The free energy change for the following reaction are given below:
`C_(2)H_(2)(g)+(5)/(2)O_(2)(g) to 2CO_(2)(g)+H_(2)O(l),DeltaG^(@)=-1234J`
`C(s)+O_(2)(g)toCO_(2)(g),DeltaG^(@)=-394kJ`
`H_(2)(g)+(1)/(2)O_(2)(g)toH_(2)O(l),DeltaG^(@)=-237kJ`
what is the standard free energy change for the reaction?
`H_(2)(g)+2C(s)toC_(2)H_(2)(g)`

Options

A. `-209kJ`
B. `-2259kJ`
C. `+2259kJ`
D. `209kJ`

Answer

D

Explanation

`C_(2)H_(2)(g)+(5)/(2)O_(2)(g) to 2CO_(2)(g)+H_(2)O(l),DeltaG^(@)=-1234kJ` . . (i)
`C(s)+O_(2)(g) to CO_(2)(g),DeltaG^(@)=-394kJ` . . (ii)
`H_(2)(g)+(1)/(2)O_(2)(g) to H_(2)O(l),DeltaG^(@)=-237kJ` . . (iii)
Eqs. (ii)+(iii)-(i).
`2C(s)+H_(2)(g)toC_(2)H_(2)(g)`
`DeltaG^(@)=2(-394)+(-237)-(-1234)=209kJ`.