Consider the reaction `AhArr B` at 1000 K. At time 't' the temperature of the system was increased to 2000 K and the system was allowed to reach equilibrium. Throughout this experiment the partial pressure of A was maintained at 1 bar. Given below is the plot of the partial pressure of B with time.
What is the ratio of the standard Gibbs energy of the reaction at 1000 K to that at 2000 K ?

Answer

0.25

Explanation

Use `DeltaG^(@)=-RT ln K_(P)" at equilibrium"`
`DeltaG_(1)^(@)=-RT_(1) ln K_(P_(1))" ….(1)"`
`DeltaG_(2)^(@)=-RT_(2) ln K_(P_(2))" ….(2)"`
`(DeltaG_(1)^(@))/(DeltaG_(2)^(@))=(T_(1))/(T_(2))xx(lnK_(P_(1)))/(lnK_(P_(2)))`
`=(1000)/(2000)xx(ln(10))/(ln(100))`
`=(1)/(2)xx(1)/(2)=(1)/(4)=0.25`