Dry air is bubbled through 25 litres of water at a rate of 15 litres (STP)/min. The air leaving the liquid is saturated with water at 25 degrees celcius and 1.5 atm. How long it will take for all of the water to vaporize.
To find out how long it will take for all of the water to vaporize, we need to determine the rate at which water vaporizes and then calculate the total time required.
First, let's calculate the rate at which water vaporizes:
1. Convert the given quantities to the same units:
- 25 liters of water
- 15 liters (STP)/min of air (standard temperature and pressure conditions)
2. Use the molar volume of gas at STP, which is approximately 22.4 liters/mol, to convert the liters of air to moles of air:
- 15 liters (STP)/min * (1 mol/22.4 liters) = 0.6696 mol/min of air
3. Using the ideal gas law equation, PV = nRT, we can determine the number of moles of water vaporized per minute:
- Given conditions:
- Temperature (T) = 25 degrees Celsius (convert to Kelvin: 25 + 273 = 298 K)
- Pressure (P) = 1.5 atm
- Assuming the system operates at equilibrium, we can use the saturated vapor pressure of water at 25 degrees Celsius: 23.8 mmHg (or 0.03154 atm)
- Convert mmHg to atm: 23.8 mmHg * (1 atm/760 mmHg) = 0.03154 atm
- Let's substitute the values into the equation:
- (0.03154 atm) * V = (0.6696 mol/min) * (0.0821 L.atm/(mol.K)) * (298 K)
- Solve for V (the volume of water vaporized per minute):
- V = ((0.6696 mol/min) * (0.0821 L.atm/(mol.K)) * (298 K)) / (0.03154 atm)
- V ≈ 34.85 L/min
Now that we know the rate at which water vaporizes (34.85 L/min), we can calculate the total time it takes to vaporize 25 liters of water:
25 liters ÷ 34.85 L/min ≈ 0.717 minutes
Therefore, it will take approximately 0.717 minutes (or about 43.02 seconds) for all of the water to vaporize.