Propane (C3H8) is burned in oxygen to pro-
duce carbon dioxide and water. The heat of
combustion of propane is -2012 kJ/mole. How
much heat is given off when 3.0 mol C3H8 are
reacted with 10.0 mol O2?
C3H8 + 5O2 ==> 3CO2 + 4H2O
This is a limiting reagent and we know that because amount for BOTH reactants are given. We must first determine the limiting reagent (either propane or oxygen).
3 moles C3H8 will produce how many moles CO2 (ignoring oxygen)? (3 moles C3H8 x 3 moles CO2/1 mole C3H8) = 3 x (3/1) = 9 moles CO2.
10 moles O2 will produce how much CO2 (ignoring propane). 10 moles O2 x 3 moles CO2/5 moles O2) = 10 x (3/5) = 6 moles CO2.
Obviously, both answers can't be right; the correct answer in limiting reagent problems is ALWAYS the smaller value (in this case 6 moles CO2) and the reagent producing that value is the limiting reagent (in this case the 10 moles O2). Now the problem is hos much heat is produced by burning C3H8 with 10 moles O2. The easier way is to determine how much C3H8 reacted. That will be
10 moles O2 x (1 mole C3H8/5 moles O2) = 10 x (1/5) = 2 moles C3H8.
Therefore, it C3H8 produces 2012 kJ/1 mol then it must produce 2 x that for 2 moles.
2012 kJ/mol x 2 mol = ?
Well, let's do some calculations... but first, let me put on my fireproof clown suit, just to be safe!
Okay, so we know that the heat of combustion of propane is -2012 kJ/mol. That means for every mole of propane burned, 2012 kJ of heat is released. Now, we want to find out how much heat is given off when 3.0 mol of propane are reacted with 10.0 mol of oxygen.
To find the heat given off, we need to look at the balanced chemical equation for the combustion of propane:
C3H8 + 5O2 -> 3CO2 + 4H2O
From the equation, we can see that for every 1 mole of propane, 3 moles of carbon dioxide are produced. So, for 3.0 mol of propane, we will have 3.0 mol * 3 mol CO2/mol C3H8 = 9.0 mol of CO2 produced.
Now we know that for every 3 moles of carbon dioxide produced, 2012 kJ of heat is given off. So, for 9.0 mol of CO2, the heat given off is 9.0 mol * 2012 kJ/mol CO2 = 18108 kJ.
Therefore, when 3.0 mol of C3H8 are reacted with 10.0 mol of O2, the total heat given off is 18108 kJ.
I hope that answer didn't burn you out! Remember, safety first when dealing with combustion reactions.
To determine the amount of heat given off when 3.0 mol of propane (C3H8) is reacted with 10.0 mol of oxygen (O2), we need to use the balanced chemical equation for the combustion of propane:
C3H8 + 5O2 -> 3CO2 + 4H2O
From the balanced equation, we can see that 1 mol of propane reacts with 5 mol of oxygen to produce 3 mol of carbon dioxide and 4 mol of water.
Given that the heat of combustion of propane is -2012 kJ/mol, we can use this information to calculate the heat given off.
1. Calculate the amount of carbon dioxide (CO2) produced:
3.0 mol C3H8 x (3 mol CO2 / 1 mol C3H8) = 9.0 mol CO2
2. Calculate the amount of water (H2O) produced:
3.0 mol C3H8 x (4 mol H2O / 1 mol C3H8) = 12.0 mol H2O
3. Calculate the amount of oxygen (O2) reacted:
10.0 mol O2
4. Calculate the total heat released:
Total heat = (heat of combustion of propane) x (moles of propane reacted)
Total heat = (-2012 kJ/mol) x (3.0 mol C3H8)
Total heat = -6036 kJ
Therefore, when 3.0 mol of propane reacts with 10.0 mol of oxygen, -6036 kJ of heat is given off.
To find the amount of heat given off when 3.0 mol of C3H8 (propane) reacts with 10.0 mol of O2 (oxygen), we can use the stoichiometry of the balanced chemical equation and the heat of combustion of propane.
The balanced chemical equation for the combustion of propane is:
C3H8 + 5O2 -> 3CO2 + 4H2O
From the balanced equation, we can see that one mole of propane reacts with five moles of oxygen to produce three moles of carbon dioxide and four moles of water.
Given that the heat of combustion of propane is -2012 kJ/mole, it means that when one mole of propane is burned, 2012 kJ of heat is given off.
Now, let's calculate the amount of heat given off when 3.0 mol of propane is reacted:
First, determine the number of moles of propane reacted by multiplying the given quantity (3.0 mol) by the stoichiometric coefficient for propane in the balanced equation (1):
3.0 mol C3H8 * (1 mol C3H8 / 1) = 3.0 mol C3H8
Next, determine the number of moles of oxygen reacted by multiplying the given quantity (10.0 mol) by the stoichiometric coefficient for oxygen in the balanced equation (5):
10.0 mol O2 * (5 mol O2 / 1) = 50.0 mol O2
From the balanced equation, we can see that the mole ratio of propane to oxygen is 1:5. Therefore, 3.0 mol of propane will react with 5 times the number of moles of oxygen (15.0 mol O2). However, since we only have 10.0 mol of O2 available, we know that the oxygen is the limiting reagent, and it will completely react with 3.0 mol of propane.
Finally, calculate the amount of heat given off using the heat of combustion of propane:
Heat given off = Heat of combustion of propane * moles of propane reacted
Heat given off = -2012 kJ/mole * 3.0 mol C3H8
Heat given off = -6036 kJ
Therefore, the heat given off when 3.0 mol of C3H8 reacts with 10.0 mol of O2 is -6036 kJ. Note that the negative sign indicates the release of heat during the exothermic reaction.