Ethanol has a heat of vaporization of 38.56 kJ/mol and a normal boiling point of 78.4 °C. Using the Clausius-Clapeyron equation, what is the vapor pressure of ethanol at 15 °C?
A
1.02 atm
B
0.12 atm
C
0.45 atm
D
0.78 atm
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1
Start by understanding the Clausius-Clapeyron equation, which relates the vapor pressure of a substance at two different temperatures. The equation is: , where is the heat of vaporization, is the universal gas constant, and and are the temperatures in Kelvin.
Convert the temperatures from Celsius to Kelvin. The normal boiling point of ethanol is 78.4 °C, which converts to K. The temperature at which you want to find the vapor pressure is 15 °C, which converts to K.
Use the Clausius-Clapeyron equation to find the natural logarithm of the ratio of the vapor pressures at the two temperatures. Plug in the values: = 38.56 kJ/mol (convert to J/mol by multiplying by 1000), = 8.314 J/(mol·K), = 351.4 K, and = 288.15 K.
Calculate the difference in the reciprocals of the temperatures: - . This will be used in the Clausius-Clapeyron equation.
Solve for the vapor pressure at 15 °C by rearranging the Clausius-Clapeyron equation to find , using the known vapor pressure at the boiling point (1 atm) and the calculated value from the previous steps.