F Y I

Last update 6:30pm Jan. 31, 1998; more to do yet!

Term Test Example Problems

In the DOS version, the problems are placed in the DIALOGUE, and you may work on the problems as you usually do in other modules.

There is no indication as to what is covered in this module, and that is intentional. It's only a practice, and you might use the dialogue as if you are writing the term test.

As a practice, try to time yourself. Record the number of questions you have answered in 50 minutes. Keep track of your score as you do the problems. It might give you an indication as to the real situation.

Some of the problems are related to acid-base equilibrium. Chapters on acid and base have not been covered yet in 1998.

Confidence Building Questions

• Which group of substances is correctly arranged in order from the highest to the lowest boiling point?
  a. HF > H₂ > NaF
  b. HF > NaF > H₂
  c. NaF > HF > H₂
  d. NaF > H₂ > HF
  e. H₂ > NaF > HF
  
  

  Hint...
  NaF : ionic bond; HF : polar covalent bonding : H₂ : covalent Check the list in c, and give reason for that order.

  Answer c
  Consider...
  Excellent NaF : ionic bond; HF : polar covalent bonding : H₂ : covalent

• Which one of the following has the highest molar heat of vaporization
  a. An ionic melt, such as NaNO₃
  b. A molecular liquid, such as CCl₄
  c. A monoatomic liquid, such as liquefied argon
  d. A hydrogen-bonded liquid, such as pure acetic acid
  e. A hydrogen-bonded liquid, such as water
  
  

  Hint...
  An ionic melt requires more energy.

  Answer a
  Consider...
  Name the intermolecular forces and compare their strength of interaction.

• How many ions are there in one unit cell of solid sodium chloride?
  a. One sodium and one chloride
  b. Two sodiums and two chlorides
  c. Two sodiums and four chlorides
  d. Four sodiums and four chlorides
  e. Thirteen sodiums and fourteen chlorides
  
  

  Hint...
  Please refer to your lab manual for the answer. 4 Na⁺ and 4 Cl^-.

  Answer d
  Consider...
  Describe the crystal structure of NaCl.

• Which one of the following sets shows the three cubic unit cells arranged in order of increasing fraction of occupied space?
  

  a.  Simple        < face-centered < body-centered
  b.  Simple        < body-centered < face-centered 
  c.  Body-centered < simple        < face-centered 
  d.  Body-centered < face-centered < simple        
  e.  Face-centered < body-centered < simple
  

  
  

  Hint...
  Is the list in b reasonable?.

  Answer b
  Consider...
  Describe the simple cubic, body centered cubic and face centered cubic structures in terms of sphere packing. Which one occupies the least space?

• Identical hard spheres are arranged in each of the cubic lattices. In which one of the following series does the density increase from left to right? Abbreviations: sc = simple cubic, bcc = body-centred cubic,

    fcc = face-centred cubic
    -------------->
  a. fcc   bcc  sc
  b. bcc   fcc  sc
  c. fcc   sc   bcc
  d. sc    bcc  fcc
  e. sc    fcc  bcc
  

  Hint...
  The sc arrangement occupies the most space, whereas the fcc type takes the least space.

  Answer d
  Consider...
  A test to see if you know the various arrangement.

• In an ideal NaCl structure, Cl^- ions are arranged in a closest-packed, face-centred cubic lattice and Na⁺ ions occupy the octahedral sites of the Cl^- lattice. If the radius of Cl^- is r_- and the radius of Na⁺ ions is r₊, what is the edge length of the unit cell?

  a. 2 r- + r+
  b. 2 r- + 2 r+
  c. 2 r- - 2 r+
  d. (r-2 + r+2)1/2
  e. 2 (r-2 + r+2)1/2
  

  Hint...
  Draw a diagram of one face of the unit cell. Along the edge, is two half of one type of ions, and one whole one.

  Answer b
  Consider...
  Test your understanding of the NaCl structure.

