Question

(b) Calculate the temperature of the product mixture if the methane and air are both at an initial temperature of 0.0°C. Assume a stoichiometric ratio of methane to oxygen from the air, with air being 21% O₂ by volume (c of CO₂ = 57.2 J/mol·K; c of H₂O(g) = 36.0 J/mol·K; c of N₂ = 30.5 J/mol·K).

Answer 1

Temperature of the product mixture is 10314.79 K

Given Data,

 Mass = 37.196 g

 Temperature = - 0.2°C

Given reaction is shown as:

 CH₄ + 2O₂ →CO₂ + 2H₂O

Hence,

Moles of CH₄ burned = Mass of  CH₄/ Molar mass of  CH₄

                                   = 37.196g/16.0491g

                                   = 2.32 mol

Now,

moles of O₂ needed = 2.32 × 2

                                   = 4.64 moles

Moles of CO₂ produced = 2.32 moles

Moles of H₂O produced = 2.32 × 2

                                         = 4.64 moles

Now,

 Given

 Formation of CO₂= 393.5 × 10³ J/m

  Formation of H₂O = 285.8×10³ J/m

Hence,

 Heat absorbed by methane + heat absorbed by oxygen =  Formation of     CO₂+Formation of H₂O

   Now,

2.32×35.14 ×dT + 4.64×29.214×dT = 2.32× 393.5 × 10³ + 4.64× 285.8×10³

 81.52dT+135.55dT = 2239032

dT = 10314.79 K

Thus from the above conclusion we can say that ,Temperature of the product mixture is 10314.79 K.

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