Thermodynamics

23. (a) The state of a thermodynamic system is described by its measurable or macroscopic (bulk) properties. We can describe the state of a gas by quoting its pressure (p), volume (V), temperature (T), amount (n) etc. Variables like p, V, T are called state variables or state functions because their values depend only on the state of the system and not on how it is reached. Example: Volume of water in a pond, is a state function, because change in volume of its water is independent of the route by which water is filled in the pond, either by rain or by tube well or by both.

22. q_rev = (-Δ_fH^? ) = - (- 286kJ mol^-1) = 286 x 103 Jmol^-1 = 286000 J mol^-1

ΔS  _{(surroundings)} = q_rev/ T = 286000 J mol^-1 / 298 K

                        =  959.73 J mol^-1 K^-1

21. For NO (g), Δ_rH° is a +ve value. So, it is unstable in nature.

For NO₂  (g), Δ_rH° is a -ve value. So, it is stable

20. ΔG° = -RT ln K = - 2.303 RT log K

Putting the values of

R = 8.314 J K^-1 mol^-1,

T = 300 K and

K =10; we get

ΔG° = - 2.303 x 8.314 J K^-1 mol^-1 x 300 K and K x log 10

        = - 5527 J mol^-1

        = -5.527 kJ mol^-1

19. ΔH° = ΔU° + Δ^ng RT

ΔU° = -10.5 kJ, Δ^ng = 2-3 = -1 mol, R = 8.314 x 10^-3 kJ mol^-1, T = 298 K

ΔH° = (- 10.5 kJ) + [ (- 1 mol) x (8.314 x 10^-3 kJ mol^-1) x (298 K)]

       = -10.5 kJ – 2.478 kJ

       = -12.978 kJ

According to Gibbs Helmholtz equation:

ΔG° = ΔH° - TΔS°

        = (- 12.978 kJ) – (298 K) x (- 0.0441 kJ K^-1)

        = -12.978 + 13.142

        = 0.164 kJ

Since the value of ΔG° is positive, the reaction is non-spontaneous.

18. ? H: negative (-ve) because energy is released in bond formation

? S: negative (-ve) because entropy decreases when atoms combine to form molecules.

17. As per the Gibbs Helmholtz's equation:

ΔG = Δ H - TΔ S

For ΔG=0; 

ΔH=TΔS

Or  T=ΔH/ΔS

T = (400 KJ mol^-1)/ (0.2 KJ K^-1 mol^-1)

= 2000 k

Thus, reaction will be in a state of equilibrium at 2000 K and will be spontaneous above this temperature

16. Change in internal energy (? U) for an isolated system is zero for it does not exchange any energy with the surroundings. But entropy tends to increase in case of spontaneous reaction. Therefore? S > 0 or positive.