The total pressure in a flask containing air and ethanol at 25.7 C is 878 mm Hg. The pressure of the air in the flask at 25.7 C is 762 mm Hg. If the flask is immersed in a water bath at 45.0 C, the total pressure is 980 mm Hg. The vapor pressure of ethanol at the new temperature is____ mm Hg.

To find the vapor pressure of ethanol at the new temperature, we need to use the concept of Dalton's law of partial pressures.

Dalton's law states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of the individual gases. In this case, the total pressure in the flask is due to the partial pressure of air and the partial pressure of ethanol vapor.

First, we can find the partial pressure of air in the flask at the new temperature using the given information. We know that the pressure of air in the flask at 25.7 °C is 762 mm Hg. To maintain the same pressure when the flask is immersed in a water bath at 45.0 °C, we assume that the volume and the volume of the air remain constant, and the increase in the total pressure is solely due to the increase in the partial pressure of ethanol vapor.

Using the ideal gas law, we can write:

PV = nRT

Where:
P is the pressure
V is the volume
n is the number of moles of gas
R is the ideal gas constant
T is the temperature in Kelvin

Since the volume and the number of moles remain constant, we can simplify the equation to:

P1/T1 = P2/T2

Where:
P1 is the initial pressure
T1 is the initial temperature
P2 is the final pressure
T2 is the final temperature

Rearranging the equation, we get:

P2 = (P1 * T2) / T1

Now, we can plug in the values:

P1 = 762 mm Hg
T1 = 25.7 °C + 273.15 (convert to Kelvin)
T2 = 45.0 °C + 273.15 (convert to Kelvin)

P2 = (762 * (45.0 + 273.15)) / (25.7 + 273.15)

Solving this, we find that the partial pressure of air in the flask at the new temperature is approximately 857 mm Hg.

Now, we can find the vapor pressure of ethanol at the new temperature by subtracting the partial pressure of air from the total pressure:

Vapor pressure of ethanol = Total pressure - Partial pressure of air
= 980 mm Hg - 857 mm Hg

Therefore, the vapor pressure of ethanol at the new temperature is approximately 123 mm Hg.

To find the vapor pressure of ethanol at the new temperature, you need to subtract the pressure of the air in the flask at the new temperature from the total pressure in the flask at the new temperature.

Step 1: Calculate the pressure of the air in the flask at the new temperature.
Using Charles' Law, which states that the volume of a gas is directly proportional to its temperature (when pressure is constant), we can find the pressure of the air at the new temperature.

[P1 / T1] = [P2 / T2]
Where P1 = pressure at initial temperature, T1 = initial temperature, P2 = pressure at new temperature, T2 = new temperature.

P1 = 762 mm Hg (initial pressure of air)
T1 = 25.7°C (initial temperature)
P2 = ? (pressure of air at new temperature)
T2 = 45.0°C (new temperature)

Converting temperatures to Kelvin:
T1 = 25.7 + 273.15 = 298.85 K
T2 = 45.0 + 273.15 = 318.15 K

Substituting values into the equation:
[762 mm Hg / 298.85 K] = [P2 / 318.15 K]

Cross-multiplying and solving for P2:
P2 = (762 mm Hg * 318.15 K) / 298.85 K
P2 ≈ 811 mm Hg

Step 2: Calculate the vapor pressure of ethanol at the new temperature.
Subtracting the pressure of the air at the new temperature from the total pressure at the new temperature will give us the vapor pressure of ethanol.

Vapor pressure of ethanol = Total pressure at new temperature - Pressure of air at new temperature
Vapor pressure of ethanol = 980 mm Hg - 811 mm Hg
Vapor pressure of ethanol ≈ 169 mm Hg

Therefore, the vapor pressure of ethanol at the new temperature is approximately 169 mm Hg.