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27 February, 08:04

Gasoline (which can be considered to be octane, C8H18) burns in oxygen to produce carbon dioxide and water. What volume (L) of oxygen at STP is necessary to react with 1.0 gal of gasoline? (The density of gasoline is 0.81 g/mL. 1 gal = 3.78 L)

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  1. 27 February, 08:08
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    We need 7.504 L of O2

    Explanation:

    Step 1: Data given

    Volume of gasoline = 3.78 L

    Density of gasoline = 0.81 g/mL

    Molar mass octane = 114.23 g/mol

    Step 2: The balanced equation

    2C8H18 + 25O2 → 16CO2 + 18H2O

    Step 3: Calculate mass of gasoline

    Density = mass / volume

    Mass = density * volume

    Mass octane = 0.81 g/mL * 3.78 L

    Mass octane = 3.0618 grams

    Step 4: Calculate moles octane

    Moles octane = mass octane / molar mass

    Moles octane = 3.0618 grams / 114.23 g/mol

    Moles octane = 0.0268 moles

    Step 5: Calculate moles of O2

    For 2 moles octane we need 25 moles O2 to produce 16 moles CO2 and 18 moles H2O

    For 0.0268 moles octane we need 12.5 * 0.0268 = 0.335 moles O2

    Step 6: Calculate volume O2

    1 mol = 22.4 L

    0.335 moles O2 = 0.335 * 22.4 L = 7.504 L

    We need 7.504 L of O2
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