A gas mixture containing 3.5L of ethylene and methane on complete combustion at 298K produce 6L of co₂ . find the amount of heat evolve on burning one litre of the gas mixture.the enthalpy of combustion of ethylene and methane are -1423kJ and -890kJrespectively....pls solve the problem.......

To determine the amount of heat evolved from burning one liter of the gas mixture containing ethylene and methane, we first need to analyze the combustion reactions of both gases and how they contribute to the total heat released. Let's break this down step by step.

Understanding the Combustion Reactions

The combustion reactions for ethylene (C₂H₄) and methane (CH₄) can be represented as follows:

• C₂H₄ + 3 O₂ → 2 CO₂ + 2 H₂O (Enthalpy of combustion: -1423 kJ/mol)
• CH₄ + 2 O₂ → CO₂ + 2 H₂O (Enthalpy of combustion: -890 kJ/mol)

Calculating Moles of Gases

We know that the gas mixture contains 3.5 L of ethylene and methane, and upon complete combustion, it produces 6 L of CO₂. To find the moles of each gas in the mixture, we can use the ideal gas law, where 1 mole of gas occupies 22.4 L at standard temperature and pressure (STP). However, since we are working at 298 K, we can still use the volume directly for our calculations, as the ratio remains the same.

Determining the Contribution of Each Gas

Let’s denote the volume of ethylene as Vₑ and the volume of methane as Vₕ. The total volume of the gas mixture is:

Vₑ + Vₕ = 3.5 L

From the combustion reactions, we can see that:

• 1 L of C₂H₄ produces 2 L of CO₂.
• 1 L of CH₄ produces 1 L of CO₂.

Let’s assume that Vₑ = x L and Vₕ = (3.5 - x) L. The total CO₂ produced can be expressed as:

2x + (3.5 - x) = 6

Simplifying this equation gives:

2x + 3.5 - x = 6

x + 3.5 = 6

x = 2.5 L

This means that:

Vₑ = 2.5 L (ethylene)

Vₕ = 3.5 - 2.5 = 1 L (methane)

Calculating Heat Evolved

Now we can calculate the heat evolved from the combustion of each gas:

• For ethylene:

  Heat evolved = Vₑ (in moles) × Enthalpy of combustion

  Vₑ = 2.5 L = 2.5 / 22.4 moles ≈ 0.1116 moles

  Heat from ethylene = 0.1116 moles × (-1423 kJ/mol) ≈ -158.5 kJ

• For methane:

  Vₕ = 1 L = 1 / 22.4 moles ≈ 0.0446 moles

  Heat from methane = 0.0446 moles × (-890 kJ/mol) ≈ -39.6 kJ

Total Heat Evolved

Now, we sum the heat evolved from both gases:

Total heat = -158.5 kJ - 39.6 kJ ≈ -198.1 kJ

Finding Heat Evolved per Liter of Gas Mixture

Since the total heat evolved from the combustion of the entire gas mixture (3.5 L) is approximately -198.1 kJ, we can find the heat evolved per liter:

Heat per liter = Total heat / Total volume

Heat per liter = -198.1 kJ / 3.5 L ≈ -56.6 kJ/L

Thus, the amount of heat evolved on burning one liter of the gas mixture is approximately -56.6 kJ. This negative sign indicates that heat is released during the combustion process.