On a warm day, the saturated vapour pressure of water at an ambient temperature of 25^\cir… — JAMB UTME

On a warm day, the saturated vapour pressure of water at an ambient temperature of $25^\circ\text{C}$ is $24\text{ mmHg}$ . If the actual partial pressure of water vapour in the air at this temperature is $18\text{ mmHg}$ , what is the relative humidity of the atmosphere?

$75\%$ Answer
B
$133\%$
C
$25\%$
D
$43\%$

Answer

The relative humidity of the atmosphere is

75\%

The relative humidity is defined as the ratio of the partial vapour pressure of water present in the air to the saturated vapour pressure at the ambient temperature, expressed as a percentage. Dividing

18\text{ mmHg}

24\text{ mmHg}

yields

0.75

, which equals

75\%

Step-by-Step Solution

Identify the formula for relative humidity.

\text{Relative Humidity} = \left(\frac{\text{Partial Vapour Pressure}}{\text{Saturated Vapour Pressure at same temp}}\right) \times 100\%

Relative humidity measures how close atmospheric air is to saturation at a given temperature.

Substitute the given values into the formula.

\text{Relative Humidity} = \left(\frac{18\text{ mmHg}}{24\text{ mmHg}}\right) \times 100\%

The partial pressure is

18\text{ mmHg}

and the saturated vapour pressure is

24\text{ mmHg}

Calculate the final percentage.

\text{Relative Humidity} = 0.75 \times 100\% = 75\%

Simplifying

\frac{18}{24}

gives

\frac{3}{4}

, which corresponds to

0.75

75\%

Key Concept

Relative humidity is the ratio of the actual mass (or partial pressure) of water vapour in a given volume of air to the maximum mass (or saturated vapour pressure) of water vapour that the same volume of air can hold at that same temperature, expressed as a percentage.

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