Chemistry 2000, Fall 96, Assignment 2 Solutions

1. 1. The graphite-diamond coexistence curve slopes up as the temperature increases. Therefore, it is necessary to use higher pressures to get diamonds when the temperature is raised. It should be easier to make diamonds at lower temperatures.
   2. The diamond-liquid coexistence curve (i.e. the melting curve) has a positive slope. This means that as the pressure increases, the melting temperature increases.
   3. Since the diamond-graphite coexistence curve intersects the P axis at , 1atm should be right at the bottom of this diagram. The liquid phase is not observed at low pressures (lower than the triple point which, from the diagram, occurs at about ). Therefore, if graphite is heated above at 1atm, it should sublime.
2. 1. The boiling temperature of water decreases as we decrease the pressure so we should be able to boil water by sufficiently reducing the pressure of gas over it.
   2. The temperature generally drops overnight. Vapour pressure decreases when the temperature is reduced. If the temperature drops enough, the partial pressure of water in the air becomes greater than the vapour pressure. The water vapour is no longer in equilibrium and it condenses. Condensation occurs preferentially on surfaces (like grass) acting as nucleators.
3. The total vapour pressure of the solution is the sum of the vapour pressures of hexane and cyclohexane. Therefore

   

   The pressures of hexane and cyclohexane in the mixture are related to their mole fractions so we have

   

   Furthermore, the mole fractions of hexane and cyclohexane have to add to 1:

   

   If we solve this last equation for and substitute the result into the previous equation, we get

   

   This gives us and, therefore, .

   

   We want a percentage by mass so what we really want is . If we divide the top and bottom of this expression by , we get

   

   The mixture is 21% cyclohexane by mass.

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

   

   Since NaCl dissociates into and , 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

   

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

   

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

   

   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.