methanol and ethanol are common organic solvents. if the mole fraction of CH3OH in a mixture of the two solvents is 0.4 what is the mole fraction of methanol in the vapor in equilibrium wih the liquid mixture at room temperature 25 celius. the vapor pressure ofmethanol and ethanol at 25 celius are 122.7 torr and 58.9 torr
PCH3OH = XCH3OH*Po = 0.4*122.7
PC2H5OH = XC2H5OH*Po = 0.6*58.9
Total P = PCH3OH + PC2H5OH
XCH3OH vapor = PCH3OH/total P
Note the spelling of celsius.
To find the mole fraction of methanol in the vapor in equilibrium with the liquid mixture, you can use Raoult's Law, which states that the vapor pressure of a component in a mixture is directly proportional to its mole fraction in the mixture.
First, let's calculate the mole fraction of ethanol in the mixture. Since the mole fraction of methanol is given as 0.4, we can subtract this value from 1 to find the mole fraction of ethanol.
Mole fraction of ethanol (C2H5OH) = 1 - 0.4 = 0.6
According to Raoult's Law, the vapor pressure of methanol (CH3OH) in the mixture is the mole fraction of methanol multiplied by its vapor pressure at 25 degrees Celsius.
Vapor pressure of methanol = Mole fraction of methanol * Vapor pressure of pure methanol
Vapor pressure of methanol = 0.4 * 122.7 torr = 49.08 torr
Similarly, the vapor pressure of ethanol in the mixture is the mole fraction of ethanol multiplied by its vapor pressure at 25 degrees Celsius.
Vapor pressure of ethanol = Mole fraction of ethanol * Vapor pressure of pure ethanol
Vapor pressure of ethanol = 0.6 * 58.9 torr = 35.34 torr
Now, to find the mole fraction of methanol in the vapor, we need to divide the vapor pressure of methanol by the total vapor pressure.
Mole fraction of methanol in the vapor = Vapor pressure of methanol / Total vapor pressure
Total vapor pressure = Vapor pressure of methanol + Vapor pressure of ethanol
Total vapor pressure = 49.08 torr + 35.34 torr = 84.42 torr
Mole fraction of methanol in the vapor = 49.08 torr / 84.42 torr ≈ 0.581
Therefore, the mole fraction of methanol in the vapor in equilibrium with the liquid mixture at room temperature is approximately 0.581.