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 400C , 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
To find the vapor pressure of ethanol at the new temperature, we need to calculate the pressure of air in the flask at the new temperature using the given information and the gas law formula.
First, let's write down the values given:
- Initial total pressure (P1) = 878 mm Hg
- Pressure of air at initial temperature (P1_air) = 762 mm Hg
- Initial temperature (T1) = 25°C = 257°C
- Final total pressure (P2) = 980 mm Hg
- Final temperature (T2) = 40°C = 400°C
We can use the gas law equation P1T1 = P2T2 to calculate the pressure of air at the new temperature.
P1_air * T1 = P2_air * T2
Substituting the given values:
762 mm Hg * 257°C = P2_air * 400°C
Now we can solve for P2_air:
P2_air = (762 mm Hg * 257°C) / 400°C
P2_air = 491.775 mm Hg (rounded to three decimal places)
Next, we can find the vapor pressure of ethanol at the new temperature by subtracting the pressure of air at the new temperature from the total pressure:
Vapor pressure of ethanol at new temperature = total pressure at new temperature - pressure of air at new temperature
Vapor pressure of ethanol at new temperature = 980 mm Hg - 491.775 mm Hg
Vapor pressure of ethanol at new temperature = 488.225 mm Hg (rounded to three decimal places)
Therefore, the vapor pressure of ethanol at the new temperature is approximately 488.225 mm Hg.