The combustion reaction of propane (C3H8), a gas used for heating, is shown in the following thermochemical equation: C3H8+ 502 -->3CO2+4H2O deltaH = -2221kJ Calculate how much propane gas must be burned to obtain one amount of heat of 8 x 107 J, if the process has a yield of 60%
If the yield were 100%, you would need this.
44 g C3H8 (1 mol) will produce 2221 kJ of heat, so you will need
44 g x (8 x 10^4 kJ/2221 kJ) = 1585 g to produce 8 x 10^7 J. For a reaction that is only 60% efficient, you will need
% yield = (actual yield/theoretical yield)*100
60 = (1585/X)*100 = ? where X = amount of C3H8 that must be used initially to produce 8E4 kJ @ 60% efficiency.
To calculate the amount of propane gas that must be burned to obtain 8 x 10^7 J of heat with a yield of 60%, we need to follow these steps:
Step 1: Convert the heat value from joules to kilojoules.
8 x 10^7 J = 8 x 10^7 / 1000 = 8 x 10^4 kJ
Step 2: Calculate the amount of heat produced from burning one mole of propane.
According to the balanced equation, the combustion of propane produces -2221 kJ of heat for every one mole of propane burned.
Step 3: Calculate the amount of heat obtained with a 100% yield.
Let's assume x moles of propane are required to produce 8 x 10^4 kJ of heat with a 100% yield. Using the equation:
-2221 kJ/mol * x mol = 8 x 10^4 kJ
x = 8 x 10^4 kJ / -2221 kJ/mol
x ≈ -36.02 mol
Step 4: Calculate the amount of propane gas needed with a 60% yield.
Since the yield is 60%, we need to multiply the amount of propane calculated in Step 3 by the reciprocal of the yield:
-36.02 mol * (1 / 0.6)
≈ -60.04 mol
Take note that moles must be positive, so we can round up the value to 60 moles of propane gas.
Therefore, approximately 60 moles of propane gas must be burned to obtain 8 x 10^7 J of heat with a yield of 60%.
To calculate how much propane gas must be burned, we need to use the given yield of 60% and the heat of the reaction.
Step 1: Convert the given heat value from joules to kilojoules:
8 x 10^7 J = 8 x 10^4 kJ
Step 2: Use the yield to calculate the actual amount of heat obtained:
Actual heat = Yield × Theoretical heat
Actual heat = 0.60 × -2221 kJ (note that we use the negative value of the heat because it represents an exothermic reaction)
Actual heat = -1332.6 kJ
Step 3: Determine the amount of propane gas that must be burned:
According to the balanced equation, the molar ratio between propane and heat is 1:2221 kJ.
So to calculate the moles of propane gas, we divide the actual heat (-1332.6 kJ) by the molar ratio:
Moles of propane gas = Actual heat / Molar ratio
Moles of propane gas = -1332.6 kJ / (-2221 kJ/mol)
Moles of propane gas = 0.6 mol
Step 4: Convert moles of propane gas to grams:
To convert moles to grams, we need to multiply by the molar mass of propane (C3H8).
Molar mass of propane = (3 × atomic mass of carbon) + (8 × atomic mass of hydrogen)
Molar mass of propane = (3 × 12.01 g/mol) + (8 × 1.01 g/mol)
Molar mass of propane = 44.11 g/mol
Mass of propane gas = Moles of propane gas × Molar mass of propane
Mass of propane gas = 0.6 mol × 44.11 g/mol
Mass of propane gas = 26.47 g
Therefore, approximately 26.47 grams of propane gas must be burned to obtain a heat of 8 x 10^7 J with a yield of 60%.