Answer:- Second choice, 104 = -2222 -[X +(-1144)] is correct.
Solution:-It's based on Hess's law. For solving this type of problems, we adjust all the equations for which the delta H value is given, in a way so that we get the equation for which delta H is asked to calculate. For this, we might have to multiply or divide the equations and some times the equations might also be required to flip means reactants and products are switched.
The equation for which we are asked to calculate delta H, has 3C and [tex]3O_2[/tex] on reactant side.
If we look at the three given equations then third equation has 3C on product side. Since, we need 3C on reactant side, this third equation needs to be flipped. When an equation is flipped then sign of delta H is changed. This equation looks as:
[tex]3C+4H_2\rightarrow C_3H_8 (\Delta H=-104kJ)[/tex]
Our equation does not have propane so to cancel it, we need to write the second equation same as it's given:
C_3H_8+5O_2\rightarrow 3CO_2+4H_2O(\Delta H=-2222 kJ)
Our desired equation also does not have water. So, to cancel out water, we need the first equation but it has to flip so that we could have water on opposite side:
[tex]4H_2O\rightarrow 4H_2+2O_2(\Delta H=1144kJ)[/tex]
To get the delta H of our desured equation we add all the delta H values we have here from all three new equations:
[tex]\Delta H=(-104kJ)+(-2222kJ)+(1144kJ)[/tex]
If we write X in place of [tex]\Delta H[/tex] then:
X = -104 -2222 + 1144
It could rearranged as:
104 = -2222 - X + 1144
So, the only correct option is the second option, 104 = -2222 - X + 1144 . It can also be written as:
104 = -2222 -[X +(-1144)]
