To determine the heat required to produce 1.0 kg of calcium carbide (CaC₂) at constant pressure and 25°C, we need to know the enthalpy change of the reaction and the stoichiometry of the reaction.
The chemical equation for the production of calcium carbide is:
CaO + 3C → CaC₂ + CO
Given that the reaction occurs at constant pressure, we can assume the reaction is taking place under standard conditions, where the reactants and products are in their standard states.
The enthalpy change (ΔH) of the reaction can be obtained from the standard enthalpy of formation values for the substances involved:
ΔH = [ΣΔHf(products)] - [ΣΔHf(reactants)]
The standard enthalpy of formation for calcium carbide (CaC₂) is -59.8 kJ/mol.
Now, let's calculate the heat required:
Calculate the molar mass of calcium carbide: Molar mass of CaC₂ = (40.08 g/mol) + 2(12.01 g/mol) = 64.10 g/mol
Convert the mass of calcium carbide to moles: Moles of CaC₂ = mass / molar mass Moles of CaC₂ = 1.0 kg / 64.10 g/mol = 15.59 mol
Calculate the heat required: Heat required = ΔH × moles of CaC₂ Heat required = (-59.8 kJ/mol) × 15.59 mol = -932.7 kJ
Note: The negative sign indicates that the reaction is exothermic, meaning it releases heat.
Therefore, the heat required to produce 1.0 kg of calcium carbide at constant pressure and 25°C is approximately 932.7 kJ.