Final answer:
The mass of C₂H₄ that must burn to give 56.0 kJ of heat is 28.0 grams.
Step-by-step explanation:
The question is asking for the mass of C₂H₄ needed to produce a certain amount of heat. This is an example of stoichiometric calculations and enthalpy changes, which involve using the balanced equation and stoichiometry to determine the amount of reactant needed to produce a given amount of product. In this case, we need to use the balanced equation for the combustion of C₂H₄:
2C₂H₄ + 3O₂ → 4CO₂ + 4H₂O
We can see that 2 mol of C₂H₄ reacts with 3 mol of O₂ to produce 4 mol of CO₂. From the balanced equation, we can determine the molar ratio between C₂H₄ and CO₂ is 2:4 (or 1:2).
To find the mass of C2H₄ required to produce 56.0 kJ of heat, we need to use the molar mass of C₂H₄:
Molecular weight of C₂H₄= 2(12.01 g/mol) + 4(1.01 g/mol) = 28.05 g/mol
Using the molar ratio, we can set up a proportion:
(1 mol C₂H₄ / 2 mol CO₂) = (mass C₂H₄ / 56.0 kJ)
Solving for the mass of C₂H₄:
mass C₂H₄ = (1 mol C₂H₄ / 2 mol CO₂) * (56.0 kJ)
mass C₂H₄ = 28.0 kJ
Therefore, the mass of C₂H₄ that must burn to give 56.0 kJ of heat is 28.0 grams.