Question

From the Clausius-Clapeyron Equation for the liquid-vapor transition line and the following known data for a substance X, obtain the Antoine Equation for the vapor pressure of liquid as a function of temperature. You will need to set the values of the constants A, B, and C in the equation of the form Ln Po = A-B / (T + C). The known data for substance X are: normal boiling T = 86 ºC DHvap at normal boiling T = 35 kJ / mol. Clearly specify the units in which your equation handles pressure and temperature.

Answer 1

The Clausius-Clapeyron equation describes the relationship between the vapor pressure of a liquid and its temperature. To obtain the Antoine equation for the vapor pressure of the liquid as a function of temperature, the Clausius-Clapeyron equation can be rearranged.

Step-by-step explanation:

The Clausius-Clapeyron equation describes the relationship between the vapor pressure of a liquid and its temperature. The equation is given by:

ln P = (AHvap/R)((1/T2)-(1/T1))

where P is the vapor pressure, T1 and T2 are the temperatures at which the vapor pressures are known, AHvap is the enthalpy of vaporization, and R is the universal gas constant. To obtain the Antoine equation for the vapor pressure of the liquid as a function of temperature, the Clausius-Clapeyron equation can be rearranged:

ln P = A - (B / (T + C))

where A = (AHvap / R) and C = 1/T1.

Answer 2

The Clausius-Clapeyron equation is a linear relationship that expresses the nonlinear relationship between the vapor pressure of a liquid and temperature. To obtain the Antoine equation for the vapor pressure of a liquid as a function of temperature, we need to set the values of the constants A, B, and C in the equation. By substituting known data for substance X into the Clausius-Clapeyron equation and rearranging, we can solve for the constants A, B, and C.

Step-by-step explanation:

The Clausius-Clapeyron equation is a linear relationship that expresses the nonlinear relationship between the vapor pressure of a liquid and temperature. In the equation, P is the pressure, ΔHvap is the heat of vaporization, R is the universal gas constant, T is the absolute temperature, and C is a constant. To obtain the Antoine equation for the vapor pressure of a liquid as a function of temperature, we need to set the values of the constants A, B, and C in the equation of the form Ln(Po) = A - B / (T + C).

To set the values of A, B, and C, we can use the known data for substance X. The normal boiling point is the temperature at which the vapor pressure equals atmospheric pressure at sea level. From the given data, the normal boiling temperature (T₁) is 86 ºC (or 359.15 K) and the heat of vaporization (ΔHvap) at the normal boiling temperature is 35 kJ/mol.

By substituting these values into the Clausius-Clapeyron equation and rearranging, we can solve for the constants A, B, and C to obtain the Antoine equation for the vapor pressure of the liquid as a function of temperature.