The saturated vapour pressure of water in an enclosed space is 25\text{ mmHg}. If the rela… — JAMB UTME

The saturated vapour pressure of water in an enclosed space is $25\text{ mmHg}$ . If the relative humidity within the space is measured to be $64\%$ , what is the partial pressure of the water vapour in $\text{mmHg}$ ?

Answer: 16 mmHg

Answer

The partial pressure of the water vapour in the enclosed space is

16\text{ mmHg}

Relative humidity is defined as the ratio of the actual partial pressure of water vapour present in a given volume of air to the saturated vapour pressure at the same temperature, expressed as a percentage:

\text{R.H.} = \frac{P}{\text{S.V.P.}} \times 100\%

. Rearranging this equation gives

P = \frac{\text{R.H.} \times \text{S.V.P.}}{100} = \frac{64 \times 25}{100} = 16\text{ mmHg}

Step-by-Step Solution

Identify the given parameters and state the relative humidity formula.

Relative Humidity (R.H.) =

64\%

, Saturated Vapour Pressure (S.V.P.) =

25\text{ mmHg}

\text{R.H.} = \frac{P}{\text{S.V.P.}} \times 100\%

Relative humidity relates the actual partial vapour pressure present to the maximum saturated vapour pressure possible at that temperature.

Substitute the values into the equation and solve for partial pressure

P

64 = \frac{P}{25} \times 100 \implies 64 = 4P \implies P = 16\text{ mmHg}

Dividing

100

25

yields a factor of

4

, allowing clean mental computation.

Key Concept

Relationship between relative humidity, partial vapour pressure, and saturated vapour pressure.

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