If 10.00 g of water are introduced into an evacuated flask of volume 2.500 L at 65 degreed celcius, calculate the mass of water vaporized. (Hint: Assume that the volume of the remaining liquid water is negligible; the vapor pressure of water at 65 degrees celsius is 187.5 mmHg.)
you know pressure, volume, and temp. Solve for moles of water vapor.
PV=nRT
convert n to grams of H2O
n = (pv)/ (RT)
= (187.5 * 2.50) / (62.4 * 338) = 0.0222 mol H20
0.0222 mol H20 * 18.02g/mol = 0.4 g H20 vaporized
To calculate the mass of water vaporized, you can use the ideal gas law equation:
PV = nRT
where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
First, convert the given temperature from Celsius to Kelvin:
65°C + 273.15 = 338.15 K
Next, convert the given pressure from mmHg to atm:
187.5 mmHg ÷ 760 mmHg/atm = 0.2467 atm
Since the flask is evacuated, the initial pressure is 0 atm.
Now, we can use the ideal gas law to find the number of moles of water vapor:
P1V1 = nRT
0 atm * 2.500 L = n * 0.0821 L·atm/mol·K * 338.15 K
0 = n * 27.728815
n = 0 mol
The number of moles of water vapor is 0 because there is no vapor present.
Since the initial mass of water is 10.00 g and no water has vaporized, the mass of water vaporized is also 0 g.
To calculate the mass of water vaporized, we need to use the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
First, we need to convert the given pressure from mmHg to atm. Since 1 atm = 760 mmHg, we can calculate the pressure in atm as follows:
P (in atm) = 187.5 mmHg / 760 mmHg/atm
Next, we can rearrange the ideal gas law equation to solve for n, the number of moles of water vapor:
n = PV / RT
We are given the pressure (P), volume (V), and temperature (T), but we need to convert the temperature from degrees Celsius to Kelvin.
T (in Kelvin) = 65 degrees Celsius + 273.15
Now, we can plug in the values:
n = (P (in atm) * V (in L))/(R * T (in Kelvin))
The ideal gas constant, R, is 0.0821 L·atm/mol·K.
Once we have the number of moles (n) of water vapor, we can calculate the mass of water vaporized using the molar mass of water (H2O), which is 18.015 g/mol.
Mass of water vaporized = n * molar mass of water
To summarize the steps for the calculation:
1. Convert the pressure from mmHg to atm.
2. Convert the temperature from degrees Celsius to Kelvin.
3. Calculate the number of moles of water vapor using the ideal gas law.
4. Calculate the mass of water vaporized using the number of moles and the molar mass of water.