• A metal has a face-centered cubic lattice, a density of 11.4 g/mL, and an atomic radius of 175 pm. What is its relative atomic mass? [Avogadro number = 6.022e23]

  a.  207.2 g / mol
  b.  197.0 g / mol
  c.  107.9 g / mol
  d.  106.4 g / mol
  e.   72.6 g / mol
  

  
  

  Hint...
  For a face-centered cubic lattice, edge = 2.82 r, ===> Volume = (2.82 r)³. Since, 1 pm = 10^-12 m or 10^-10 cm, and density = mass / Vol. Remember, there are 4 atoms per unit cell for a face-centered cubic lattice.

  Answer a
  Consider...
  What element is it: lead, gold, silver, palladium, or germanium?

• For the reaction Cl₂ + CO = Cl₂CO, the rate law is: rate = k [Cl₂]^3/2 [CO]. What are suitable units for the rate constant, k?
  a. M^-5/2 s^-1
  b. M^+5/2 s^-1
  c. M^-3/2 s^-1
  d. M^+3/2 s^-1
  e. M^-1 s^-1
  
  

  Hint...
  
  

  Hint...
  The rate must have the unit M s^-1. What are the units for k so that the units for rate is M s^-1?

  Answer c
  Consider...
  The units for k are hints of the order of the reaction.

• Choose the correct equation for the reaction 3O₂ (g) ---> 2O₃ (g)

  a. Rate         = k [O2]3
  b. Rate         = k [O2]3 - [O3]2 / k
  c. 1/2 d[O3]/dt = - 1/3 d[O2]/dt
  d. d[O2]/dt     = - d[O3]/dt
  e. d[O3]/d[O2]  = 1
  

  
  

  Hint...
  One of these gives you the proper relationship.

  Answer c
  Consider...
  For the reaction a A + b B = c C, what is the relationship between d[A]/dt and d[C]/dt? Make sure you know how to represent rate.

• What is the rate law for the reaction 2N₂O₅(g) ----> 4 NO₂ (g) + O₂ (g) from the data below:

       [N2O5]o/M  [O2]o/M  Initial rate  M-1 s-1
       --------  --------  ----------------
    1.  0.15      0.30          46
    2.  0.20      0.60          61
    3.  0.20      0.30          61
  a.   Rate  = k(exp) [N2O5]
  b.   Rate  = k(exp) [N2O5]2
  c.   Rate  = k(exp) [N2O5] [O2]
  d.   Rate  = k(exp) [N2O5]2 [O2]
  e.   Rate  = k(exp) [N2O5] [O2]-1
  

  
  

  Hint...
  The rate does not depend on [O₂] and is first order respect to [N₂O₅]. Use 2 and 3 to show that the rate is independent of [O₂] and use 1 and 3 to show that the rate is first order with respect to [N₂O₅] Try a.

  Answer a
  Consider...
  To find out the rate, you may also use the Trial and Error method by assuming the orders to be 1 or 2.

• What is the approximate value for k(exp) for the reaction (in seconds, molarity as appropriate), 2N₂O₅(g) ----> 4 NO₂ (g) + O₂ (g) ?

       [N2O5]o/M  [O2]o/M  Initial rate  M-1 s-1
       --------  --------  ----------------
    1.  0.15      0.30          46
    2.  0.20      0.60          61
    3.  0.20      0.30          61
  You need to figure out the order.
  a.  300
  b.  500
  c.  1000
  d.  2000
  e.  5000
  

  
  

  Hint...
  use 46 / 0.15 or 61 / 0.20 gives a an approximated value for k. Try a.

  Answer a
  Consider...
  What is rate when [N₂O₅] = 0.50 mole?

• What is the half-life for run 1 of this reaction 2N₂O₅(g) -> 4 NO₂ (g) + O₂ (g)?

       [N2O5]o/M  [O2]o/M  Initial rate  M-1 s-1
       --------  --------  ----------------
    1.  0.15      0.30          46
    2.  0.20      0.60          61
    3.  0.20      0.30          61
  Figure out the order.
  a.  500s
  b.  22 * 10-3 s
  c.  11 * 10-3 s
  d.  2.3 * 10-3 s
  e.  0.35* 10-3 s
  

  Hint...
  Half-life of a first order reaction does not depend on concentration. t(1/2) = ln 2 / k

  Answer d
  Consider...
  What is the half-life if k = 0.100 /s?

