Question

Calculate the change in entropy (in J/K) when 52.8 g of nitrogen gas is heated at a constant pressure of 1.50 atm from 16.5 ºC to 62.8 ºC. (The molar specific heats are Cv is 20.8 J/(mol-K) and Cp is 29.1 J/(mol-K) .)

Answer 1

Given, mass of nitrogen gas = 52.8 g ,

therefore moles of nitrogen gas (N₂) = mass / molar mass =( 52.8 g / 28 g/mol) = 1.886 mol N₂ gas.

and T_i = (16.5 + 273) K = 289.5 K , T_f = (62.8 +273)K = 335.8 K , C_p = 29.1 J/mol K

We have the relation as,

Tds = dh - vdp,

At constant pressure,dp=0
so, Tds = dh

=> ds = dh/T

=> ds = (Cp/T)dT

=> S = nCp x ln(Tf / Ti)

=>S = nCp x ln(Tf/Ti)

=> S = (1.886 mol) x 29.1 J/mol K x ln(335.8 K/289.5 K)

=> S = 54.8826 x ln (1.159) J/K

=> S = 54.8826 x 0.147 J/K

=> S =  8.067 J/K

Therefore, the change in entropy = 8.067 J/K