The total pressure in a flask containing air and ethanol at 257C is 878 mm Hg. The pressure of the air in the flask at 257C is 762 mm Hg. If the flask is immersed in a water bath at 450C, the total pressure is 980 mm Hg. The vapor pressure of ethanol at the new temperature is ______ mm Hg.

(Hint: you will need to correct the pressure of air at the new temperature using the Gas Law: P1T1 = P2T2)

This is the second time this question has been posted. My answer remains the same, and I did correct for the change in temperature. Perhaps another teacher will give an independent opinion.

To find the vapor pressure of ethanol at the new temperature, we need to use the ideal gas law formula:

PV = nRT

Where:
P = pressure
V = volume
n = moles of gas
R = ideal gas constant
T = temperature

First, let's calculate the number of moles of air present in the flask. We know that the pressure of the air at 25°C is 762 mm Hg. We'll use the ideal gas law to find the number of moles.

P1V1 = nRT1

P1 = 762 mm Hg
V1 = volume (unknown)
n = moles of air (unknown)
R = ideal gas constant (known)
T1 = 25°C (298K)

Now we can rearrange the equation to solve for the number of moles:

n = (P1V1) / (RT1)

Next, let's calculate the volume of the flask. The volume doesn't change with temperature, so we can assume it remains the same. Let's denote the volume of the flask as V2.

Now, let's calculate the pressure of the air at the new temperature using the ideal gas law. We'll denote this pressure as P2.

P1V1 = P2V2

P1 = 762 mm Hg
V1 = volume of the flask (unknown)
P2 = pressure of the air at the new temperature (unknown)
V2 = volume of the flask (known)

Now we can solve for P2:

P2 = (P1V1) / V2

Now that we have the pressure of the air at the new temperature, we can use Dalton's law of partial pressures to find the pressure of ethanol.

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 each individual gas.

Total pressure = pressure of air + pressure of ethanol vapor

Total pressure at 45°C = 980 mm Hg
Pressure of air at 45°C = P2 (calculated above)

Let's denote the pressure of ethanol vapor as Pe.

Total pressure at 45°C = P2 + Pe
Pe = Total pressure at 45°C - P2

Now, we can substitute the values to find the pressure of ethanol vapor at the new temperature:

Pe = 980 - P2

Finally, we have the pressure of ethanol vapor at the new temperature, which is the vapor pressure.