Question

Use the simple transition-state theory to calculate the rate constant for the hydrogen exchange reaction: H+H₂⇋H₂+H The barrier height is 38.2 kJ mol⁻¹at 300 K. The activated complex structure is a

symmetric linear arrangement of the three atoms with the internuclear distance of 0.90×10⁻¹⁰ m. The vibrational wave numbers for H₃ are 2184 cm⁻¹(symmetric stretch) and
979 cm⁻¹ (doubly degenerate bend). H₂ has only one vibrational mode and its vibrational wave number is 4395.2 cm⁻¹. The H₂ equilibrium distance is 0.7416 x 10⁻¹⁰ m. The electronic partition functions of H and H₃ are 2. qₜ=(2πmkt/h²)³/² V qᵣ=8π²IkT/σh² qᵥ=1/1e⁻ʰᵛ/ᵏᵀ

Answer 1

The rate constant for the hydrogen exchange reaction can be calculated using the simple transition-state theory. The given information about the barrier height, activated complex structure, vibrational wave numbers, and electronic partition functions can be used to determine the necessary values for the calculations.

Step-by-step explanation:

The simple transition-state theory can be used to calculate the rate constant for the hydrogen exchange reaction. The rate constant can be obtained using the equation: k = (kBT/h) * e(-ΔG‡/RT), where kB is the Boltzmann constant, T is the temperature in Kelvin, h is the Planck's constant, ΔG‡ is the barrier height, R is the gas constant, and e is the base of the natural logarithm.

In this case, the barrier height is given as 38.2 kJ mol-1 at 300 K. Converting the barrier height to J (joules), we have ΔG‡ = (38.2 * 1000) J mol-1. Plugging this value along with the other constants into the equation, we can calculate the rate constant.

Using the given information for the activated complex structure, vibrational wave numbers, and partition functions, we can obtain the necessary values to perform the calculations. It is important to note that the partition functions for H and H₃ depend on their electronic states and vibrational modes.

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