What mass of octane must be burned in order to liberate 5410 kJ of heat?
To determine the mass of octane that must be burned in order to liberate 5410 kJ of heat, we need to use the concept of molar mass and the balanced chemical equation for the combustion of octane.
Octane (C₈H₁₈) is a hydrocarbon, and its combustion reaction can be represented by the following balanced equation:
C₈H₁₈ + 12.5O₂ → 8CO₂ + 9H₂O
From the equation, we can see that 1 mole of octane reacts with 12.5 moles of oxygen gas (O₂) to produce 8 moles of carbon dioxide (CO₂) and 9 moles of water (H₂O).
First, we need to calculate the amount of heat released per mole of octane. By looking at the balanced equation, we can see that the combustion of octane liberates 5410 kJ of heat per mole of octane.
Now, to find the mass of octane required, we'll use the following steps:
1. Convert the given heat value from kJ to J (1 kJ = 1000 J):
5410 kJ = 5410 × 1000 J = 5,410,000 J
2. Calculate the number of moles of octane:
Using the equation Q = nΔH, where Q is the heat released, n is the number of moles, and ΔH is the molar enthalpy of combustion, we can rearrange the equation to solve for n:
n = Q / ΔH
n = 5,410,000 J / 5410 kJ/mol = 1000 mol
3. Finally, calculate the mass of octane:
To find the mass, we need to multiply the number of moles (n) by the molar mass of octane (C₈H₁₈). The molar mass of octane can be calculated by summing the atomic masses of its elements:
Molar mass of octane = (8 × atomic mass of carbon) + (18 × atomic mass of hydrogen)
Using the atomic masses of carbon (12.01 g/mol) and hydrogen (1.008 g/mol), we can determine the molar mass of octane:
Molar mass of octane = (8 × 12.01 g/mol) + (18 × 1.008 g/mol) ≈ 114.23 g/mol
Finally, we can calculate the mass of octane:
Mass = number of moles × molar mass
Mass = 1000 mol × 114.23 g/mol
Mass ≈ 114,230 g or 114.23 kg
Therefore, approximately 114.23 kg of octane must be burned to liberate 5410 kJ of heat.
Do you have the heat of combustion? If not you can calculate it this way.
2C8H18 + 25O2 ==> 16CO2 + 18H2O
dHrxn = dH combustion = (n*dHo formation products) - n*dHo reactants).
So you will obtain that many kJ for 228 g octane. Convert that to grams needed for 5410 kJ.
Post your work if you get stuck.