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6 January, 13:20

An automobile engine has a cylinder with a volume of 500.0 L that is filled with air (21.00 % oxygen) at a temperature of 55.00 C and a pressure of 2.000 atm. What is the mass of octane, C8H18 that must be injected to reacted with all of the oxygen in the cylinder to produce carbon dioxide and water?

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  1. 6 January, 17:12
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    The answer to the question is

    35.64 grams of octane, C₈H₁₈ must be injected to reacted with all of the oxygen in the cylinder to produce carbon dioxide and water

    Explanation:

    Firstly we wrte the equation for the reaction as follows

    2C₈H₁₈+25O₂ → 16CO₂+18H₂O

    From where it is seen that 2 moles of octane combine with 25 moles of O₂ to form 16 moles of CO₂ and 18 moles of H₂O

    However the conyainer contains

    500.0 L of air containing 21.00 % oxygen

    Which is 0.21 * 500 = 105 L = ‪0.105‬ m³ of oxygen gas

    drom the combined gas equation we have

    PV = nRT hence n = PV / (RT) where P = 2.000 atm = ‪202650‬ Pa, T = 55.00 C = ‪328.15‬ K and R = 8.314 has units of J / (mol K).

    21278.25/2728.24 = 7.8 moles of O₂

    Therefore since 25 moles of O₂ react with 2 moles of C₈H₁₈ then

    1 mole of O₂ will react with 1/25 moles of C₈H₁₈ this gives and 7.8 moles will react with 7.8/25 moles of C₈H₁₈

    One mole of C₈H₁₈ weighs 114.23 g

    Then 7.8/25 moles C₈H₁₈ weigh 35.64 grams

    The mass of octane, C₈H₁₈ that must be injected to reacted with all of the oxygen in the cylinder to produce carbon dioxide and water is 35.64 grams
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