FCH 361: Spring, 2013
FINAL EXAM (1.5 hours)
USEFUL DATA: Ideal Gas Constant, R = 0.08206 L atm K-1 mol-1 = 8.314 J K-1 mol-1;
Boltzmann constant, kB = 1.3807x10-23 J K-1; Avogadro’s Number, NA = 6.022x1023 mol-1;
Planck’s constant, h = 6.63x10-34 J s, Mass of electron = 9.109x10-31 kg; Charge on electron =
1.602x10-19 Coulomb (in magnitude); vacuum permittivity 0 = 8.854x10-12 J-1 Coulomb2 m-1;
Speed of light in vacuum, c = 3x108 m s-1
1. Consider the elementary (single-step) reaction: A  2 B. The rate for the forward reaction is
known to follow third-order kinetics with respect to [A] and to be independent of [B]. The rate
of the reverse reaction can be neglected. The initial concentrations of A and B are 10 mol L-1 and
1.0 mol L-1, respectively. Five (5) minutes after the reaction starts, the concentration of B is
found to equal 2.0 mol L-1. Use these data to calculate (i) the rate constant for this reaction, and
(ii) how long it takes for the concentration of B to reach 5.0 mol L-1.
(20)
2. A beam of electrons is travelling linearly, parallel to the x-axis, at a steady speed. Each
electron in the beam is travelling with a steady speed equal to precisely 108 m s-1. Calculate:
(i) the de Broglie wavelength of the electrons in this beam, (ii) the kinetic energy of an electron
in this beam, (iii) the wavelength of a photon for which the energy of the photon equals the
kinetic energy of one of the electrons in the beam, and (iv) the energy of a photon for which the
wavelength equals the de Broglie wavelength of the electrons in the beam.
(20)
3. Consider molecules of oxygen (O2) in the gas phase. The atomic weight for oxygen equals 16
gram mol-1, and the force constant k for the bond between the O atoms equals 1182 N m-1.
Calculate the ratio of the numbers of O2 molecules that are expected to be found in the first
excited vibrational state (vibrational quantum number n = 1) to the number that are expected to
be in the vibrational ground state (vibrational quantum number n = 0) at the following
temperatures: (i) T = 300 K, and (ii) T = 1000 K.
(20)
4. Consider a particle of mass m that is confined to a one-dimensional box of length L. Suppose
that the wavefunction that describes the state of the particle is known to be given by the
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expression:  x   1  x   2  x   a 3  x  , where the quantity “a” is unknown. The functions 1 ,
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2 and 3 represent normalized solutions to the Schrodinger equation for the particle-in-a-box
problem with the quantum numbers n = 1, n = 2, and n = 3, respectively. The wavefunction ψ is
itself also properly normalized. Based on this information:
(i) Suggest a value for the coefficient a, and:
(ii) Calculate the average energy of the particle in the state described by the wavefunction ψ.
(That is: suppose measurements of the energy were performed upon 1000 such particles, each in
the state ψ. What would be the average measured value for the energy, averaged over the
collection of 1000 such measurements upon the 1000 identically prepared particles ?)
(20)
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5. Consider a particle (in one dimension, x) that is known to be located somewhere in the region:
0  x  L . Suppose that it is known that the wavefunction of the particle is of the form:
 x   a x , where the quantity “a” is unknown.
(i) Use the requirement that the wavefunction ψ must be properly normalized to determine the
quantity a, and:
(ii) Calculate the average value of x for the particle in the state described by the wavefunction ψ.
(That is: suppose measurements of x were performed upon 1000 such particles, each in the state
ψ. What would be the average measured value for x, averaged over the collection of 1000 such
measurements upon the 1000 identically prepared particles ?)
(20)
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