Answer:
The value is
![H = 0.036 \ kg/m^3](https://img.qammunity.org/2021/formulas/physics/college/1xy16oyhk5dic38hw3zm44l2o1wv3s3t6p.png)
Step-by-step explanation:
From the question we are told that
The saturation density of air is
![\rho = 0.04 \ kg/m^3](https://img.qammunity.org/2021/formulas/physics/college/7yy8izc9bxqepbqj9vicfpj2tjodmwoufu.png)
The temperature for this saturation density to occur
![T_s = 96^o F](https://img.qammunity.org/2021/formulas/physics/college/yulm3y83s7cunzssc4upy4w13egd0c1kvs.png)
The relative humidity at this temperature is
![R_h = 90\% = 0.90](https://img.qammunity.org/2021/formulas/physics/college/fe591uw6gfoo9vk444i43nn1obw65shwtx.png)
Generally the relative humidity is mathematically represented as
![R_H = (H)/(\rho)](https://img.qammunity.org/2021/formulas/physics/college/sg3o2cbgbqsibvwgodg8jhaz18p2prxccf.png)
Here H represents humidity
=>
![0.90 = (H)/(0.04)](https://img.qammunity.org/2021/formulas/physics/college/x6vx9gddlvtkk2vsjrgffmebgnnomfshfa.png)
=>
![H = 0.90 * 0.04](https://img.qammunity.org/2021/formulas/physics/college/qamz6lfyi4vldkzpsj6l9cttjl5h5cmel3.png)
=>
![H = 0.036 \ kg/m^3](https://img.qammunity.org/2021/formulas/physics/college/1xy16oyhk5dic38hw3zm44l2o1wv3s3t6p.png)