Question

2. The Clausius-Claperyron equation may be integrated assuming a temperature independent enthalpy: ſ“ din p = 6 REJAT In P2 AH 1 11 RTTI Use the Clausius-Clapeyron equation to determine the boiling point of water on top of Mt. Whitney given the following information. Avap Hm(H2O) = 40.7 kJ/mol, p(Mt. Whitney) = 5.88 x 10' Pa, and Tvap = 373 K in San Rafael at a pressure of 1.02 x 10 Pa. In the following questions, we will estimate the change in a quantity as follows y(x2) – y(x1) = Ay = [z(x) dx Ayz ()(2-2) or Ay = 2(1) A.x where the final equation is the approximation we will use. 3. The density of K(s) is 0.862 g/cm3. Estimate the change in chemical potential of K(s) if the pressure is increased from 1.00 x 109 Pa to 1.20 x 10' Pa. 4. The molar entropy of C12(9) is 223.07 J/mol-Kat 298 K. Estimate the change in the chemical potential of C12 (9) if the temperature is increased to 450 K.

Answer 1

Multiple questions, not specified question to be answered ; so, as per guideline only first one will be answered:

Integrated form of clausius -clapeyron equation :

ln (p2 /p1) = - ($\Delta$Hm /R ) (1/T₂ - 1/T₁ )

we have ,  $\Delta$_vapHm = 40.7 KJ /mol

p(Mt. whitney )= 5.88*10⁴ Pa :   T_vap (Mt. whitney ) = ? = T₁

p(st. rafael )= 1.02*10⁵ Pa and T_vap = 373 K = T₂

Using Integrated form of clausius -clapeyron equation :

ln (1.02*10⁵ Pa /5.88*10⁴ Pa) = - (40.7 KJ /mol  / 8.314 J/K-mol ) (1/373 K - 1/T₁ )

0.55 = - (4895.36  K) (2.68*10^-3 /K - 1/T₁ )

1.12 *10^-4 /K = -(2.68*10^-3 /K - 1/T₁ )

1/T₁ = 2.792*10^-3 /K

T₁ = T_vap (Mt. whitney ) = 358.17 K