I am not to sure how to approach the problem...

Hydrazine is used as a rocket fuel because its reaction with oxygen is extremely exothermic:
N2H4(liquid) + O2(g) ==> N2(g) + 2H2O(liquid) ΔH(reaction) = -615 kJ mol-1
What is the enthalpy of this reaction if water were produced in the gaseous rather than the liquid form? Note that 40.7 kJ mol-1 is the molar enthalpy of vaporization of water.

Think of some of the energy released has been used to transform water(l) to water(g) and adjust accordingly.

Watch the stoichiometric coefficient of H2O.

got it, thank you

To determine the enthalpy of the reaction if water were produced in the gaseous form instead of liquid, you need to account for the molar enthalpy of vaporization of water.

First, let's define the enthalpy change for the reaction when water is produced in the liquid form:

N2H4(liquid) + O2(g) → N2(g) + 2H2O(liquid) ΔH(reaction) = -615 kJ mol-1

Now, we need to consider the enthalpy change for the transformation of liquid water to gaseous water. The molar enthalpy of vaporization of water (ΔHvap) is 40.7 kJ mol-1. This value represents the amount of energy required to convert one mole of liquid water to vapor at a constant temperature and pressure.

Since two moles of water are produced in the reaction, we need to multiply the molar enthalpy of vaporization (40.7 kJ mol-1) by 2 to account for the enthalpy change when both moles of liquid water are converted to gaseous form. Thus, the enthalpy change for the transformation of liquid water to gaseous water is:

2 mol H2O(liquid) × ΔHvap = 2 × 40.7 kJ mol-1 = 81.4 kJ

Now, we can calculate the enthalpy of the reaction if water were produced in the gaseous form. To do this, we subtract the enthalpy change for the transformation of liquid water to gaseous water from the original enthalpy of the reaction:

ΔH(reaction with gaseous water) = ΔH(reaction with liquid water) - Enthalpy change for vaporization
= -615 kJ mol-1 - 81.4 kJ
= -696.4 kJ mol-1

Therefore, the enthalpy of the reaction if water were produced in the gaseous form is -696.4 kJ mol-1.