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Question

If "$T_m$" is the average absolute temperature, "$R$" is the universal gas constant, then the quantitative relationship between activation Energy, "$E$" and Z - value is :

The correct answer is
$$E = \frac{2.3 R T_m^2}{Z}$$

Solution: Activation Energy and Z-Value Relationship

The question asks for the quantitative relationship between Activation Energy ($E$), average absolute temperature ($T_m$), the universal gas constant ($R$), and the Z-value.

The specific quantitative relationship presented in the options is derived from kinetic theories or specific models of reaction rates. The correct formula is:

$E = \frac{2.3 R T_m^2}{Z}$

Where:

  • $E$ denotes the Activation Energy.
  • $R$ represents the universal gas constant.
  • $T_m$ is the average absolute temperature.
  • $Z$ is the Z-value. In chemical kinetics contexts, this often relates to the collision frequency factor or steric considerations. The factor 2.3 commonly appears when converting between natural logarithms and base-10 logarithms.

This equation indicates that activation energy ($E$) is directly proportional to the square of the average absolute temperature ($T_m^2$) and inversely proportional to the Z-value ($Z$), scaled by the universal gas constant ($R$) and the factor 2.3.

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Important Questions from Miscellaneous

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