Question

The plot of \(\log K\) versus \(\dfrac{1}{T}\) is a straight line. The intercept and slope of this line are respectively given by (Where \(K\) is the equilibrium constant.)

• A. \(\dfrac{\Delta S^\circ}{2.303R},\ -\dfrac{\Delta H^\circ}{2.303R}\)
• B. \(\dfrac{\Delta S^\circ}{R},\ -\dfrac{\Delta H^\circ}{R}\)
• C. \(-\dfrac{\Delta S^\circ}{2.303R},\ \dfrac{\Delta H^\circ}{2.303R}\)
• D. \(-\dfrac{\Delta H^\circ}{2.303R},\ \dfrac{\Delta S^\circ}{2.303R}\)

Hint:

For \(\log K\) vs \(1/T\) plots, intercept gives \(\Delta S^\circ\) and slope gives \(\Delta H^\circ\) — both divided by \(2.303R\).

Answer 1

The Correct Option is A

To solve this problem, we need to understand the relationship between the equilibrium constant \( K \), temperature \( T \), and the thermodynamic quantities enthalpy change \( \Delta H^\circ \) and entropy change \( \Delta S^\circ \). This relationship is commonly known as the Van 't Hoff equation, which relates these quantities in the following way:

The Van 't Hoff equation is expressed as:

\[\log K = \dfrac{\Delta S^\circ}{2.303R} - \dfrac{\Delta H^\circ}{2.303R}\cdot\dfrac{1}{T}\]

Where:

• K is the equilibrium constant.
• \Delta H^\circ is the standard enthalpy change.
• \Delta S^\circ is the standard entropy change.
• R is the universal gas constant (8.314 J/mol·K).
• T is the temperature in Kelvin.

The equation is in the form of a straight line equation \( y = mx + c \), where:

• y is \(\log K\)
• x is \(\dfrac{1}{T}\)
• m is the slope of the plot, which equals \(-\dfrac{\Delta H^\circ}{2.303R}\)
• c is the intercept, which equals \(\dfrac{\Delta S^\circ}{2.303R}\)

Thus, the intercept and slope of the \(\log K\) versus \(\dfrac{1}{T}\) plot are respectively:

• Intercept: \(\dfrac{\Delta S^\circ}{2.303R}\)
• Slope: \(-\dfrac{\Delta H^\circ}{2.303R}\)

Therefore, the correct answer is:

\(\dfrac{\Delta S^\circ}{2.303R},\ -\dfrac{\Delta H^\circ}{2.303R}\)

The other options can be ruled out because they either reverse the roles of enthalpy and entropy in the intercept and slope or misplace the constants. The Van 't Hoff equation specifically relates these quantities in the manner explained above.