Question

If ${N_2}$ gas is bubbled through water at $293\,K$, how many millimoles of ${N_2}$ gas would dissolve in $300$ moles of water, if ${N_2}$ exerts a partial pressure of $1\,bar$. Given Henry's law constant for ${N_2}$ at $293\,K$ is $75.00\,Kbar$.

Answer 1

We know mathematically Henry’s law is expressed as,
$P = Kx$
Where, P is the pressure.
X is the mole fraction.
K is Henry’s law constant.

Complete step by step answer:
Let us see Henry’s law statement.
Henry’s law states that at a constant temperature the amount of gas that dissolves in a given liquid is directly proportional to the pressure of the gas which is in equilibrium with that liquid.
Let us write the given information.
The number of moles of water $= 300\,moles$
The partial pressure $= 1\,bar$
Henry’s constant of nitrogen $= 75.00\,Kbar$
Substitute the values.
$P = Kx$
$1\,bar = 75000x$
$x = \dfrac{1}{{75000}} = 1.33 \times {10^{ - 5}}$
Let us calculate the millimoles of nitrogen.
Mole fraction $= \dfrac{{{N_2}\,moles\left( n \right)}}{{{N_2}\,moles\left( n \right) + 300}}$
$\dfrac{{{N_2}\,moles\left( n \right)}}{{{N_2}\,moles\left( n \right) + 300}} \simeq \dfrac{{{N_2}\,moles\left( n \right)}}{{300}} = 1.33 \times {10^{ - 5}}$
The number moles of nitrogen (n) = $300 \times 1.33 \times {10^{ - 5}}$
The number moles of nitrogen (n) = $0.00399\,moles$
$\therefore$ The millimoles of nitrogen $3.99\,millimoles.$

Additional Information:
We must know that Henry's law is applicable only in certain conditions. The conditions are,
It works only if the molecules are at equilibrium.
It does not work for gases at high pressure. For example, Nitrogen at high pressure it becomes soluble and it is harmful in the blood supply.
It does not work if there is a chemical reaction between the solute and solvent. For example, Hydrochloric acid reacts with water by a dissociation reaction to generate hydronium and chloride ions.

Note:
We have to remember to convert the Henry’s constant in $Kbar$ to $bar$.
$1\,kbar = 1000\,bar$
$75.00\,kbar = 75000\,bar$
Mole fraction gives the number of molecules of a component in the mixture divided by total number of moles in the mixture.
$Mole\,fraction\,\left( x \right) = \dfrac{{Moles\,of\,solute}}{{Moles\,of\,Solute + \,Moles\,of\,solvent}}$