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# Question fc3a5

Jan 4, 2017

The molar solubilities of ${\text{NH}}_{3}$ and ${\text{CO}}_{2}$ in water are 30 mol/L and 0.017 mol/L, respectively. The ratio of their solubilities is 1800:1.

#### Explanation:

Henry's law states that the solubility of a gas ($C$) in a liquid is directly proportional to the partial pressure of the gas ($P$) above the liquid:

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} C = k P \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

where

$k$ is a proportionality constant called Henry's law constant

If the two gases are in equal proportion,

${P}_{\text{NH₃" = P_"CO₂" = "0.5 atm}}$

Then

${C}_{\text{NH₃" = kP_"NH₃" = "61 mol·L"^"-1"color(red)(cancel(color(black)("atm" ^"-1"))) × 0.5 color(red)(cancel(color(black)("atm"))) = "30 mol/L}}$

${C}_{\text{CO₂" = kP_"CO₂" = "0.034 mol·L"^"-1"color(red)(cancel(color(black)("atm" ^"-1"))) × 0.5 color(red)(cancel(color(black)("atm"))) = "0.017 mol/L}}$

C_"NH₃"/C_"CO₂" = (30 color(red)(cancel(color(black)("mol/L"))))/(0.017 color(red)(cancel(color(black)("mol/L")))) = 1800#

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