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
From the first two sentences, you know the partial pressure of the ethanol at the initial condition.
Then, use the combined gas law to get the second pressure, ignoring the air.
To find the vapor pressure of ethanol at the new temperature, we need to use the ideal gas law equation:
P1 × T1 = P2 × T2
where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature.
First, let's calculate the new pressure of air in the flask based on the given data. We know that the initial pressure of air at 25°C is 762 mm Hg, and the final pressure is 980 mm Hg at 45°C. Let's plug these values into the equation:
P1 × T1 = P2 × T2
762 mm Hg × (25°C + 273) K = 980 mm Hg × (45°C + 273) K
Now we can solve for P1, the initial pressure of air at the new temperature:
P1 = (980 mm Hg × (45°C + 273) K) / (25°C + 273) K
Next, we want to find the vapor pressure of ethanol at the new temperature. We know that the total pressure in the flask at 45°C is 980 mm Hg, and the total pressure in the flask at 25°C is 878 mm Hg. However, the pressure at 25°C includes the contribution of air pressure. To determine the vapor pressure of ethanol, we need to subtract the pressure of air at 25°C from the total pressure at 25°C.
Vapor pressure of ethanol at new temperature = Total pressure at 45°C - Pressure of air at 25°C
Now, let's calculate the vapor pressure of ethanol at the new temperature:
Vapor pressure of ethanol at new temperature = 980 mm Hg - P1
Substitute the value of P1 we calculated earlier to get the final answer.