The output of a diesel generator, which contains a mixture of CO2 and H2O gases, is collected in a sealed vessel at 447 K. As the mixture cools to 298 K, the pressure falls from 3.0 atm to 0.80 atm. What is the ratio of CO2 to H2O in the mixture?
Have you tried using Avagadro's hypothesis or the ideal gas laws?
Yeah. - They don't work -_-
At 298K, the water vapor has condensed to liquid, so the gas mixture left is CO2 + a little water vapor due to partial pressure of water.
So look up th partial pressure of water at 298K. Subtract that from .8 atm, and you have the pressure of CO2. Solve for the moles of CO2 in the gas given PVT. Now, go back to the origianl pressure. You know moles of CO2, solve for the partial pressure given VTn. Subtract that from 8.0atm, and you have the pressure of the water vapor. Solve for the moles water vapor.
Cheers Bob. You are awesome!
Thank you for your kind words! I'm here to help. Let's break down the steps to find the ratio of CO2 to H2O in the mixture:
Step 1: Find the partial pressure of water vapor at 298K
At 298K, water vapor has condensed to a liquid. We need to find the partial pressure of water vapor at this temperature. You can look up the table or use a vapor pressure calculator to find the corresponding value. Let's say the partial pressure of water vapor at 298K is P_water.
Step 2: Calculate the pressure of CO2
Subtract the partial pressure of water vapor (P_water) from the final pressure (0.80 atm) to get the pressure of CO2.
Pressure of CO2 = Final pressure - P_water
Step 3: Calculate the moles of CO2
Use the ideal gas law (PV = nRT) to calculate the moles of CO2. Plug in the values of pressure (pressure of CO2), volume (assumed constant since it is a sealed vessel), temperature (298K), and the gas constant (R). Solve for n (moles of CO2).
n_CO2 = (Pressure of CO2 * Volume) / (R * Temperature)
Step 4: Calculate the pressure of water vapor
Now, let's go back to the original pressure (3.0 atm). We know the moles of CO2, so we can calculate the partial pressure of water vapor using the remaining pressure (3.0 atm - pressure of CO2).
Pressure of water vapor = Original pressure - Pressure of CO2
Step 5: Calculate the moles of water vapor
Again, use the ideal gas law to calculate the moles of water vapor. Plug in the values of pressure (pressure of water vapor), volume, temperature (298K), and the gas constant (R). Solve for n (moles of water vapor).
n_water vapor = (Pressure of water vapor * Volume) / (R * Temperature)
Step 6: Determine the ratio of CO2 to H2O
Finally, calculate the ratio of CO2 to H2O by dividing the moles of CO2 by the moles of water vapor.
Ratio of CO2 to H2O = Moles of CO2 / Moles of water vapor
By following these steps, you should be able to find the ratio of CO2 to H2O in the mixture.