The total pressure in a flask containing air and ethanol at 25.7C is 878 mm Hg. The pressure of the air in the flask at 25.7C is 762 mm Hg. If the flask is immersed in a water bath at 30.0C , the total pressure is 980 mm Hg. The vapor pressure of ethanol at the new temperature is mm Hg.

Question

The total pressure in a flask containing air and ethanol at 25.7C is 878 mm Hg. The pressure of the air in the flask at 25.7C is 762 mm Hg. If the flask is immersed in a water bath at 30.0C , the total pressure is 980 mm Hg. The vapor pressure of ethanol at the new temperature is mm Hg.

I have seen that others have posted the same problem, but it seems that the answer i plug in is wrong.

Answer 1

To solve this problem, we need to use the ideal gas law and the concept of Dalton's law of partial pressures.

The ideal gas law equation is:
PV = nRT

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

First, let's convert the given temperatures to Kelvin:
25.7°C + 273.15 = 298.85 K
30.0°C + 273.15 = 303.15 K

Now, let's find the number of moles of air in the flask at 25.7°C:
From Dalton's law of partial pressures, the pressure of air is the difference between the total pressure and the vapor pressure of ethanol:
Pressure of air = Total pressure - Pressure of ethanol
= 878 mmHg - Pressure of ethanol at 25.7°C

Next, we can calculate the number of moles of air using the ideal gas law equation:
n = PV / RT

We know:
P = Pressure of air
V = volume of air (which is constant)
R = ideal gas constant

By rearranging the equation, we can solve for n:
n = (P * V) / (R * T)

So, the number of moles of air can be determined.

Moving on to the next condition, when the flask is immersed in a water bath at 30.0°C, the total pressure is 980 mmHg. We are asked to find the vapor pressure of ethanol at this new temperature.

Again, we'll use Dalton's law of partial pressures:
Total pressure = Pressure of air + Pressure of ethanol
Pressure of ethanol = Total pressure - Pressure of air

Now, using the ideal gas law, we can calculate the vapor pressure of ethanol:
n = (P * V) / (R * T)

We know:
n = number of moles of ethanol (which we need to find)
P = Pressure of ethanol
V = volume of ethanol (which is constant)
R = ideal gas constant
T = temperature in Kelvin (which is 303.15 K in this case)

By rearranging the equation, we can solve for P to find the vapor pressure of ethanol at the new temperature.

Remember to double-check your calculations and units to ensure accuracy.