Answer :
Final answer:
To estimate the vapor pressure of ethanol at 45.0 °C, the Clausius-Clapeyron equation and given data points at 20.0 °C and 63.5 °C are used to first calculate the enthalpy of vaporization. Next, the equation is used again with the new temperature to solve for the unknown vapor pressure.
Explanation:
To estimate the vapor pressure of ethanol at 45.0 °C, one can use the Clausius-Clapeyron equation, which relates the vapor pressure and temperature to the enthalpy of vaporization (ΔHvap). The equation is as follows:
ln(P2/P1) = -ΔHvap/R * (1/T2 - 1/T1)
We already have the information required to estimate ΔHvap from two known vapor pressures at two different temperatures:
- The vapor pressure of ethanol at 20.0 °C is 5.95 kPa.
- The vapor pressure of ethanol at 63.5 °C is 53.3 kPa.
Let's denote the vapor pressure at 20.0 °C as P1, the temperature at 20.0 °C as T1, the vapor pressure at 63.5 °C as P2, and the temperature at 63.5 °C as T2. We then plug these values, along with the R (ideal gas constant, 8.314 J/mol·K), into the Clausius-Clapeyron equation to calculate ΔHvap. Remember to convert the temperatures to Kelvin by adding 273.15 to the Celsius temperatures.
After finding ΔHvap, we can use it to estimate the vapor pressure at another temperature (45.0 °C) by choosing one of the given temperature-pressure combinations as a reference point (T1, P1), with the new temperature (45.0 °C) serving as T2. By rearranging the Clausius-Clapeyron equation, the unknown vapor pressure (P2) can be solved.
