Answer to Question #94363 in General Chemistry for India Washington

Question

The equilibrium vapor pressure of liquid hydrogen at 16 K is 0.213 bar. The standard (1 bar) boiling point is 20.3 K. Use the Clausius-Clapeyron equation to estimate the enthalpy of vaporization of hydrogen.

Answer 1

The Clausius-Claperyron Equation relates the ln of the vapor pressure to the enthalpy of vaporization, and temperature change. ln P vap = - change of enthalpy / RT + ln constant. Thus - change of enthapy / RT is the slope of this line. The problem gives two points on this line. 16 K , 0.213 bar and 20.3 K , 1 bar. The two point form of this equation is ln ( P1/ P2) = (- heat of vaporization / R ) ( 1/T2 - 1/T1) with R = 8.314 J/Mole K.

Subituting in ln (0.213/1) =(-ht of vaporization /8.314) ( 1/20.3 - 1/ 16).

Rearranging: -ln (0.213)(8.314) / (1 /20.3 - 1/16) = ht of vaporization

-1.54646 (8.314) / ( 0.04926 - 0.0625) = ht of vaporization

-12.857/-.01324 = 971.09 Joules

round to correct significant figures of 3: 971 Joules/mole