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Consider a gas whose (p, V, T) behavior can be described by the equation of state

P= nRT/V+ n2bRT/ V2, it is not an ideal gas!!!!!

Where b= 0.0515l mol-1 is a constant. The molar heat capacity at constant volume of the gas is independent of temperature and has a value 3R/2.

A number of moles n of such a gas are initially in a container of volume V1= 2l at a temperature T1= 300K and pressure p1= 9atm. The walls of the container are adiabatic. The clamps that keep one of the walls at a fixed position are released, and the wall moves against a constant pressure pex that is three times the value of the initial pressure p1 inside the container. The motion of the wall stops when equilibrium is achieved.

(a) Calculate the final temperature T2 of the gas.

(b) What is the molar heat capacity at constant pressure of the gas? Justify

(c) Calculate the change in the enthalpy H of the gas in the process.

(d) Calculate the work w in the process.

(e) Calculate the change in entropy of the gas S in the process.

Problem 2

The standard molar entropy of Pb (s) at 298.15K and 1 bar is 64.80J K-1 mol-1 . The molar heat capacity of Pb (s) at constant pressure of 1 bar is

Cmp (T) = 22.13+ 0.01172T + 1.00*105T2

Where the units of T and Cmp are, respectively, K and J K-1 mol-1. The melting point of lead at 1 bar is 327.4oC, and the molar enthalpy of fusion under these conditions is 4770J mol-1. The molar heat capacity at constant pressure of 1 bar of Pb(l) is

Cmp (T)= 32.51 – 0.00301T,

Where the units of T and Cmp are, respectively, K and J K-1mol-1.

Calculate the standard molar entropy of Pb(l) at 5000C.

Calculate delta G0 for the transformation

Pb(s, 298.15K, 1bar) ----Pb(l, 600.55K, 1 bar).

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# Physical chemistry

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