 1 by the corresponding water moles factor to find the total moles of water produced.
Step 3: Calculate the heat released.
The heat released during the combustion of each fuel can be calculated using the equation:
q = ΔH · n
Where:
q = heat released
ΔH = enthalpy of combustion (heat of formation) of the respective fuel
n = moles of the respective fuel
The values for the enthalpy of combustion (ΔH) for each fuel can be found in reference tables. Here are the approximate values for ΔH:
ΔH_ch4 = -890 kJ/mol
ΔH_c2h6 = -1566 kJ/mol
ΔH_c3h8 = -2220 kJ/mol
Multiply the respective ΔH values by the moles of each fuel calculated in Step 1 to find the heat emitted by each component.
Step 4: Sum up the heat emitted.
Add up the heat emitted by each component to find the total heat emitted during the complete combustion of the fuel mixture.
Make sure to watch the units and convert them if necessary.
By following these steps, you will be able to determine the amount of heat emitted during the complete combustion of the fuel mixture in the 1.58 L tank.