Physical chemistry

1)  a)  One  mole  of  an  ideal  gas  with Cv
=  3R/2  undergoes  the  transformations
described  in  the  following  list  from  an  initial  state  described  by  T  =  300  K  and  P  =
1.00 bar. Calculate  Q,  W,  ?U,  ?H, and  ?S for each process
i. The gas is heated to 450 K at a constant external pressure of 1.00 bar.
ii. The gas is heated to 450 K at a constant volume corresponding to the initial
volume.
iii.  The  gas  undergoes  a  reversible  isothermal  expansion  at  300  K  until  th e
pressure is half of its initial value.
b) Calculate ?SSURR
and  ?STOTAL
for each   of the processes described in a). Which of
the processes is /are   a spontaneous process? The state of the surroundings for each
part is as follow:
i. 450 K, 1.00 bar
ii. 450 K,  1.00 bar
iii. 300 K, 0.50 bar

2) a) i. Draw a standard phase diagram for a pure component and indicate on it the
different phases, the triple point and the critical point.
ii. Which equation is used to calculate the phase boundaries?
iii. In which condi tions are the phase boundaries assimilated to straight lines?
b) Ice melts under pressure. This has been used as an explanation for the possibility
of ice-skating. Let’s check the facts.
? ice
=  0.917  g  cm
– 3
;  ? water  =  1.000  g  cm
– 3
;  M
water  =  18.02  g  mol
– 1
;
?fus
H°ice
= 6.030 kJ mol
– 1
;  at  atmospheric  pressure  P1
=  101 ,325  Pa,  the  melting
temperature of ice is T
1
= 273.15 K.
i.   An ice -skater of 80 kg uses 2 mm wide and 220 mm long blades. Calculate
the melting temperature of water under the blades.
ii.   The ice  of a n ice rink is usually kept at –6 °C. Does the ice melt under the
pressure of the ice skater?

3) a) i.  What  are  the  conditions  of  ideality  for  two  components  to  form  an  ideal
solution?
ii.  What  are  the  two  cases  where  a  real  solution  can  be  approximat ed  to  an
ideal solution? Briefly explain.
b) A 2 L closed bottle of carbonated water contains 9 g of dissolved CO2
.  Henry’s law
constant for the solubility of CO 2
in water at 25 °C = 0.163  × 10
4
atm
Vapour pressure of pure water at 25 °C = 3,200 Pa
i.  Explain briefly  why  Henry’s  law  can  be  used  to  calculate  the partial vapour
pressure of CO 2
in the bottle.
ii. Calculate the total vapour pressure in the bottle .
iii.  Calculate  the  volume  of  CO
2
degasing  once  the  bottle  is  open  at
atmospheric pressure . Assume CO2 is a perfect g as.

4) The  attractive  electrostatic  interaction  energy  between  two  molecules  having
permanent dipoles and oriented in the most favourable arrangement is given by:

|q1
| = 0.32e and | q2 | = 0.28e
l
1
= 112 pm and l
2
= 178 pm

a) Calculate the dipole  moments (µ 1
and  µ 2
in C m) for the two molecules.
b)  Calculate  the  electrostatic  interaction  energy  (in  kJ  mol
– 1
)  between  these   two
dipolar molecules when r = 0.5 nm.