Question

What is Henry's constant for neon dissolved in water given \[{{{C}}_{{{Ne}}}}{{ = 23}}{{.5mL/L}}\] solution and STP volume \[{{22,414 mL/mole}}\] gas and pressure \[\left( {{{1 atm}}} \right)\]?
A. \[0.00105\]
B. \[{{0}}{{.11004}}\]
C. \[{{0}}{{.00115}}\]
D. \[{{0}}{{.00015}}\]

Answer 1

Hint: The relation between pressure and solubility of a gas in a solvent is known as Henry’s law. According to this law, solubility of gas is directly proportional to the partial pressure of gas, Henry’s constant is the constant of proportionality. From the given concentration of neon, the number of moles can be found and hence, Henry’s constant can be determined.

Complete step by step answer:
Henry’s law is a gas law; it states that the solubility of a gas is directly proportional to the partial pressure of gas above the surface of the liquid.
Dalton also included that liquid solubility of a gas that is dissolved in a liquid is directly proportional to the partial pressure of that gas above the liquid when the temperature is kept constant. The proportionality constant is called Henry’s constant; it is denoted by \['{K_H}'\]. Different gases have different \['{K_H}'\] at the same temperature. The higher the value of \['{K_H}'\] the lower the solubility.
There are two forms of the law,
\[{{P}}\,\,\propto \,\,{{C}}\]
\[{{S }}\,\propto \,\,{{P}}\]
The proportionality is \['{K_H}'\], the equation becomes,
\[{{P = }}{{{K}}_{{H}}}\, \times \,\,{{C}}\]
\[{{S = }}{{{K}}_{{H}}}{{P}}\]
Where,
‘P’ is the partial pressure of the gas in the atmosphere above the liquid.
‘S’ is the solubility of gas in liquid.
‘C’ denotes the concentration of the dissolved gas.
\['{K_H}'\] is the Henry’s law constant of the gas.
As per the question,\[{{ 1L}}\] of solution contains \[{{23}}{{.5 mL}}\], volume at STP is given as \[{{22,414 mL}}\]
Number of moles of neon \[{{ = }}\,\,\dfrac{{{{23}}{{.5}}}}{{{{22414}}}}{{ = }}\,{{0}}{{.001048 moles}}\]
Thus, the concentration of the solution is \[{{0}}{{.001048M}}\] i.e., the solubility is \[{{0}}{{.001048M}}\]
According to Henry's law
\[{{S = }}{{{K}}_{{H}}}{{P}}\]
\[{{0}}{{.001048 = }}{{{K}}_H}\times{{ l}}\,{{atm }}\]
\[{{{K}}_H}{{ = }}\,{{0}}{{.001048 Lat}}{{{m}}^{{{ - 1}}}}{{ = 0}}{{.00105 Lat}}{{{m}}^{{{ - 1}}}}\]

So, the correct answer is A.

Additional information:
Equilibrium constant \[{{{K}}_{{c}}}\] for a reverse reaction is the inverse of the equilibrium constant for the reaction in forward direction. Catalyst does not affect equilibrium but increases the rate of the chemical reaction.

Note: Henry’s law has many applications. The amount of oxygen that dissolves in the bloodstream is directly proportional to the partial pressure of oxygen in air. Day to day example of Henry’s law is given by carbonated soft drinks, the gas above the drink is almost pure carbon dioxide at a pressure slightly higher than the atmospheric pressure. When the bottle is opened some of the gas escapes producing a pop sound. This is due to the lower pressure above the liquid and carbon dioxide comes out as bubbles.Mole fraction, molarity, molality, mass percentage etc are different methods to express concentration.