Instructions For Writing Final Examinations

Do any four of A1 to A5, 10 marks each. For more space, use the back of the previous page.

  1. To calculate the size of a sphere that just fits in a tetrahedral site, we place four spheres of radius r at alternate corners of a cube, and a small sphere with radius r in the tetrahedral site, which is at the centre of the cube. [Each part is worth 2 marks]
    1. What is the length of the face diagonal in terms of r? Draw a diagram to show why.
    2. What is the cubic edge length, a, in terms of r? Show details of your derivation.
    3. What is the body diagonal in terms of only r?
    4. What is the length of body diagonal of the cube in terms of both r and t?
    5. Express t in terms of r.

  2. The formation of HI from its elements is believed to follow the mechanism. [2 marks each]
    I2(g) ® 2 I(g) k1
    2 I(g) ® I2(g) k2
    H2(g) + 2 I(g) ® 2 HI(g) k3
    1. Give the overall reaction equation.
    2. Give the rate expression for - d[H2]/dt
    3. Apply the steady-state approximation and derive the expressin for [I].
    4. Derive the rate law from the given mechanism.
    5. E. Under what condition does the rate law become rate = k [I2]?

  3. A 1.00-L reaction flask containing 0.100-mol of phosphorus pentachloride, PCl5, is allowed to come to equilibrium at 525 K: PCl5 (g) = PCl3 (g) + Cl2(g). The amount of chlorine in the equilibrium mixture is 0.047 mol as determined by experiment.
    1. What is the equilibrium concentration of PCl5 (g).
    2. Calculate the partial pressure of PCl2 (g).
    3. Calculate the value of equilibrium constant Kc.
    4. Calculate the value of equilibrium constant Kp.
    5. The volume of the mixture is allowed to expand to 2.00 L by opening a valve connected to another identical container. What is the value of Kc when equilibrium is re-established at the same temperature? Show details of calculation or explain why.

  4. The pKa of trichloroacetic acid, CCl3COOH, is 0.7 at 298 K. You are provided with a 20.00 mL solution whose concentration is 0.100 M.
    1. Calculate the pH of the trichloroacetic acid solution.
    2. Calculate the Ka value for trichloroacetic acid.
    3. Calculate the pH of the solution after 5.00 mL of 0.100 NaOH solution has been added to your sample.
    4. What is the pH of the solution after 15.00 mL of 0.100 NaOH solution has been added to your sample.
    5. What is the pH of the solution after 20.00 mL of 0.100 NaOH solution has been added to your sample.

  5. For the galvanic cell Pt | H2 (1 atm) | H+ (1 M) || Ag+ (0.10) | Ag
    1. What is the standard cell potential of the cell?
    2. What is the cell potential of the Galvanic cell?
    3. What are the half reactions for the electrodes?
    4. What is the overall chemical reaction for the cell?
    5. Give the expression for Q?

  6. The sodium chloride structure is common to many substances, including the structures of metal oxides with formula MO.
    1. Draw a 3-dimensional diagram show the arrangement of the Na+ and Cl- ions.
    2. If the radii of Na+ and Cl- are r+ and r- respectively, what is teh edge length, a, of the face-centred unit cell of NaCl?
    3. How many Na+ and how many Cl- ions are there in a fcc unit cell?
    4. Iron crystallizes in a body-centred cubic structure with unit cell edge of 286 pm. Estimate the radius of iron atom.
    5. What is the distance between the centres of the two neighboring iron atoms?

  7. The data below were obtained for the decomposition of N2O5 at 318 K.
       t =    0     600   1200   2400   3600   4800   6000   7200
    P(N2O5) 0.348 0.257  0.190  0.105  0.058  0.033  0.018  0.010 Atm
    
    1. What is the rate law for the reaction? Give arguments for your answer.
    2. What is the rate constant at 318 K? Show detail calculation.
    3. The proposed mechanism is N2O5 -k1-> NO2 + NO3
      NO2 + NO3 -k-1-> N2O5
      These two steps reach fast equilibrium.
      NO3 -k2-> NO + O2
      NO + NO3 -k3-> 2 NO2
      Apply the steady state approximation to both NO and NO3 to derive the rate law. Comment on this in view of your answer in the first part
    4. The rate constants as a function of temperature were determined
          T/K    338      308      273
          k     3.64e-4  3.11e-5  1.15e-6
      
      Determine the activation energy for the reaction.

  8. A solution contains 0.100 M each of Cd(NO3)2, Mn(NO3)2, and Zn(NO3)2. The H2S gas is added in very small amounts to and dissolved in the solution.
    1. What is the first trace of precipitate formed?
    2. Calculate the maximum value of [S2-] before any precipitate is formed.
    3. Calculate [S2-] just before the last metal ion forms a precipitate.
    4. Calculate the concentrations of the first two metal ions just before the last metal ions forms a precipitate.
    5. It is desirable to separate one of the metal ions by precipitation. At what pH should the solution be maintained if a saturated
      H2S solution has a total concentration of 0.10 M?

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