Answered: By using photons of specific…

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Question

By using photons of specific wavelengths, chemists can dis-sociate gaseous HI to produce H atoms with certain speeds.When HI dissociates, the H atoms move away rapidly, whereasthe heavier I atoms move more slowly. (a) What is the longestwavelength (in nm) that can dissociate a molecule of HI? (b) If aphoton of 254 nm is used, what is the excess energy (in J) overthat needed for dissociation? (c) If this excess energy is carriedaway by the H atom as kinetic energy, what is its speed (in m/s)?

Expert Solution

Step 1

The bond energy of HI = 295 kJ/mol.

The energy of 1 molecule of HI using the Avogadro's number:

$\begin{array}{rcl} E {(HI)}_{molecule} & = & \frac{295 \times 10^{3} J}{6.023 \times 10^{23}} \\ = & 48.979 \times 10^{- 20} J / molecule . \end{array}$

Step 2

a) Then, the maximum wavelength per molecule is:

$\begin{array}{rcl} λ & = & \frac{h c}{E} \\ λ & = & \frac{6.626 \times 10^{- 34} J . s \times 3 \times 10^{8} m / s}{4.8979 \times 10^{- 19} J / molecule} \\ = & 4.058 \times 10^{- 7} m \\ = & 405.8 nm \end{array}$

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