Answer:
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
