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5 July, 01:20

A 19.0 g sample of liquid methane is heated at a constant pressure of 1 atm from a temperature of 109.1 K to a temperature of 185.3 K. How much energy in kJ is required?

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  1. 5 July, 01:21
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    The energy required is 12.887KJ

    Explanation:

    There are two separate heat inputs involved in this problem:

    q₁ = heat added to vaporize the methane at 109.1 K q₂ = energy added to heat the vapor from 109.1 K to 185.3 K

    q = q₁ + q₂

    q = nΔH + mCΔT

    where;

    n is number of moles of methane

    ΔH is the molar enthalpy of vaporization of methane = 8.17 kJ/mol

    m is the mass of methane = 19g

    C is the specific heat capacity of gaseous methane = 2.20 J/g. K

    ΔT = T₂ - T₁ = 185.3 - 109.1 = 76.2 K

    n = Reacting mass/Molar mass

    molar mass of methane (CH₄) = 16g/mol

    n = 19/16 = 1.1875 mol

    ⇒q₁ = nΔH = 1.1875 X 8.17 = 9.702 kJ

    ⇒q₂ = mCΔT, = 19 X 2.2 X 76.2 = 3185.16 J = 3.18516KJ

    q = q₁ + q₂, ⇒ 9.702 kJ + 3.18516KJ = 12.887KJ

    Therefore, the energy required is 12.887KJ
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