The Dew Point. The vapor pressure of water (see Problem) decreases as the temperature decreases. If the amount of water vapor in the air is kept constant as the air is cooled, a temperature is reached, called the ?dew point?, at which the partial pressure and vapor pressure coincide and the vapor is saturated. If the air is cooled further, vapor condenses to liquid until the partial pressure again equals the vapor pressure at that temperature The temperature in a room is 30.0°C. A meteorologist cools a metal can by gradually adding cold water. When the can temperature reaches 16.0°C, water droplets form on its outside surface. What is the relative humidity at the 30.0°C air in the room? The table lists the vapor pressure of water at various temperatures: Temperat Vapour ure? ?(°C) Pressure? ?(Pa) 10.0 1.23 × 103 12.0 1.40 × 103 14.0 1.60 × 103 16.0 1.81 × 103 18.0 2.06 × 103 20.0 2.34 × 103 22.0 2.65 × 103 24.0 2.99 × 103 26.0 3.36 × 103 28.0 3.78 × 103 30.0 4.25 × 103 Problem: Meteorology. The ?vapor pressure is the pressure of the vapor phase of a substance when it is in equilibrium with the solid or liquid phase of the substance. The ?relative humidity is the partial pressure of water vapor in the air divided by the vapor pressure of water at that same temperature, expressed as a percentage The air is saturated when the humidity is 100%. (a) The vapor pressure of water at 20.0°C is 2.34 × 103 Pa If the air temperature is 20.0°C and the relative humidity is 60%, what is the partial pressure of water vapor in the atmosphere (that is, the pressure due to water vapor alone)? (b) Under the conditions of part (a), what is the mass of water in 1.00 m3 of air? (The molar mass of water is 18.0 g/mol. Assume that water vapor can be treated as an ideal gas.)
Solution 89P 0 The room temperature was 30 c. After adding water, the temperature of the can reached at 16 c. 0 0 3 The vapour pressure at 30 c is 4.25 × 10 Pa. 0 3 The vapour pressure at 16 cwas 1.81 × 10 Pa. The relative humidity is, 1.81×10 Pa 4.25×10 Pa × 100 = 42.58 %. Conclusion: The relative humidity is 42.58 %.
