The equation ln(p 2 /p 1 ) =-(H o vap /R) [(1/T 2 ) -(1/T 1 )] is derived assumi

Question

The equation    ln(p2/p1) =-(Hovap/R) [(1/T2) -(1/T1)] is derived assuming that the value forHvap is independent of temperature. A betterequation may be obtained by including a term to account for thedependence of Hovap on temperature.Let Hvap = a + b (T - To) where a = Hovap, the enthalpy ofvaporization at To, the normal boiling point of theliquid, and b = Cp,m = Cp,m(g) -Cp,m(l) is the difference between the constant pressuremolar heat capacities of the gas and liquid.

Using the equation Hvap = a + b (T -To) and the equation d ln(p)/dT =Hvap/RT2, find an improved expressionfor ln(p2/p1) that takes into account the temperature dependenceof Hvap.

Explanation / Answer

d [ ln(p)] / dT = (a + bT - bT0)/RT2 d [ ln(p)] / dT = (a - b*T0)/RT2 + b/RT ln[p2] - ln [p1] =   -(a-b*T0)/RT +(b/R)*ln(T)             eval from T1 to T2 ln(p2/p1) = [(b*T0 - a)/R]*(1/T2 - 1/T1) + (b/R)*ln(T2/T1)

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.