<u>Answer:</u> The number of molecules of carbon dioxide gas are ![2.815\times 10^{21}](https://tex.z-dn.net/?f=2.815%5Ctimes%2010%5E%7B21%7D)
<u>Explanation:</u>
To calculate the molar solubility, we use the equation given by Henry's law, which is:
![C_{CO_2}=K_H\times p_{CO_2}](https://tex.z-dn.net/?f=C_%7BCO_2%7D%3DK_H%5Ctimes%20p_%7BCO_2%7D)
where,
= Henry's constant = ![0.034mol/L.atm](https://tex.z-dn.net/?f=0.034mol%2FL.atm)
= molar solubility of carbon dioxide gas
= pressure of carbon dioxide gas = 0.250 atm
Putting values in above equation, we get:
![C_{CO_2}=0.034mol/L.atm\times 0.250atm\\\\C_{CO_2}=8.5\times 10^{-3}M](https://tex.z-dn.net/?f=C_%7BCO_2%7D%3D0.034mol%2FL.atm%5Ctimes%200.250atm%5C%5C%5C%5CC_%7BCO_2%7D%3D8.5%5Ctimes%2010%5E%7B-3%7DM)
To calculate the number of moles for given molarity, we use the equation:
![\text{Molarity of the solution}=\frac{\text{Moles of solute}}{\text{Volume of solution (in L)}}](https://tex.z-dn.net/?f=%5Ctext%7BMolarity%20of%20the%20solution%7D%3D%5Cfrac%7B%5Ctext%7BMoles%20of%20solute%7D%7D%7B%5Ctext%7BVolume%20of%20solution%20%28in%20L%29%7D%7D)
Molarity of carbon dioxide = ![8.5\times 10^{-5}M](https://tex.z-dn.net/?f=8.5%5Ctimes%2010%5E%7B-5%7DM)
Volume of solution = 0.550 L
Putting values in above equation, we get:
![8.5\times 10^{-3}M=\frac{\text{Moles of }CO_2}{0.550L}\\\\\text{Moles of }CO_2=(8.5\times 10^{-3}mol/L\times 0.550L)=4.675\times 10^{-3}mol](https://tex.z-dn.net/?f=8.5%5Ctimes%2010%5E%7B-3%7DM%3D%5Cfrac%7B%5Ctext%7BMoles%20of%20%7DCO_2%7D%7B0.550L%7D%5C%5C%5C%5C%5Ctext%7BMoles%20of%20%7DCO_2%3D%288.5%5Ctimes%2010%5E%7B-3%7Dmol%2FL%5Ctimes%200.550L%29%3D4.675%5Ctimes%2010%5E%7B-3%7Dmol)
According to mole concept:
1 mole of a compound contains
number of molecules
So,
moles of carbon dioxide will contain =
number of molecules
Hence, the number of molecules of carbon dioxide gas are ![2.815\times 10^{21}](https://tex.z-dn.net/?f=2.815%5Ctimes%2010%5E%7B21%7D)