Question

contamination from accidental discharges of organic compounds used by large industries, airports, small businesses, and homeowners poses a challenging problem for amelioration. soil contaminated with polyaromatic hydrocarbons can be treated with hot air and steam to drive out the contaminants. of 30.0 m3 of air at 100. oc and 98.6 kpa with a dew point of 30. oc is introduced into the contaminated soil, and in the soil the gas cools to 14oc at a pressure of 109.1 kpa, what fraction of the water vapor in the gas at 100. oc will condense out in the soil if the gas does not escape too rapidly from the soil?

Answer 1

98.7% of the water vapor in the gas at 100°C will condense out in the soil.

How to find fraction?

To determine the fraction of water vapor that condenses out in the soil, compare the partial pressures of water vapor at the initial and final conditions.

Initial conditions:

Temperature: 100°C

Pressure: 98.6 kPa

Dew point: 30°C

Final conditions:

Temperature: 14°C

Pressure: 109.1 kPa

To calculate the partial pressure of water vapor at the initial conditions, use the following equation:

`P_v = P_(sat) * RH`

where:

`P_v` = partial pressure of water vapor

`P_{sat` = saturation vapor pressure at the given temperature

RH = relative humidity

The relative humidity can be calculated using the following equation:

`RH = (P_(act) / P_(sat)) * 100\%`

where

`P_{act` = actual vapor pressure.

Find the saturation vapor pressure at 30°C from a table of vapor pressures. At 30°C, the saturation vapor pressure is 4.24 kPa.

Plugging in the values for
`P_{sat` and RH:

`P_v` = 4.24 kPa × (30.0% / 100%)

= 1.272 kPa

At 14°C, the saturation vapor pressure of water is 1.22 kPa.

To calculate the partial pressure of water vapor at the final conditions, use the following equation:

`P_v = P_(sat) * (P_(act) / P_(initial))`

where

`P_{initial` = initial partial pressure of water vapor.

Plugging in the values for
`P_{sat`,
`P_{act`, and
`P_{initial`:

`P_v` = 1.22 kPa × (1.272 kPa / 98.6 kPa)

= 0.016 kPa

To find the fraction of water vapor that condenses:

Fraction of water vapor that condenses =
`(P_(initial) - P_(final)) / P_{initial`

Plugging in the values for
`P_{initial` and
`P_{final`:

Fraction of water vapor that condenses = (1.272 kPa - 0.016 kPa) / 1.272 kPa

= 0.987

Therefore, 98.7% of the water vapor in the gas at 100°C will condense out in the soil.