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:

$\text{Percent humidity}=\text{Relative humidity}\times \frac{p-p^o_v}{p-p_v}\times 100$   ..........(1)

The formula used for relative humidity is:

$\text{Relative humidity}=\frac{p_v}{p^o_v}$       ...........(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:

$0.80=\frac{p_v}{17.5mmHg}$

$p_v=14mmHg$

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

$\text{Percent humidity}=0.80\times \frac{750-17.5}{750-14}\times 100$

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

Therefore, the percent humidity is 79.62 %