1) Derive the Clausius-Clapeyron equation for an ideal gas and ideal liquid: Liquid (Phase A) ↔...

1) Derive the Clausius-Clapeyron equation for an ideal gas and ideal liquid: Liquid (Phase A) ↔ Gas (Phase B) Begin with the equation relating chemical potential of the two phases (?A , ?B ), assuming these phases are at equilibrium (as they are assumed to be along the liquid-gas coexistence curve on a P-T phase diagram) Include all necessary detail in your derivation to demonstrate your understanding.

Then, Using the equation you derived in number 1, determine at which pressure and temperature water assumes the triple point. Assume ideal behavior. One-liquid-gas equilibrium point is (698 Pa, 275 K) and one solid-gas equilibrium point is (511 Pa, 271 K). Note: ΔHvap= 40 kJ/mol, ΔHfus= 6 kj/mol)

Expert Solution

genius_generous answered 2 years ago

Derive Clapeyron equation and Clausius modification for liquid-vapor equilibrium conditions.

The Clausius-Clapeyron equation and the Antoine equation. The vapor pressure of a liquid can be written...

The Clausius-Clapeyron equation and the Antoine equation. The vapor pressure of a liquid can be written in the empirical form known as the Antoine equation, ln (p / p ◦ ) = A1 − (A2 /(T + A3)) where A1, A2, and A3 are empirical constants determined from measurements, and T is the temperature in Kelvin. (a) Starting with this equation, derive an equation for the enthalpy of vaporization as a function of temperature. (b) For ethanol (l), A1 =...

1. By using the Clausius-Clapeyron equation, lnP=??HvapRT+C, derive the relationship between the vapor pressures, P1 and...

1. By using the Clausius-Clapeyron equation, lnP=??HvapRT+C, derive the relationship between the vapor pressures, P1 and P2, and the absolute temperatures at which they were measured, T1 and T2. Express your answer in terms of T1, T2, ?Hvap, and the gas constant R. ln(P1/P2)= 2. Gasoline is a mixture of hydrocarbons, a major component of which is octane, CH3CH2CH2CH2CH2CH2CH2CH3. Octane has a vapor pressure of 13.95 torr at 25?C and a vapor pressure of 144.78 torr at 75?C. Use these...

a) Combining the barometric distribution with the Clausius-Clapeyron equation, deduce an equation that relates the boiling...

a) Combining the barometric distribution with the Clausius-Clapeyron equation, deduce an equation that relates the boiling point of a liquid to the temperature of the atmosphere, temperature (Ta) and altitude (h). In b) and c) suppose ta = 20 ° C. b) For water, tb = 100 ° C at 1 atm and ΔH vap = 40,670 kJ / mol. What is the boiling point on the top of a mountain with h = 4754 m? c) For diethyl ether,...

A) Use the Clapeyron equation to estimate (in bar/K) the slope of the solid-liquid phase boundary...

A) Use the Clapeyron equation to estimate (in bar/K) the slope of the solid-liquid phase boundary of water given the enthalpy of fusion is 6.008 kJ/mol and the densities of ice and water at T=0oC are 0.91671 and 0.99984 gm/cm3 respectively. B) In the preceding problem, what is the pressure required to lower the melting point of ice by 1C, in bars? C) The standard molar entropy of rhombic sulfur is 31.80 J/K mol and that of monoclinic sulfur is...

To derive the ideal-gas equation, we assume that the volume of the gas atoms/molecules can be...

To derive the ideal-gas equation, we assume that the volume of the gas atoms/molecules can be neglected. Given the atomic radius of krypton, 1.1 Å, and knowing that a sphere has a volume of 4πr3/3, calculate the fraction of space that Kr atoms occupy in a sample of krypton at STP. Express your answer using two significant figures.

9) Using the Clausius-Clapeyron equation determine the vapor pressure of water at 50.0 C. The molar...

9) Using the Clausius-Clapeyron equation determine the vapor pressure of water at 50.0 C. The molar heat of vaporization of water is 40.7 kJ/mol. (Review Sample Exercise: Example 13-4) ln ( R = 8.314 J ) = ∆Hvap P2 P1 R mol∙K ( 1 − T1 ; T = Kelvin; P = Consistent units 10) Referring to the figure below, describe the phase changes (and the temperatures at which they occur) when CO2 is heated from −80 °C to 0...

in the clausius-clapeyron equation lnP= ((-Hvap/R)(1/T))+C can someone explain to me what is C?

Estimate the vapor pressure of ethyl ether at 40 degree celcius using the Clausius-Clapeyron equation based...

Estimate the vapor pressure of ethyl ether at 40 degree celcius using the Clausius-Clapeyron equation based on the experimental values as follows. Remember that T in the Clausius-Clapeyron equation is absolute and pressure is in mmHg. p* (mmhg) 19.0 112.51 442.0 Temprature(degree celcius) -40.0 -10.0 20.0

In an ideal solution of A and B, 2.75 mol are in the liquid phase and...

In an ideal solution of A and B, 2.75 mol are in the liquid phase and 4.255 mol are in the gaseous phase. The overall composition of the system is ZA = 0.420, and xA = 0.310. Calculate yA.

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