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 the
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 conditions 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.
?i
ce = 0.917 g cm–3; ?water = 1.000 g cm–3; Mwater = 18.02 g mol–1;
?fusH°ice = 6.030 kJ mol–1; at atmospheric pressure P1 = 101,325 Pa, the melting
temperature of ice is T1 = 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 an 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 approximated 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 CO2 in water at 25 °C = 0.163 × 104 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 CO2 in the bottle.
ii. Calculate the total vapour pressure in the bottle.
iii. Calculate the volume of CO2 degasing once the bottle is open at
atmospheric pressure. Assume CO2 is a perfect gas.
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
l1 = 112 pm and l2 = 178 pm
a) Calculate the dipole moments (µ1 and µ2 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.