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Chemistry 2720 Practice Problem Solutions

  1. This is a coupled reaction problem. The coupled reaction is

    displaymath182

    The maximum ratio of PEP to pyruvate is obtained when tex2html_wrap_inline184 , so we want

    displaymath186

    The activity of phosphate is irrelevant (at least, in this problem) so we have

    displaymath188

    This is not a very large ratio, but it is considerably better than what would be obtained without ATP and may be sufficient if only a small amount of phosphoenolpyruvate is needed.

    1. There are at least two different approaches to this problem:
      Method 1
      Boiling has to do with the process tex2html_wrap_inline190 . We begin by computing the equilibrium constant at 298K:

      eqnarray30

      At the boiling point, K=1. (Make sure you understand why that is before proceeding.) We use the formula which relates equilibrium constants to temperature, which we rearrange to the form

      eqnarray35

      Method 2
      At the normal boiling point, liquid water is in equilibrium with 1atm of steam thus K=1 for the process tex2html_wrap_inline190 . This implies that tex2html_wrap_inline198 . Therefore tex2html_wrap_inline200 . (This is Trouton's rule.) Since we can calculate tex2html_wrap_inline202 (as above) and tex2html_wrap_inline204 , we can compute the temperature T at which tex2html_wrap_inline208 , i.e. the boiling point:

      eqnarray61

    2. Both of these methods underestimate the boiling point by tex2html_wrap_inline210 for essentially the same reason: Both assume that tex2html_wrap_inline202 is independent of temperature, which is not quite right. The second method also assumes that tex2html_wrap_inline204 is independent of temperature.
  2. We start with dE. dE=dq+dw. If we take a reversible path, tex2html_wrap_inline220 and tex2html_wrap_inline222 , so tex2html_wrap_inline224 . Since H=E+PV,

    eqnarray86

    Therefore tex2html_wrap_inline230 .

    Note: If I put a differential derivation on a test or exam, it will be an optional question. If you learn how to do these, they are quite easy. However, make sure that you can at least interpret a differential (i.e. relate the differential to derivatives of state functions) that is given to you.

    1. Imagine taking a sample of water at 298K and warming or cooling it reversibly to temperature T. Adding the change in entropy to the entropy at the starting temperature, we get

      eqnarray91

      where T is in Kelvin and the entropy is in tex2html_wrap_inline236 .

    2. Take a Taylor series near tex2html_wrap_inline238 :

      eqnarray109

      where tex2html_wrap_inline291 .

    3. Here are some entropies calculated with the two equations:

      tabular128

      The approximation is valid to 1% for tex2html_wrap_inline246 up to about 80K, although the approximation is better on the high-temperature side than on the low-T side.

  3. The hydrogen bonds should result in considerable organization of the molecules in solution. Accordingly, HF should be less available for chemical or physical processes than its concentration would indicate. We therefore expect its activity coefficient to be less than 1.
  4. Let us say that the Debye-Hückel correction is only significant if tex2html_wrap_inline248 . (This is somewhat arbitrary and you could of course pick a different number.) To obtain a conservative estimate of the maximum ionic strength for ideal behaviour, take the largest reasonable values for tex2html_wrap_inline250 and tex2html_wrap_inline252 : There are few anions stable in solution whose charges are other than -1 or -2 so take tex2html_wrap_inline258 . There are some +3 and +4 cations so take tex2html_wrap_inline264 . The critical ionic strength is therefore

    displaymath266

    Below an ionic strength of tex2html_wrap_inline268 , we can be reasonably assured of ideal behaviour. We also know that above 0.01mol/L, the Debye-Hückel equation yields poor results so we should use Debye-Hückel theory when tex2html_wrap_inline270 .

  5. Let s be the solubility in mol/L. Omitting the division by the standard concentration, we have

    displaymath274

    or

    displaymath276

    Since the charges on the calcium and oxalate ions are +2 and -2, tex2html_wrap_inline282 . Accordingly

    displaymath284

    Start iteration with the guesstimate tex2html_wrap_inline286 :

    tabular149

    The molar mass of calcium oxalate is 128.10g/mol so the solubility is tex2html_wrap_inline300 . Note that the ionic strength of the saturated solution is tex2html_wrap_inline302 , which is well within the range of applicability of Debye-Hückel theory.

  6. We want a freezing point depression of tex2html_wrap_inline349 . Using the freezing-point depression formula, the total concentration of solutes should therefore be

    displaymath351

    Since NaCl dissociates into tex2html_wrap_inline353 and tex2html_wrap_inline355 , this is twice the concentration of either sodium or chloride ions (i.e. twice the formal concentration of sodium chloride). The formal concentration of sodium chloride should therefore be 1.4mol/kg. We have 18000kg of solvent so

    displaymath367

  7. The first step is to compute the concentration of the solution from the osmotic pressure measurement:

    displaymath359

    In the more conventional concentration units, this is tex2html_wrap_inline361 . Since 100mL of water (0.100L) of water was used, the number of moles of the forensic sample is tex2html_wrap_inline363 . The mass was 2.841mg so the molar mass of the unknown substance is

    displaymath365

    From the chemical formula, we know that the molar mass of MDA is 179.218g/mol. It seems quite likely that the material brought in by the police officer is MDA. Further tests on the sample should be ordered.

  8. If the osmotic pressure is rising, then the total concentration of solutes must be increasing. This suggests that the starch is breaking down into its constituent units.

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Marc Roussel
Tue Nov 19 12:38:58 MST 1996