Question

Air at 293 K and 750 mm Hg pressure has a relative humidity of 80%. What is its percent humidity? The vapour pressure of water at 293 K is 17.5 mm Hg. (a) 80.38 (b) 80 (c) 79.62 (d) 78.51

Answer 1

Answer : The correct option is, (c) 79.62

Explanation :

The formula used for percent humidity is:

`\text{Percent humidity}=\text{Relative humidity}* (p-p^o_v)/(p-p_v)* 100` ..........(1)

The formula used for relative humidity is:

`\text{Relative humidity}=(p_v)/(p^o_v)` ...........(2)

where,

`p_v` = partial pressure of water vapor

`p^o_v` = vapor pressure of water

p = total pressure

First we have to calculate the partial pressure of water vapor by using equation 2.

Given:

`p=750mmHg`

`p^o_v=17.5mmHg`

Relative humidity = 80 % = 0.80

Now put all the given values in equation 2, we get:

`0.80=(p_v)/(17.5mmHg)`

`p_v=14mmHg`

Now we have to calculate the percent humidity by using equation 1.

`\text{Percent humidity}=0.80* (750-17.5)/(750-14)* 100`

`\text{Percent humidity}=79.62\%`

Therefore, the percent humidity is 79.62 %