Please explain how enthalpies 1, 2, and 3 were calculated.

Given enthalpies:
- $ H(1) = 35.7 \, \text{kJ/mol} $
- $ H(2) = 32.0 \, \text{kJ/mol} $
- $ H(3) = -1.26 \, \text{kJ/mol} $

Context: This is related to a chemical engineering problem involving energy transfer, specifically energy balance on a condenser. The process involves partially condensing acetone (denoted as Ac) out of a gas stream containing 66.9 moles of acetone vapor, with the balance being nitrogen.

The enthalpies in the problem are likely derived from the energy balance on a condenser equipment, factoring in the thermodynamic changes as acetone gas partially condenses into liquid form.

Explanation:

In the given problem, the enthalpies of acetone (H(1), H(2), H(3)) are likely calculated using the principles of thermodynamics. Specifically, these might be measurements of enthalpy changes related to condensation reactions or phase changes. Energy balance on a condenser equipment involves keeping track of the energy entering, exiting, and being stored within the condenser system, which includes the energy in the form of enthalpy from chemical species such as acetone.

Enthalpy (H) is a thermodynamic quantity defined as the sum of a system's internal energy plus the product of its pressure and volume. For example, in chemical reactions, the change in enthalpy can be found from the difference in the enthalpies of reactants and products.

And in a condenser like the one in this scenario, when acetone switches from its gaseous form to liquid form (partial condensation), it releases heat, which changes its enthalpies (denoted here as H(1), H(2), and H(3)).

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