The free energy change for the following reactions are given below
`C_(2)H_(2)(g)+(5)/(2)O_(2)(g)to2CO_(2)(g)+H_(2)O(l)`, `DeltaG^(@)=-1234 kJ`
`C(s)+O_(2)(g)toCO_(2)(g)`, `DeltaG^(@)=-394 kJ`
`H_(2)(g)+(1)/(2)O_(2)(g)toH_(2)O(l)`, `DeltaG^(@)=237 kJ`
What is the standard free energy change for the reaction
`H_(2)(g)+2C(s)toC_(2)H_(2)(g)` ?

Options

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

Answer

D

Explanation

`(1) C_(2)H_(2)(g)+(5)/(2)O_(2)(g)to2CO_(2)(g)+H_(2)O(l)` , `DeltaG^(@)=1234 kJ`
`(2) C(s)+O_(2)(g)toCO_(2)(g)` , `DeltaG^(@)=-394 kJ`
`(3) H_(2)(g)+(1)/(2)O_(2)(g)toH_(2)O(l)` , `DeltaG^(@)=-237 kJ`
To get : `H_(2)(g)+2C(s)toC_(2)H_(2)`, `DeltaG=?`
Solve Eq. No. `(3)+2xx"Eq. No."(2)-"Eq.No."(1)`
`DeltaG=(-237kJ)+2xx(-394kJ)-(-1234 kJ)`
`=-237kJ-0.788kJ+1234kJ=209kJ`