Question

Estimate the adiabatic flame temperature of an acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) cutting torch, in \(^{\circ} \mathrm{C}\), which uses a stoichiometric amount of pure oxygen.

Short answer

Question: Estimate the adiabatic flame temperature of an acetylene cutting torch which uses a stoichiometric amount of pure oxygen. Answer: The adiabatic flame temperature for the acetylene-oxygen combustion can be around 3100-3300 °C depending on specific conditions and assumptions made during the experiment.

Step-by-step solution

Write the balanced chemical equation for the combustion of acetylene in pure oxygen

to estimate the adiabatic flame temperature, first, we need to write the balanced chemical equation for the combustion of acetylene (C2H2) in pure oxygen (O2). The products of combustion are carbon dioxide (CO2) and water (H2O). The balanced chemical equation is: C2H2 + 2.5 O2 -> 2 CO2 + H2O This balanced equation shows that one mole of acetylene reacts with 2.5 moles of pure oxygen to produce 2 moles of carbon dioxide and 1 mole of water.

Calculate the heat of reaction

The heat of reaction (ΔH) is the difference in the enthalpy of the products and the reactants. We can find the enthalpy values for the reactants and products from standard enthalpy of formation tables. The equation for heat of reaction is: ΔH = ΣH_products - ΣH_reactants The standard enthalpy of formation values are as follows: C2H2: +226.7 kJ/mol O2: 0 kJ/mol (since O2 is an element in its standard state) CO2: -393.5 kJ/mol H2O: -241.8 kJ/mol (vapor) Substituting these values into the equation, we get: ΔH = (2 × (-393.5) + 1 × (-241.8)) - (1 × (+226.7) + 2.5 × 0) ΔH = -1308.6 kJ/mol

Calculate the adiabatic flame temperature

The adiabatic flame temperature is the temperature at which the heat released by the reaction is equal to the heat absorbed by the system. In this case, the heat absorbed by the system is given by: q = ΔH / ΔT Rearranging the equation to find ΔT, we get: ΔT = ΔH / q Assuming adiabatic conditions, the heat absorbed by the system (q) is 0, making the equation: ΔT = ΔH / 0 Since dividing by zero is undefined, this implies that the adiabatic flame temperature is the highest possible temperature the reaction can reach. We know that the heat of the reaction is negative, meaning the reaction is exothermic and releases heat. However, we cannot provide an exact temperature using the above equation. It's important to note that experimentally determined adiabatic flame temperatures for the acetylene-oxygen combustion are around 3100-3300 °C depending on the specific conditions and assumptions made during the experiment. In this problem, we cannot reach an exact value for the adiabatic flame temperature using the given information, but we now know that the experimentally determined adiabatic flame temperatures for the acetylene-oxygen combustion can fall between 3100-3300 °C.