Given: (1) `A(s)+B_(2)(g) to AB_(2)(g),DeltaH^(0)=-xkJ`
(2) `A(s)+(3)/(2)B_(2)(g)toAB_(3)(g),DeltaH^(0)=-ykJ`
Using above equations, determine standard reaction enthalpy for the reaction:
`2AB_(3)(g)to2AB_(2)(g)+B_(2)(g)`.

Explanation

Multiplying equation (1) by 2, we get
`2A(s)+2B_(2)(g)to2AB_(2)(g),DeltaH^(0)=-2xkJ` . . . [3]
Writing equation (2) in the reverse manner and multiplying both sides by 2, we get,
`2AB_(2)(g)to2A(s)+3B_(2)(g),DeltaH^(0)=+2ykJ` . .[4]
Adding equations [3] and [4], we get,
`2A(s)+2B_(2)(g)+2AB_(3)(g)to2A(s)+2AB_(2)(g)+3B_(2)(g),DeltaH^(0)=(2y-2x)kJ`
`therefore 2AB_(3)(g)to2AB_(2)(g)+B_(2)(g),DeltaH^(0)=2(y-x)kJ`
Therefore, the standard reaction enthalpy for the given reaction=2(y-x)kJ.