Van't Hoff equation is

Options

A. `((d)/(dT)) `in k =`(-Delta H)/(RT^(2)) `
B. `((d)/(dT)) `in k =+`(-Delta H)/(RT^(2)) `
C. `((d)/(dT)) `in k =`(-Delta H)/(RT) `
D. K = A. `e^(-(Delta H)/(RT))`

Answer

**Step-by-Step Solution:**

1. **Understanding Van't Hoff Equation**: The Van't Hoff equation describes how the equilibrium constant (K) of a chemical reaction changes with temperature. It is particularly useful in thermodynamics and chemical kinetics.

2. **Components of the Equation**: The equation relates the change in the equilibrium constant (K) to the change in temperature (T) and the standard enthalpy change (ΔH) of the reaction.

3. **Formulation**: The Van't Hoff equation can be expressed mathematically as:
\[ \frac{d \ln K}{dT} = \frac{\Delta H}{RT^2} \]
where:
- \( K \) = equilibrium constant
- \( T \) = absolute temperature (in Kelvin)
- \( R \) = ideal gas constant (8.314 J/(mol·K))
- \( \Delta H \) = standard enthalpy change of the reaction

4. **Interpretation of the Equation**: This equation indicates that the rate of change of the natural logarithm of the equilibrium constant with respect to temperature is directly proportional to the standard enthalpy change of the reaction and inversely proportional to the square of the temperature.

5. **Historical Context**: The Van't Hoff equation was proposed by the Dutch chemist Jacobus Hendrikus van 't Hoff in 1884, which is significant in the field of physical chemistry.

**Final Form of the Van't Hoff Equation**:
\[ \frac{d \ln K}{dT} = \frac{\Delta H}{RT^2} \]

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