1 mol zinc reacts with 1 mol sulfuric acid in a bomb calorimeter. I know since volume is constant work done will be zero .. but why will the internal energy decrease?? I know that the reaction is not endothermic or exothermic so there is no heat change involved, and as E = w + Q, the internal energy should also have been unaffected. But in an mcq book, the answer clearly states that the internal energy is decreasing.
Internal energy loosely can be seen as the measure of energy which are stored in the substance. Internal energy is equal to $$\Delta E = q + w ~~~~~~~~(where ~~w = -p\Delta V)$$ Since we know that volume is constant, w = 0. Also, now we need to determine the sign of q. Where you got stuck is saying that the reaction is neither endothermic or exothermic. Any reaction between a strong acid with a reactive metal will be exothermic. This means that heat energy is released from the system into the surroundings (water). That is why the water gets hot and forms the foundation of how the bomb calorimeter works.
Therefore, since we know that heat is transferring from the system to the surroundings, q must be negative. Therefore, $\Delta E$ will be negative, meaning that the internal energy decreased.
If the reaction is exothermic, and the system you choose includes both the insulated chamber and its mixture of reactants and products, then the change in internal energy of this system will be zero. However, if the system you choose includes only the mixture of reactants and products, then heat will be transferred from the mixture to the chamber, and the internal energy of your mixture will decrease.