Respuesta :
Given:
Henry's law constant at 30 deg. celcius =4.48x10^-5 M/mmHg
Total pressure of the gases= 1 atm= 760 mmHg
Pressure of water vapor=31.8 mmHg
We will firstly determine the pressure of the carbon dioxide gas by using Dalton's Law of partial pressures:
[tex]\begin{gathered} P_T=P_{CO_2}+P_{H_2O} \\ 760mmHg=P_{CO_2}+31.8mmHg \\ P_{CO_2}=760mmHg-31.8mmHg \\ P_{CO_2}=728.2\text{ }mmHg \end{gathered}[/tex]By determining the pressure of the carbon dioxide gas we can now use the Henry's Law of Gas Solubility to detemine the molar concentration:
[tex]\begin{gathered} C_{CO_2}=k_H\times P_{CO_2} \\ C_{CO_2}:molarity\text{ }of\text{ }gas \\ k_H:the\text{ }Henry\text{ }Law\text{ }Constant=4.48\times10^{-5}MmmHg^{-1} \\ P_{CO_2}:the\text{ }partial\text{ }pressure\text{ }of\text{ }the\text{ }gas=728.2mmHg \\ \\ C_{CO_2}=4.48\times10^{-5}MmmHg^{-1}\times728.2mmHg \\ C_{CO_2}=0.033M \end{gathered}[/tex]Now thaat we have the molar concentration we will convert this mass concentration:
[tex]\begin{gathered} mass\text{ }concentration=molar\text{ }mass\times molar\text{ }concentration \\ mass\text{ }concentration=44.01gmol^{-1}\times0.033molL^{-1} \\ mass\text{ }concentration=1.45gL^{-1} \end{gathered}[/tex]We convert this mass concentration to g/mL:
[tex]1.45\frac{g}{L}\times\frac{1L}{1000mL}=1.45\times10^{-3}gmL^{-1}[/tex]Answer: The concentration of the CO2 is 1.45x10^-3 g/mL.
