The propane fuel(C3H8) used in gas barbecues burns according to the following equation:
C3H8(g) + 5O2(g) --> 3CO2(g) + 4H2O(g)
∆Ho rxn = -2044kj
If a pork roast must absorb 2200 kj to fully cook, and if only 10% of the heat produced by the barbecue is actually absorbed by the roast, what mass of CO2 is emitted into the atmosphere during the grilling of the pork roast?
thanks
my question says if pork roast must absorb 2000 KJ to fully cook.
And the answer is 1290KJ, but I am not sure how this answer was generated....need help Please
To find the mass of CO2 emitted into the atmosphere during the grilling of the pork roast, we need to calculate the amount of heat produced by burning propane and then determine the amount of CO2 produced.
Step 1: Calculate the heat produced by burning propane:
From the given equation, we can see that the molar ratio between C3H8 and ∆Ho rxn is 1:2044/3.
∆Ho rxn = -2044 kJ/mol
Step 2: Calculate the heat produced by burning one mole of propane:
According to the equation for the combustion of propane, the molar quantity of propane used is 1 mole (C3H8). Therefore, the heat produced by one mole of propane is -2044 kJ/mol.
Step 3: Calculate the heat absorbed by the roast:
Since only 10% of the heat produced by the barbecue is actually absorbed by the roast, the amount of heat absorbed by the roast is:
Heat absorbed = 0.1 * 2200 kJ = 220 kJ
Step 4: Calculate the moles of propane burned to produce 220 kJ of heat:
Moles of C3H8 = Heat absorbed / (-2044 kJ/mol)
Moles of C3H8 = 220 kJ / (-2044 kJ/mol)
Step 5: Calculate the moles of CO2 produced (from the balanced chemical equation):
From the balanced chemical equation, we can see that the molar ratio between C3H8 and CO2 is 1:3.
Therefore, the moles of CO2 produced are:
Moles of CO2 = Moles of C3H8 * (3 mol CO2 / 1 mol C3H8)
Step 6: Calculate the mass of CO2 emitted into the atmosphere:
To calculate the mass of CO2, we need to know the molar mass of CO2, which is approximately 44 g/mol.
Mass of CO2 = Moles of CO2 * Molar mass of CO2
Mass of CO2 = Moles of CO2 * 44 g/mol
Now you can substitute the values into the equations to find the mass of CO2 emitted into the atmosphere.
To determine the mass of CO2 emitted into the atmosphere during the grilling of the pork roast, we need to follow a few steps.
Step 1: Calculate the amount of heat produced by the barbecue.
Since we know that only 10% of the heat produced by the barbecue is absorbed by the roast, we need to calculate the total amount of heat produced. We can use the given ∆Ho rxn value to calculate the molar enthalpy of combustion for propane.
The molar enthalpy of combustion (∆Hcomb) is the enthalpy change when one mole of a substance is completely burned in excess oxygen. In this case, propane (C3H8) is completely burned in excess oxygen (O2).
The balanced chemical equation for the combustion of propane tells us that 1 mole of C3H8 produces 2044 kJ of heat. Therefore, the molar enthalpy of combustion (∆Hcomb) for propane is -2044 kJ/mol.
Step 2: Calculate the heat absorbed by the roast.
We are given that the roast must absorb 2200 kJ of heat to be fully cooked. However, only 10% of the heat produced by the barbecue is absorbed by the roast. So, we need to calculate the total heat produced and then find 10% of that value.
Let's represent the heat produced by the barbecue as Q1: Q1 = -2044 kJ (since ∆Ho rxn = -2044 kJ)
To find the heat absorbed by the roast (Q2), we can use the equation:
Q2 = 0.1 * Q1
Q2 = 0.1 * (-2044 kJ)
Therefore, Q2 = -204.4 kJ (10% of the heat produced by the barbecue).
Step 3: Calculate moles of CO2 produced.
From the balanced chemical equation, we see that for every 3 moles of CO2 produced, 1 mole of C3H8 is consumed.
Let's assume X moles of C3H8 are used in the barbecue. Then according to the equation, 3X moles of CO2 are produced.
Step 4: Calculate the mass of CO2 produced.
To calculate the mass of CO2, we need to know the molar mass of CO2, which is approximately 44 g/mol.
The number of moles of CO2 (3X) can be converted to grams using the molar mass of CO2:
Mass of CO2 = 3X * Molar mass of CO2
Mass of CO2 = 3X * 44 g/mol
Finally, we need to solve for X to find the mass of CO2 produced.
To summarize, the steps are as follows:
1. Calculate the total heat produced by the barbecue (Q1) using the given ∆Ho rxn.
2. Calculate the heat absorbed by the roast (Q2) by finding 10% of Q1.
3. Use the balanced chemical equation to relate moles of CO2 produced to moles of C3H8 consumed (3 moles of CO2 per 1 mole of C3H8).
4. Convert the number of moles of CO2 to grams using the molar mass of CO2 to calculate the mass of CO2 produced.
By following these steps, you should be able to determine the mass of CO2 emitted into the atmosphere during the grilling of the pork roast.