# Question #7ee50

##### 1 Answer

#### Explanation:

Your goal here is to figure out the enthalpy change of reaction for

#"D + F " -> " G + M", " "DeltaH_"rxn" = ? color(white)(aaaaa)color(red)("(*)")#

by using the *thermochemical equations* that describe the following reactions

#"G + C " -> " A + B" color(white)(aaaa)DeltaH_1 = +"277 kJ"" " " "color(blue)((1))#

#"C + F " -> " A" color(white)(aaaaaaaa)DeltaH_2 = +"303 kJ"" " " "color(blue)((2))#

#color(white)(aaa.)"D " ->" B + M" color(white)(aa.a)DeltaH_3 = - "158 kJ"" " " "color(blue)((3))#

Now, **Hess' Law** tells you that the enthalpy change of a reaction is **independent** of the number of steps needed to get from the products to the reactants.

Simply put, it doesn't matter how you get from the products to the reactants, the enthalpy change will **always** be the same for a given reaction.

Notice that in your target equation, you need **product**, but that equation **flip** equation

When you flip a chemical equation, you **must** change sign of the enthalpy change of reaction!

In this case, *endothermic reaction*, so it will be produced in an *exothermic reaction*.

#"Flip" color(white)(.)color(blue)((1)):" " "A + B " -> " G + C" color(white)(aaaa)DeltaH_"1 flip" = -"277 kJ"#

Now notice what happens when you **add** equation **flipped** and equation

#"A + B " -> " G + C" color(white)(aaaa)DeltaH_"1 flip" = -"277 kJ"#

#"C + F " -> " A" color(white)(aaaaaaaaaa)DeltaH_2 = +"303 kJ"#

#color(white)(aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa)/color(white)(a)#

#color(red)(cancel(color(black)("A"))) + "B" + color(red)(cancel(color(black)("C"))) + "F " -> " G" + color(red)(cancel(color(black)("C"))) + color(red)(cancel(color(black)("A")))#

which is equivalent to

#"B + F " -> " G" #

Since you've **added** the two reactions, you must also 8*add*8 the enthalpy changes of reaction

#DeltaH_"1 flip + 2" = DeltaH_"1 flip" + DeltaH_2#

#DeltaH_"1 flip + 2" = -"277 kJ" + "303 kJ"#

#DeltaH_"1 flip + 2" = +"26 kJ"#

This means that I can get from

Notice that in order to get **add** the above single-step equation and equation

#"B + F " -> " G" color(white)(aaaaaaaa)DeltaH_"1 flip + 2" = +"26 kJ"#

#color(white)(aaaa)"D " ->" B + M" color(white)(aaaaaaaa)DeltaH_3 = - "158 kJ"#

#color(white)(aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa)/color(white)(a)#

#color(red)(cancel(color(black)("B"))) + "D + F " -> " G" + color(red)(cancel(color(black)("B"))) + "M"#

which is equivalent to equation

#"D + F " -> " G + M"#

The enthalpy change for this reaction will be

#DeltaH_"rxn" = DeltaH_"1 flip + 2" + DeltaH_3#

#DeltaH_"rxn" = + "26 kJ" + (-"158 kJ")#

#color(darkgreen)(ul(color(black)(DeltaH_"rxn" = -"132 kJ")))#