Chemistry Effect of temperature change in Le Chatelier's Principle

AI Thread Summary
The discussion focuses on the relationship between temperature changes and equilibrium constants in the context of Le Chatelier's Principle, expressed by the equation involving ΔH, R, and temperatures T1 and T2. Participants seek to understand how to derive this equation, which illustrates how the equilibrium constant (K) varies with temperature due to changes in enthalpy (ΔH). The Clausius-Clapeyron equation is mentioned as a relevant concept for this derivation. The challenge lies in applying these principles to accurately calculate the shifts in equilibrium constants with temperature variations. Understanding this relationship is crucial for predicting the behavior of chemical systems under different thermal conditions.
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Homework Statement
How to derive $$
\log \left(\frac{\mathrm{K}_{2}}{\mathrm{~K}_{1}}\right)=\frac{\Delta \mathrm{H}}{2.303 \mathrm{R}}\left[\frac{1}{\mathrm{~T}_{1}}-\frac{1}{\mathrm{~T}_{2}}\right]
$$
Relevant Equations
$$
\log \left(\frac{\mathrm{K}_{2}}{\mathrm{~K}_{1}}\right)=\frac{\Delta \mathrm{H}}{2.303 \mathrm{R}}\left[\frac{1}{\mathrm{~T}_{1}}-\frac{1}{\mathrm{~T}_{2}}\right]
$$
The effect of temperature change in Le Chatelier's Principle is given by the equation $$ \log \left(\frac{\mathrm{K}_{2}}{\mathrm{~K}_{1}}\right)=\frac{\Delta \mathrm{H}}{2.303 \mathrm{R}}\left[\frac{1}{\mathrm{~T}_{1}}-\frac{1}{\mathrm{~T}_{2}}\right] $$. How to derive $$ \log \left(\frac{\mathrm{K}_{2}}{\mathrm{~K}_{1}}\right)=\frac{\Delta \mathrm{H}}{2.303 \mathrm{R}}\left[\frac{1}{\mathrm{~T}_{1}}-\frac{1}{\mathrm{~T}_{2}}\right] $$. I am not able to derive it as equilibrium constant changes.
 
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