**Heat of Combustion and Delta U**

The heat of combustion is defined as the amount of heat released when a substance undergoes complete combustion in excess oxygen. In this case, we are given the heat of combustion of ethanol in a bomb calorimeter at 298K, which is -670.48 Kcal/mole.

**Delta U and First Law of Thermodynamics**

Delta U represents the change in internal energy of a system and is related to the heat flow into or out of the system and the work done on or by the system, according to the first law of thermodynamics:

Delta U = q + w

Where:
- Delta U is the change in internal energy
- q is the heat flow into or out of the system
- w is the work done on or by the system

**Calculating Delta U**

In this case, the heat of combustion (-670.48 Kcal/mole) represents the heat flow out of the system (since combustion releases heat). Therefore, q = -670.48 Kcal.

As the combustion reaction occurs at constant volume in a bomb calorimeter, no work is done, so w = 0.

Using the first law of thermodynamics equation, we can calculate Delta U:

Delta U = q + w
Delta U = -670.48 Kcal + 0
Delta U = -670.48 Kcal

Therefore, the value of Delta U at 298K for the given reaction is -670.48 Kcal.

**Explanation**

The negative sign in the value of Delta U indicates that the reaction results in a decrease in internal energy of the system. This means that the combustion of ethanol releases energy to the surroundings in the form of heat. The magnitude of Delta U (-670.48 Kcal) represents the amount of heat released during the combustion reaction.

It is important to note that Delta U is a state function, meaning it depends only on the initial and final states of the system, regardless of the path taken to reach those states. Therefore, the value of Delta U remains the same regardless of the specific conditions or method used to determine it.

Overall, the calculation of Delta U allows us to quantify the change in internal energy of the system during a reaction and gain insight into the thermodynamic properties and behavior of the system.