Question

Henry’s Law constant for $C{{O}_ {2}} $ in water is $1.67\times {{10} ^ {8}} Pa$ at 298 K. Calculate the quantity in 1 L of soda water when packed under 2.5 atm pressure at 298 K.

Answer 1

Hint: Henry's law is a gas law that states that the amount of dissolved gas in a liquid is proportional to its partial pressure above the liquid. The proportionality factor is called Henry's law constant.

Complete step by step solution:
Henry's law states that the solubility of a gas in a liquid is directly proportional to the pressure of the gas,
We have been provided with Henry’s Law constant for $C{{O}_ {2}} $ in water is $1.67\times {{10} ^ {8}} Pa$ at 298 K,
We need to calculate the quantity of 1 L of soda water when packed under 2.5 atm pressure at 298 K,
So, as we know Henry’s Law: $P={{K}_{H}} \times x$
where 'P' denotes the partial pressure of the gas in the atmosphere above the liquid. 'x’ denotes the concentration of the dissolved gas.
So, the value of x:
\ [x=\dfrac {2.5\times 1.013\times {{10} ^ {5}}} {1.6\times {{10} ^ {8}}} \]
We know that concentration can be written as:
\[x=\dfrac{{{n}_{C{{O}_ {2}}}}} {\dfrac {1000}{18}} \]
Simplifying it further:
\[\dfrac{{{n}_{C{{O}_ {2}}}}} {\dfrac {1000}{18}} =\dfrac {2.5\times 1.013} {1.6\times 1000} \]
So, from here the value of ${{n}_{C{{O}_ {2}}}} $: ${{n}_{C{{O}_ {2}}}} =\dfrac {25}{16} \times \dfrac {1.013}{18} $,
We know the formula for calculating the mass is: mass= number of moles $\times $molar mass,
So, as we know molar mass of carbon dioxide = 44,
So, keeping this value in the above formula: mass of $C{{O}_ {2}} $ dissolved = $\dfrac {25}{16} \times \dfrac {44\times 1.013}{18} $,
So, the mass of carbon dioxide dissolved comes out to be: 3.86 grams.

Note: The main application of Henry's law in respiratory physiology is to predict how gasses will dissolve in the alveoli and bloodstream during gas exchange. The amount of oxygen that dissolves into the bloodstream is directly proportional to the partial pressure of oxygen in alveolar air.