• In a first order decomposition, A(g) ---> X(g) + Y(g). [A] decreases from 0.05 M to 0.02M in 100s. How long is required for [Y] to increase from 0 to 0.025 M?

  a. 0.69 s
  b. 25 s
  c. 76 s
  d. 120 s
  e. 157 s.
  

  
  

  Hint...
  From information provided, you have to first figure out the rate constant and use the half life formula to figure out the time.

  Answer c
  Consider...
  How long is required for 90% of [A] to decompose?

• For this reaction: 2 NO(g) + Cl₂(g) ---> 2 NOCl (g) doubling [Cl₂] alone doubles the rate of the reaction. Doubling the concentration of BOTH reactants makes the reaction go eight times as fast. The reaction is

  a.  First order in NO, first order in Cl2
  b.  First order in NO, second order in Cl2
  c.  Second order in NO, second order in Cl2
  d.  Second order in NO, first order in Cl2
  e.  zero order in NO, third order in Cl2
  

  
  

  Hint...
  The rate is directly proportional to [Cl₂] implies it is first order in Cl₂, doubling the concentration of both species, 2ⁿ = 8 ==> n = 3, minus the order of Cl₂ alone gives 3-1 = 2 ==> the order of rate respect to NO is 2.

  Answer d
  Consider...
  What is the total order of the reaction?

• Which one of the following is true for a first order reaction,

         A  ---> products?
  
  a.  1/[A]     = kt + 1/[A]o
  b.  [A]o/[A]  = kt
  c.  [A]/[A]o  = -kt
  d.  [A]o - [A] = kt
  e.  ln{[A]/[A]o} = -kt.
  

  
  

  Hint...
  If A decomposes according to first order reaction, what plots gives a straight line?

  Answer e
  Consider...
  Write two formulas of the integrated rate law for a first-order reaction.

• For the reaction X₂ + Y + Z --> XY + XZ the mechanism is believed to be

  1.  X2 + Y  ---> XY + X    k1, very slow
  2.  X  + Z  ---> XZ        k2, very fast
  

  Which one of the following rate laws is predicted by the mechanism above?
  
  1. Rate = k(exp) [X₂] [Y] [Z]
  2. Rate = k(exp) [X₂]
  3. Rate = k(exp) [X₂] [Z]
  4. Rate = k(exp) [X] [Z]
  5. Rate = k(exp) [X₂] [Y]
  
  

  Hint...
  The slow step is the rate determining step.

  Answer e
  Consider...
  What is the total order of the reaction?

• For the reaction X₂ + Y + Z --> XY + XZ the mechanism is believed to be

  1.  X2 + Y  ---> XY + X    k1, very slow
  2.  X  + Z  ---> XZ        k2, very fast
  
  What is the MOLECULARITY of the slower step?
  a.  zero
  b.  one
  c.  two
  d.  three
  e.  four
  

  
  

  Hint...
  There are no unimolecular or trimolecular elementary steps here.

  Answer c
  Consider...
  What is the molecularity of the fast step?

• For the reaction X₂ + Y + Z --> XY + XZ, the mechanism is believed to be

  1.  X2 + Y  ---> XY + X    k1, very slow
  2.  X  + Z  ---> XZ        k2, very fast
  
  What is the reactive intermediate?
  a.  X2
  b.  Y
  c.  X
  d.  Z
  e.  XY
  

  
  

  Hint...
  An intermediate is neither a reactant nor a product.

  Answer c
  Consider...
  Derive the rate law from the given mechanism.

• For the reaction X₂ + Y + Z --> XY + XZ the mechanism is believed to be

  1.  X2 + Y  ---> XY + X    k1, very slow
  2.  X  + Z  ---> XZ        k2, very fast
  

  What is the concentration of the intermediate, according to the steady state approximation?
  1. [XY][XZ] / [X₂][Y][Z]
  2. k₁[X₂][Y] - k₂[X][Z]
  3. k₁[X₂][Y] / k₂[X][Z]
  4. k₂[XZ] / k₁[XY]
  5. k₁[X₂][Y] / k₂[Z]
  
  

  Hint...
  The rate of consumption of [X] = rate of production of [X]

  Answer e
  Consider...
  Derive the rate law as if you do not know which step is fast or slow.

