What mass of octane must be burned in order to liberate 5510 kJ of heat? ΔHcomb = -5471 kJ/mol.
2C8H18 + 17O2 ==>16CO2 + 18H2O
So you have 5471 kJ for 1 mole (which is 114.23 grams); therefore,
2*molar mass C8H18 x (5510/5471) = ??
To find the mass of octane that must be burned to liberate 5510 kJ of heat, we need to use the molar enthalpy of combustion (ΔHcomb) for octane.
The given value of ΔHcomb for octane is -5471 kJ/mol. This means that for every mole of octane burned, 5471 kJ of heat is liberated.
We can use this information to calculate the moles of octane required to release 5510 kJ of heat by setting up a simple proportion:
ΔHcomb/moles of octane = heat released/5510 kJ
Rearrange the proportion to solve for moles of octane:
moles of octane = (ΔHcomb * 1 mol) / (5510 kJ)
moles of octane = (-5471 kJ/mol * 1 mol) / (5510 kJ)
moles of octane = -5471 / 5510
moles of octane ≈ -0.9939
Note: Since moles cannot be negative, we take the absolute value.
moles of octane ≈ 0.9939 mol
Now that we know the moles of octane, we can calculate the mass using the molar mass of octane.
The molar mass of octane (C8H18) is approximately 114.23 g/mol.
mass of octane = moles of octane * molar mass
mass of octane = 0.9939 mol * 114.23 g/mol
mass of octane ≈ 113.49 g
Therefore, approximately 113.49 grams of octane must be burned to liberate 5510 kJ of heat.
To determine the mass of octane required to liberate 5510 kJ of heat, we can use the given value of ΔHcomb (standard enthalpy of combustion) for octane. However, we need to convert the heat released from kilojoules to moles of octane.
Step 1: Find the molar mass of octane (C8H18).
Looking at the periodic table, the molar masses of carbon (C) and hydrogen (H) are approximately 12 g/mol and 1 g/mol, respectively. Since octane contains 8 carbon atoms and 18 hydrogen atoms, the molar mass can be calculated as follows:
Molar mass of octane = (8 × molar mass of carbon) + (18 × molar mass of hydrogen)
Molar mass of octane = (8 × 12 g/mol) + (18 × 1 g/mol)
Molar mass of octane = 96 g/mol + 18 g/mol
Molar mass of octane = 114 g/mol
Therefore, the molar mass of octane is 114 g/mol.
Step 2: Convert the given heat value to moles.
To do this, we need to use the molar enthalpy of combustion (ΔHcomb) for octane.
ΔHcomb = -5471 kJ/mol
Given that 1 mole of octane releases 5471 kJ of heat, we can set up a proportion to find the number of moles required to liberate 5510 kJ.
ΔHcomb 1 mole
-------- = -------------
-5471 kJ x moles
x = (-5471 kJ × 1 mole) / -5510 kJ
x ≈ 0.993 moles
So, 5510 kJ of heat is approximately released by 0.993 moles of octane.
Step 3: Calculate the mass of octane.
We can now calculate the mass of octane using the molar mass (114 g/mol) and the number of moles (0.993 moles).
Mass of octane = number of moles × molar mass
Mass of octane = 0.993 moles × 114 g/mol
Mass of octane ≈ 113 g
Therefore, approximately 113 grams of octane must be burned to liberate 5510 kJ of heat.