I need help with this problem
A 0.75–L bottle is cleaned, dried, and closed in a room where the air is 22oC and 44% relative humidity (that is, the water vapour in the air is 0.44 of the equilibrium vapour pressure at 22oC). The bottle is brought outside and stored at 0.0oC.
b) Would liquid water condense at 10oC?
I don't get the letter b part. I know how to get the mass of the H20 i am just stuck with letter B
vapor pressure H2O @ 22C = 19.8 mm Hg.
vapor pressure H2O @ 0C = 4.6 mm Hg.
How much water is trapped in the bottle at 22C (295K)?
19.8mm x 0.44 = 8.71 mm
n = PV/RT = (8.71 x 0.75/760*0.08206*295) = about 0.00035 mols but you should redo it more accurately.
How many mols vapor can there be in the bottle after cooling to 0C?
n = (4.6*0.75/760*0.08206*273) = about 0.0002 mols.
You have more mols than that; therefore, some of it will condense. How much. That will be about
0.00035 - 0.0002 = about 0.00015 and that x molar mass H2O = about 0.003 g (about 3 mg).
it is not deal with any delta H vapor? because i saw it changes from liquid to gas and have vapor pressure?
and if you use: pv/rt. p must be atm.
To determine whether liquid water would condense at 10°C, we need to compare the air's relative humidity at 10°C to the equilibrium vapour pressure at that temperature.
Here's how you can proceed:
1. Calculate the equilibrium vapour pressure of water at 10°C:
- Use the Antoine equation to find the saturation vapour pressure at 10°C. The Antoine equation for water is: log10(P) = A - (B / (C + T)), where P is the vapour pressure in mmHg and T is the temperature in °C.
- Look up the values for A, B, and C for water.
- Substitute T = 10°C into the equation to find the saturation vapour pressure.
2. Determine the relative humidity at 10°C:
- Convert the equilibrium vapour pressure obtained in step 1 from mmHg to the same units as the relative humidity in the problem.
- Multiply the equilibrium vapour pressure at 10°C by the relative humidity at 22°C to obtain the corresponding vapour pressure at 10°C.
3. Compare the vapour pressure obtained in step 2 to the equilibrium vapour pressure at 10°C:
- If the vapour pressure at 10°C is lower than the equilibrium vapour pressure at 10°C, liquid water would condense.
- If the vapour pressure at 10°C is equal to or higher than the equilibrium vapour pressure at 10°C, liquid water would not condense.
By following these steps, you will be able to determine whether liquid water would condense at 10°C based on the given information.