Final answer:
The standard enthalpy of formation for acetylene from elements is calculated by manipulating and combining equations for the formation of water, combustion of acetylene, and the formation of carbon dioxide, then applying Hess's Law to obtain the net enthalpy change.
Step-by-step explanation:
The calculation of the standard enthalpy of formation for acetylene (C₂H₂) from its elements can be determined using the given reactions. This process involves applying Hess's Law which allows us to find an unknown enthalpy change for a reaction by using known enthalpies for other reactions.
To use the given data for the reactions involving acetylene, we need to manipulate the reactions so that when they are added up, only the desired reaction of forming acetylene from its elements remains. First, we can take the reaction for forming water and reverse it (which changes the sign of the enthalpy) and then multiply it by 2 to have enough hydrogen for acetylene in the desired reaction. Then, we manipulate the combustion of acetylene so that acetylene is on the reactant side. Finally, we use the known enthalpy of carbon dioxide formation and multiply it by 4 to account for all the carbon atoms present in the reaction products. Adding all these appropriately manipulated reaction enthalpies will give us the net enthalpy of formation for acetylene, as the other substances will cancel each other out.
An example of such manipulation is as follows: Reverse and multiply reaction B by 2 gives us 2 H₂ (g) → 2 H₂ (g) + O₂ (g), which when applied, gives us an enthalpy of +571.6 kJ. Use reaction C as it is given, but we need to divide it by 2 because the enthalpy provided is for 2 moles of acetylene, resulting in C₂H₂ (g) + 5/2 O₂ (g) → 2 CO₂ (g) + H₂O (l) with an enthalpy of -1299.4 kJ. Lastly, use the enthalpy for CO₂ formation, multiplied by 2, gives us 2 C (graphite) + 2 O₂ (g) → 2 CO₂ (g) with an enthalpy of -787.0 kJ. Adding these together, we find the enthalpy of formation for acetylene.