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Deduce the Vant Hoff's equation. |
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Answer» Solution :This equation gives the equntitaive temperature dependance of equilibrium constant K. The relation between standard free ENERGY change `DeltaG^@` and equilibrium constant is `DeltaG^@ = -RT InK`…(1) We know that, `DeltaG^@ = DELTAH^@ -TDeltaS^@`...(2) Substituting (1) in equation (2) `-RT InK= DeltaH^@ - TDeltaS^@` Rearranging, `In K= (-DeltaH^@)/(RT)+ (DeltaS^@)/R`...(3) DIFFERENTIATING equation (3) with respect to temperature `(d(InK))/(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 their respective equilibrium constant `K_1 and K_2` `underset(K_1)OVERSET(K_2)intd(InK) = (DeltaH^@)/(R)underset(T_1)overset(T_2)int (dT)/T^2` `[InK]_(K_1)^(K_2) = (DeltaH^@)/R [-1/T]_(T_1)^(T_2)` `InK_2 - In K_1 = (DeltaH^@)/R [-1/T_2+1/T_1]` `In K_2/K_1 = (DeltaH^@)/R[(T_2-T_1)/(T_2T_1)]` `log""(K_2)/K_1 = (DeltaH^@)/(2.303R) [(T_2-T_1)/(T_2T_1)]`...(5) Equation (5) is known as integrated from of van.t Hoff equation. |
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