To calculate the mass of water vaporized, we need to determine the amount of water that has evaporated from the flask. We can do this by using the ideal gas law, which relates the pressure, volume, temperature, and amount of gas. Here's how we can solve this problem step by step:
1. Convert the given temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 65 + 273.15 = 338.15K
2. Convert the vapor pressure from mmHg to atm:
1 atm = 760 mmHg
P(atm) = P(mmHg) / 760
P(atm) = 187.5 / 760 = 0.24605 atm
3. Apply the ideal gas law equation:
PV = nRT
P: Pressure in atmospheres (0.24605 atm)
V: Volume in liters (2.500 L)
n: Amount of substance in moles (unknown)
R: Ideal gas constant (0.08206 L·atm/(mol·K))
T: Temperature in Kelvin (338.15 K)
4. Rearrange the equation to solve for the amount of substance (moles):
n = PV / RT
n = (0.24605 atm * 2.500 L) / (0.08206 L·atm/(mol·K) * 338.15 K)
n = 0.024003 mol
5. Convert moles of water to grams:
The molar mass of water (Hâ‚‚O) is approximately 18.015 g/mol.
Mass = n * molar mass
Mass = 0.024003 mol * 18.015 g/mol
Mass ≈ 0.432 g
Therefore, the mass of water vaporized is approximately 0.432 grams.