Physical chemistry homework

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.

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