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 300C, 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

3 answers

* 25.7 and 30.0 for the temperature
Did you make an error in the decimal points? Is P1T1 = P2T2 correct? I don't think so. Check all of your numbers so make sure they are right.
if you mean 30C then here is the answer

Air pressure =
763mmHg
298.7K

ethanol pressure
? mmHG
303 K

Total pressure of water=
980 mmHG
303 K

you need to change air pressure to be based on 303 K after its been placed or immersed in water.

P1/T1= P2/T2
(762 X 303)/ 298.7 = ?
? = 772.96 mmHG

now you can simply subtract the air from the total pressure under water and get the pressure of ethanol
980- 772.96= 207.04