Question

1Kg of water under a nitrogen pressure of 1 atmosphere dissolves 0.02 gm of nitrogen at 293 K. Calculate Henry’s law constant.
A. $7.2\times {{10}^{-4}}atm$
B. $7.5\times {{10}^{4}}atm$
C. $7.4\times {{10}^{4}}atm$
D. $7.8\times {{10}^{4}}atm$

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 known by Henry's law constant. Henry constant is generally temperature dependent when temperature changes, Henry constant also changes.

Complete answer:
According to this law, partial pressure of the gas is directly proportional to the concentration of the dissolved gas shown by
$P\alpha C$; where constant of proportionality given by the term K which is defined as Henry’s constant it can also be represented by ${{K}_{H}}$, Therefore, the equation is shown as:
$P={{K}_{H}}C$, it can also be expressed in terms of mole dfraction where$P={{K}_{H}}x$; where x represents mole dfraction of dissolved nitrogen.
Number of moles of water,
${{n}_{1}}=\dfrac{1000}{18}=55.55moles$
Number of moles of nitrogen solution,
${{n}_{2}}=\dfrac{0.02}{28}=7.14\times {{10}^{-4}}moles$
Mole dfraction of dissolved nitrogen is given by:
$x=\dfrac{{{n}_{2}}}{{{n}_{1}}+{{n}_{2}}}$
= $x=\dfrac{7.14\times {{10}^{-4}}}{7.14\times {{10}^{-4}}+55.55}=1.28\times {{10}^{-5}}$
Now, $P={{K}_{H}}x$
$\therefore {{K}_{H}}=\dfrac{P}{x}=\dfrac{1}{1.28\times {{10}^{-5}}}=7.8\times {{10}^{4}}atm$

Hence option D is the correct answer.

Note:
Henry law is only applicable when the molecules of the system are in equilibrium and under high pressure this law does not prove to be true and also not applicable when the gas and the solution participate in chemical reactions with each other.