Which of the following relationship(s) describe the quantitative effect of temperature on the equilibrium constant?

\frac{d l n K_{P}}{d T} = \frac{Δ H}{R T^{2}}

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\frac{d l n K_{P}}{d T} = \frac{Δ E}{R T^{2}}

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\frac{d l n K_{C}}{d T} = \frac{Δ E}{R T^{2}}

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\frac{d l n K_{C}}{d T} = \frac{Δ H}{R T^{2}}

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Solution

The correct options are
A $\frac{d l n K_{P}}{d T} = \frac{Δ H}{R T^{2}}$
C $\frac{d l n K_{C}}{d T} = \frac{Δ E}{R T^{2}}$
The quantitative effect of temperature on the equilibrium constant is given by van't Hoff equation. It is given by the expression $\frac{d l n K_{P}}{d T} = \frac{Δ H}{R T^{2}} .$
The integrated form of the equation is $l o g \frac{K_{2}}{K_{1}} = + \frac{Δ H}{2.303 R} [\frac{1}{T_{1}} - \frac{1}{T_{2}}] = \frac{Δ H}{2.303 R} [\frac{T_{2} - T_{1}}{T_{1} T_{2}}]$ .
Here, $K_{1}$ and $K_{2}$ are the values of the equilibrium constants at temperatures $T_{1}$ and $T_{2}$ respectively. $Δ H$ is the enthalpy of the reaction and R is the ideal gas constant. The quantitative effect of temperature on the equilibrium constant can also be represented by using the cell potential E. The expression is $\frac{d l n K_{C}}{d T} = \frac{Δ E}{R T^{2}} .$

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Similar questions

Consider the following liquid-vapour equilibrium.

$L i q u i d \to V a p o u r$

Which of the following relations is correct?

L i q u i d ⇌ V a p o u r

\frac{d}{d T} ln K_{c} = Δ H / R T^{2}

$Δ G = Δ H - T Δ S$ and $Δ G = Δ H + T {[\frac{d (Δ G)}{d T}]}_{p}$ , then $(\frac{d E_{c e l l}}{d T})$ is:

Δ E a n d Δ H

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