Determine whether ∆H is equal to, greater than, or less than ∆U for the following reactions. Keep in

mind that “greater than” means more positive or less negative, and “less than” means less positive or
more negative. Assume that the only significant change in volume during a reaction at constant pressure
is that associated with changes in the amounts of gases:
(a) The complete combustion of one mole of 1–butanol (l):

(b) The complete combustion of one mole of glucose, C6H12O6 (s):

(c) The decomposition of solid ammonium nitrate to produce liquid water and gaseous dinitrogen monoxide:

To determine whether ∆H is equal to, greater than, or less than ∆U for each reaction, we need to compare the enthalpy change (∆H) and the internal energy change (∆U).

∆H represents the change in enthalpy, which is the heat transfer at constant pressure. ∆U represents the change in internal energy, which is the heat transfer at constant volume.

For reactions at constant pressure, if ∆H is greater than ∆U, it means that the reaction is releasing more heat (exothermic) and has a negative value. If ∆H is less than ∆U, it means that the reaction is absorbing more heat (endothermic) and has a positive value. If ∆H is equal to ∆U, it means that the heat transfer at constant pressure is the same as the heat transfer at constant volume.

Now, let's analyze each reaction:

(a) The complete combustion of one mole of 1-butanol (l):
During combustion reactions, heat is released, so they are usually exothermic. In this case, energy is being released as heat, and the products are carbon dioxide and water. Therefore, ∆H is likely to be negative (less than ∆U).

(b) The complete combustion of one mole of glucose, C6H12O6 (s):
Similar to the previous reaction, combustion of glucose releases heat. The products of this reaction are carbon dioxide and water. Again, ∆H is likely to be negative (less than ∆U).

(c) The decomposition of solid ammonium nitrate to produce liquid water and gaseous dinitrogen monoxide:
In this case, we have a decomposition reaction. Decomposition reactions usually require energy input and are endothermic. Ammonium nitrate decomposes into water and dinitrogen monoxide. Therefore, ∆H is likely to be positive (greater than ∆U).

To summarize:
(a) ∆H is less than ∆U (negative)
(b) ∆H is less than ∆U (negative)
(c) ∆H is greater than ∆U (positive)

Please note that these predictions are based on the general trends of these reaction types. The exact values can only be determined through experimental measurements or thermodynamic calculations.