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Deduce the Vant Hoff equation. |
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Answer» Solution :This equation GIVES the quantitative temperature dependence of equilibrium constant (K). The relation between standard free energy CHANGE `(DeltaG^(@))` and equilibrium constant is `DeltaG^(@)=-RTlnK`. . . (1) We know that `DeltaG^(@)=DELTAH^(@)-TDeltaS^(@)`. . . (2) Substituting (1) in equation (2) `-RTlnK=DeltaH^(@)-TDeltaS^(@)` Rearranging In `K=(-DeltaH^(@))/(RT)+(DeltaS^(@))/(R)`. . . (3) Dierentiating equation (3) with respect to temperature, `(d("In K"))/(dT)=(DeltaH^(@))/(RT^(2))`. . . .(4) Equation 4 is known as differential from of Van't Hoff equation. On integrating the equation 4, between `T_(1)` and `T_(2)` with integrating the equation 4, between `T_(1)` and `T_(2)` with their respective equilibrium CONSTANTS `K_(1)` and `K_(2)`. `int_(K_(1))^(K_(2))d("In K")=(DeltaH^(@))/(R)int_(T_(1))^(T_(2))(dT)/(T^(2))` `["In K"]_(K_(1))^(K_(2))=(DeltaH^(@))/(R)[-(1)/(T)]_(T_(1))^(T_(2))` `"In "K_(2)-"In "K_(1)=(DeltaH^(@))/(R)-[(1)/(T_(2))+(1)/(T_(1))]` `"In"(K_(2))/(K_(1))=(DeltaH^(@))/(R)[(T_(2)-T_(1))/(T_(2)T_(1))]` `"log"(K_(2))/(K_(1))=(DeltaH^(@))/(2.303R)[(T_(2)-T_(1))/(T_(2)T_(1))]`. . . (5) Equation 5 is known as integrated from of Van't Hoff equation. |
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