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

Options

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

Answer

D

Explanation

(I) `C_(2)H_(2) (g) + 5/2 O_(2) (g) to 2CO_(2) (g) + H_(2)O (l)`,
`DeltaG^(@) = -1234` kJ
(II) `C(s)+ O_(2) (g) to CO_(2) (g), DeltaG^(@) = -394 kJ`
(III) `H_(2) (g) + 1/2 O_(2) (g) to H_(2)O (l) , DeltaG^(@) = -237 kJ`
Multiply the equation (11) by 2 and then add with equation (III) and subtract equation (1) from the sum of (II) and (III)
`2C(s) + H_(2)(g) to C_(2)H_(2)(g)`
`DeltaG^(@) =2(-394) + (-237) - 1234`
`DeltaG^(@) = 209` kJ