Final answer:
To combust 1 liter of kerosene, approximately 2.759 kg of liquid oxygen is needed. This calculation is based on the balaced chemical equation for the combustion of kerosene and the provided density of kerosene.
Step-by-step explanation:
The question requires us to calculate the mass of liquid oxygen needed to combust with 1 liter of kerosene (C₁₄H₃₀) in a rocket fuel scenario.
First, we need to determine the mass of 1 liter of kerosene. Since the density of kerosene is given as 0.792 g/ml, the mass of kerosene in 1 liter (1000 ml) will be 792 g.
Now we must write the balanced chemical equation for the combustion of kerosene with oxygen. The formula for kerosene is approximated by the formula C₁₄H₃₀:
C₁₄H₃₀ + 21.5O₂ → 14CO₂ + 15H₂O
From the balanced equation, we can see that each molecule of kerosene requires 21.5 molecules of oxygen to combust completely. The molar mass of kerosene (C₁₄H₃₀) is approximately 198 g/mol, and the molar mass of oxygen (O₂) is 32 g/mol.
So for 198g of kerosene, 21.5 moles of oxygen are required.
Therefore, to find out how much oxygen is needed for 792g of kerosene, we set up a proportion:
(198 g kerosene / 21.5 mol O₂) = (792 g kerosene / x mol O₂)
Solving for x gives us:
x = (792 g kerosene × 21.5 mol O₂) / 198 g kerosene
x = 86.22 mol O₂
To convert moles of oxygen to mass:
Mass of O₂ = 86.22 mol × 32 g/mol
= 2759.04 g O₂
Mass of O₂ in kilograms = 2759.04 g / 1000
= 2.759 kg
Therefore, the mass of liquid oxygen required for every liter of kerosene is approximately 2.759 kg, which is closest to option B (2.752 kg).