Most chemical reactions require activation energies ranging...

Most chemical reactions require activation energies ranging between 40 and $400 \mathrm{kJ} \mathrm{mol}^{-1} .$ What are the equivalents of 40 and $400 \mathrm{kJ} \mathrm{mol}^{-1}$ in terms of $(a) \mathrm{nm},(b)$ wave numbers, and $(c)$ electron volts?

Key Concepts

Avogadro's Number

Avogadro's number is the constant that defines the number of particles in one mole (approximately 6.022×10^23). It is essential when converting energy values expressed on a per-mole basis to energy per individual particle or photon, thereby linking macroscopic measurements with microscopic energies.

Planck's Equation

Planck's equation, E = hc/?, relates the energy of a photon (E) to its wavelength (?) through Planck’s constant (h) and the speed of light (c). This relationship is fundamental when converting between energy quantities and wavelength or wave number, making it crucial in spectroscopic and photochemical calculations.

Wave Numbers

Wave numbers, typically expressed in inverse centimeters (cm?¹), are a spectroscopic unit that denote the number of waves per unit distance. They are directly related to energy through the relation E = hc?, where ? (nu) represents the wave number, providing a convenient way to express energy in spectroscopic studies.

Activation Energy

Activation energy is the minimum amount of energy required to initiate a chemical reaction. It represents the barrier that reactants must overcome to be transformed into products, and plays a central role in determining the rate at which a reaction proceeds.

Energy Unit Conversion

Energy unit conversion involves translating energy values from one set of units to another (e.g., from kilojoules per mole to electron volts, inverse nanometers, or wave numbers). This process requires the use of fundamental physical constants and conversion factors such as Avogadro’s number and the relationships involving Planck’s constant and the speed of light.

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