A sample of gas collected over water at 42 degrees C occupies a volume of one liter. The wet gas has a pressure of .986 atm. The gas is dried and the dry gas occupies 1.04 L with a pressure of 1.00 atm at 90 degrees C. Using this information, calculate the vapor pressure of water at 42 degrees C.

Question

A sample of gas collected over water at 42 degrees C occupies a volume of one liter. The wet gas has a pressure of .986 atm. The gas is dried and the dry gas occupies 1.04 L with a pressure of 1.00 atm at 90 degrees C. Using this information, calculate the vapor pressure of water at 42 degrees C.

I was going to approach this problem by finding the pressure of the gas when dry at 42 degrees C, and then do
P[dry]= P[total] - P[water pressure]
but I realized this would get me nowhere as I didn't know the total pressure. Is there a better way to do this problem?

Calculate total mols H2O and gas @ 42^o C from PV = nRT.
Calculate mols dry gas from the second set of conditions @ 90^o C.
The difference in mols should be the mols H2O vapor and that put back into the PV=nRT at 42 should give P of water at 42.

Answer 1

To solve this problem, you can follow these steps:

Step 1: Calculate the number of moles of water vapor and gas at 42°C using the ideal gas law, PV = nRT, where P is the pressure in atm, V is the volume in liters, n is the number of moles, R is the gas constant (0.0821 L·atm/(mol·K)), and T is the temperature in Kelvin.

For the wet gas at 42°C:
P = 0.986 atm
V = 1 L
T = 42°C + 273.15 = 315.15 K

Using PV = nRT, we can solve for n:
n = (P * V) / (R * T)

Step 2: Calculate the number of moles of the dry gas at 90°C using the same formula.

For the dry gas at 90°C:
P = 1.00 atm
V = 1.04 L
T = 90°C + 273.15 = 363.15 K

Using PV = nRT, we can solve for n to find the number of moles of the dry gas.

Step 3: Determine the number of moles of water vapor present by finding the difference between the moles of gas at 42°C and the moles of the dry gas at 90°C.

Moles of water vapor = Moles of gas at 42°C - Moles of dry gas at 90°C

Step 4: Finally, calculate the vapor pressure of water at 42°C using the ideal gas law again.

The number of moles of water vapor (n) is calculated in step 3, and the new volume is 1 L (as it is dried). The temperature remains the same at 42°C.

Using PV = nRT, we can solve for P to find the vapor pressure of water at 42°C.

By following these steps, you can find the vapor pressure of water at 42°C based on the given information.