The question is incomplete, here is the complete question:
Calculate the solubility of hydrogen in water at an atmospheric pressure of 0.380 atm (a typical value at high altitude).
Atmospheric Gas Mole Fraction kH mol/(L*atm)
![6.70\times 10^{-4}](https://tex.z-dn.net/?f=6.70%5Ctimes%2010%5E%7B-4%7D)
![1.30\times 10^{-3}](https://tex.z-dn.net/?f=1.30%5Ctimes%2010%5E%7B-3%7D)
Ar
![1.40\times 10^{-3}](https://tex.z-dn.net/?f=1.40%5Ctimes%2010%5E%7B-3%7D)
![3.50\times 10^{-2}](https://tex.z-dn.net/?f=3.50%5Ctimes%2010%5E%7B-2%7D)
![1.40\times 10^{-3}](https://tex.z-dn.net/?f=1.40%5Ctimes%2010%5E%7B-3%7D)
![7.80\times 10^{-4}](https://tex.z-dn.net/?f=7.80%5Ctimes%2010%5E%7B-4%7D)
<u>Answer:</u> The solubility of hydrogen gas in water at given atmospheric pressure is ![1.48\times 10^{-10}M](https://tex.z-dn.net/?f=1.48%5Ctimes%2010%5E%7B-10%7DM)
<u>Explanation:</u>
To calculate the partial pressure of hydrogen gas, we use the equation given by Raoult's law, which is:
![p_{\text{hydrogen gas}}=p_T\times \chi_{\text{hydrogen gas}}](https://tex.z-dn.net/?f=p_%7B%5Ctext%7Bhydrogen%20gas%7D%7D%3Dp_T%5Ctimes%20%5Cchi_%7B%5Ctext%7Bhydrogen%20gas%7D%7D)
where,
= partial pressure of hydrogen gas = ?
= total pressure = 0.380 atm
= mole fraction of hydrogen gas = ![5.00\times 10^{-7}](https://tex.z-dn.net/?f=5.00%5Ctimes%2010%5E%7B-7%7D)
Putting values in above equation, we get:
![p_{\text{hydrogen gas}}=0.380\times 5.00\times 10^{-7}\\\\p_{\text{hydrogen gas}}=1.9\times 10^{-7}atm](https://tex.z-dn.net/?f=p_%7B%5Ctext%7Bhydrogen%20gas%7D%7D%3D0.380%5Ctimes%205.00%5Ctimes%2010%5E%7B-7%7D%5C%5C%5C%5Cp_%7B%5Ctext%7Bhydrogen%20gas%7D%7D%3D1.9%5Ctimes%2010%5E%7B-7%7Datm)
To calculate the molar solubility, we use the equation given by Henry's law, which is:
![C_{H_2}=K_H\times p_{H_2}](https://tex.z-dn.net/?f=C_%7BH_2%7D%3DK_H%5Ctimes%20p_%7BH_2%7D)
where,
= Henry's constant = ![7.80\times 10^{-4}mol/L.atm](https://tex.z-dn.net/?f=7.80%5Ctimes%2010%5E%7B-4%7Dmol%2FL.atm)
= partial pressure of hydrogen gas = ![1.9\times 10^{-7}atm](https://tex.z-dn.net/?f=1.9%5Ctimes%2010%5E%7B-7%7Datm)
Putting values in above equation, we get:
![C_{H_2}=7.80\times 10^{-4}mol/L.atm\times 1.9\times 10^{-7}atm\\\\C_{CO_2}=1.48\times 10^{-10}M](https://tex.z-dn.net/?f=C_%7BH_2%7D%3D7.80%5Ctimes%2010%5E%7B-4%7Dmol%2FL.atm%5Ctimes%201.9%5Ctimes%2010%5E%7B-7%7Datm%5C%5C%5C%5CC_%7BCO_2%7D%3D1.48%5Ctimes%2010%5E%7B-10%7DM)
Hence, the solubility of hydrogen gas in water at given atmospheric pressure is ![1.48\times 10^{-10}M](https://tex.z-dn.net/?f=1.48%5Ctimes%2010%5E%7B-10%7DM)