• For a unimolecular elementary process in aqueous solution, what are the dimensions of k, the specific rate constant?

  a.  None, k is dimensionless
  b.  s-1
  c.  M s-1
  d.  M-1 s-1
  e.  mol s-1
  

  
  

  Hint...
  Unimolecular implies the order of the reaction is first order.

  Answer b
  Consider...
  What is the dimension of k for a bimolecular elementary step?

• At 83xC a reaction is exactly 4.0 times faster than the same reaction at 66xC. What is the activation energy of this reaction? [Ideal gas constant R = 8.31 J mol^-1 K^-1]

  a.  3.7  J / mol
  b.  82   J / mol
  c.  370  J / mol
  d.  3.7 kJ / mol
  e.  82  kJ / mol
  

  
  

  Hint...
  Use ln(k₂/k₁) = -Ea/R [ 1/T2 - 1/T1], Ts are in Kelvin and you may assume k₂/k₁ = 4... The correct answer is e.

  Answer e
  Consider...
  What is the activation energy if the temperatures were 100 deg C and 50 deg C?

• Which relationship is true for the equilibrium:

       N2O4(g)  =  2 NO2(g)?
  A.   Kp = Kc (RT)-2
  B.   Kp = Kc / (RT)
  C.   Kp = Kc
  D.   Kp = Kc (RT)
  E.   Kp = Kc (RT)2
  

  
  

  Hint...
  P = C RT; Thus, Kp = Kc RT_n

  Answer D
  Consider...
  What is the relationship for the reaction, 2 NO₂ = N₂O₄

• Select the strongest acid:

  A.   hydrogen iodide
  B.   hydrocyanic acid, HCN
  C.   hydrogen fluoride
  D.   hydrogen chloride
  E.   hydrogen bromide
  

  
  

  Hint...
  HCN is a very week acid.

  Answer A
  Consider...
  Remember the trend of binary acid.

• If the pH of an aqueous solution at 279 K is 2.51, what is the [H⁺]? A change from multiple choice problem:
  

  Hint...
  Make sure you know how to calculate it. [H⁺] = 10^-pH.

  Answer 0.0031
  Consider...
  What is the pH if [H⁺] = 0.123 M?

• In which one of the following pairs is the stronger acid listed on the right?

  A.   H3C-COOH, HCN
  B.   HCl, H2CO3
  C.   H2SO4,  H2SO3
  D.   HBrO4,  HOBr
  E.   HClO2,  HClO3
  

  
  

  Hint...
  There is an obvious choice, e.

  Answer e
  Consider...
  If you puzzled about A and E, you might not be alone.

• At some temperature and for the following gas-phase reactions, we have

     H2  +  Cl2  =  2 HCl         Kc1 = 5.1e8
     H2  +  Br2  =  2 HBr         Kc2 = 3.8e4
     2 BrCl  =  Br2  +  Cl2       Kc3 = 5
  What is the value for Kc for the reaction:
     HCl  +  HBr  =  BrCl  +  H2
  

  
  

  Hint...
  Does it equal to 1 / sqrt(Kc1*Kc2*Kc3) ?

  Answer 1e-7
  Consider...
  Did you use the most efficient way to calculate it?

• What is the label (or analytical) concentration (in M) of acetic acid solution which has a pH of 3.00? Ka for acetic acid is 1.75e-5.
  

  Hint...
  Use [H⁺] = 10^-pH, and then [H⁺]² / Ka = C. Derive the above formula.

  Answer 0.057 M
  Consider...
  What is the pH for a solution if the concentration of acetic acid is 1.0 M?

• What is the [H⁺] in 0.020 M aqueous sulfuric acid at 298 K? Give the answer in M. Ka for HSO₄^- = 0.012
  

  Hint...
  Consider the ionization of HSO₄^-.

  Answer 0.027
  Consider...
  What is the [H⁺] in 0.020 M aqueous nitric acid at 298 K?