(a) Derive the integrated form of Clausius-Clapeyron equation applicable to vaporization, 1 In (2²) G Hvap R - (1/2), T2 (this equation relates the vapor pressures of liquid p₁ and p2 at temperatures T₁ and T2, respectively) by starting from the differential form that we obtained in class: dlnp_AH vap dT RT² (b) The vapor pressure of a substance at 20 °C is 58.0 kPa and its enthalpy of vaporization is 37.2 kJ mol-¹. Estimate the temperature at which its vapor pressure is 66.0 kPa. NOTE: Do not confuse the vapor pressure with the atmospheric pressure. If at temper- ature T the vapor pressure is p then the liquid and vapor are in equilibrium at those temperature and pressure. If the atmospheric pressure Patm is greater than the vapor pressure p then the liquid will not be boiling. Only when Patm = p, the liquid will be at its boiling point.
(a) Derive the integrated form of Clausius-Clapeyron equation applicable to vaporization, 1 In (2²) G Hvap R - (1/2), T2 (this equation relates the vapor pressures of liquid p₁ and p2 at temperatures T₁ and T2, respectively) by starting from the differential form that we obtained in class: dlnp_AH vap dT RT² (b) The vapor pressure of a substance at 20 °C is 58.0 kPa and its enthalpy of vaporization is 37.2 kJ mol-¹. Estimate the temperature at which its vapor pressure is 66.0 kPa. NOTE: Do not confuse the vapor pressure with the atmospheric pressure. If at temper- ature T the vapor pressure is p then the liquid and vapor are in equilibrium at those temperature and pressure. If the atmospheric pressure Patm is greater than the vapor pressure p then the liquid will not be boiling. Only when Patm = p, the liquid will be at its boiling point.
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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![(a) Derive the integrated form of Clausius-Clapeyron equation applicable to vaporization:
\[
\ln\left(\frac{p_2}{p_1}\right) = \frac{\Delta H_{\text{vap}}}{R} \left(\frac{1}{T_1} - \frac{1}{T_2}\right),
\]
(this equation relates the vapor pressures of liquid \( p_1 \) and \( p_2 \) at temperatures \( T_1 \) and \( T_2 \), respectively) by starting from the differential form that we obtained in class:
\[
\frac{d \ln p}{dT} = \frac{\Delta H_{\text{vap}}}{RT^2}
\]
(b) The vapor pressure of a substance at 20°C is 58.0 kPa and its enthalpy of vaporization is 37.2 kJ mol\(^{-1}\). Estimate the temperature at which its vapor pressure is 66.0 kPa.
NOTE: Do not confuse the vapor pressure with the atmospheric pressure. If at temperature \( T \) the vapor pressure is \( p \) then the liquid and vapor are in equilibrium at those temperature and pressure. If the atmospheric pressure \( p_{\text{atm}} \) is greater than the vapor pressure \( p \) then the liquid will not be boiling. Only when \( p_{\text{atm}} = p \), the liquid will be at its boiling point.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d6b1f03-b4bd-4f60-ae23-d8256607755b%2Ff8a2480e-7c45-49a8-92c8-e82ab26b9282%2F8ml30fq_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Derive the integrated form of Clausius-Clapeyron equation applicable to vaporization:
\[
\ln\left(\frac{p_2}{p_1}\right) = \frac{\Delta H_{\text{vap}}}{R} \left(\frac{1}{T_1} - \frac{1}{T_2}\right),
\]
(this equation relates the vapor pressures of liquid \( p_1 \) and \( p_2 \) at temperatures \( T_1 \) and \( T_2 \), respectively) by starting from the differential form that we obtained in class:
\[
\frac{d \ln p}{dT} = \frac{\Delta H_{\text{vap}}}{RT^2}
\]
(b) The vapor pressure of a substance at 20°C is 58.0 kPa and its enthalpy of vaporization is 37.2 kJ mol\(^{-1}\). Estimate the temperature at which its vapor pressure is 66.0 kPa.
NOTE: Do not confuse the vapor pressure with the atmospheric pressure. If at temperature \( T \) the vapor pressure is \( p \) then the liquid and vapor are in equilibrium at those temperature and pressure. If the atmospheric pressure \( p_{\text{atm}} \) is greater than the vapor pressure \( p \) then the liquid will not be boiling. Only when \( p_{\text{atm}} = p \), the liquid will be at its boiling point.
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