Question

If ${N_2}$ gas is bubbled through water at $293K$ , how many millimoles of ${N_2}$ gas would dissolve in $1Litre$ water. Assuming that ${N_2}$ exerts a partial pressure of $0.987bar$ . Henry’s constant = $76.8Kbar$ .

Answer 1

According to Henry's law, at a constant temperature, the amount of a given gas that dissolves in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid. Thus, there is an increase of partial pressure of the gas with an increase in the solubility of the gas which depends on the mole fraction in the liquid mixture.

Complete step by step answer:

The solubility of a gas dissolved in the aqueous solution is dependent on its mole fraction in the aqueous solution. This mole fraction is determined with the help of Henry's law.
Mathematically, Henry’s law can be written as:
$p = {K_H}x$
Where, $p =$ partial pressure of the gas dissolved in the solvent
${K_H} =$ Henry’s constant
$x =$ mole fraction of the dissolved gas
Now, in the case of nitrogen gas dissolved in the water, the mole fraction can be determined as:
${x_{{N_2}}} = \dfrac{{{p_{{N_2}}}}}{{{K_H}}}$
Where, ${p_{{N_2}}} = 0.987bar$
${K_H} = 76480bar$
Substituting the values we have:
${x_{{N_2}}} = \dfrac{{0.987}}{{76480}} = 1.29 \times {10^{ - 5}}$
1 litre of water contains = $55.5moles$
Let the number of moles of nitrogen in the aqueous solution be $a$ .
Thus, ${x_{{N_2}}} = \dfrac{a}{{a + 55.5}}$
The number of moles of nitrogen is very less in comparison to that of the moles of water.
Thus, ${x_{{N_2}}} = \dfrac{a}{{a + 55.5}} \approx \dfrac{a}{{55.5}}$
We have already calculated the value of the mole fraction. Thus, substituting the value, we have:
$1.29 \times {10^{ - 5}} = \dfrac{a}{{55.5}} \Rightarrow a = 1.29 \times {10^{ - 5}} \times 55.5$
Thus, the number of moles of nitrogen will be equal to:
$a = 7.16 \times {10^{ - 4}}mol = 7.16 \times {10^{ - 4}}mol \times \dfrac{{1000mmol}}{{1mol}}$
Hence, the amount of nitrogen in millimoles will be:
$a = 0.716mmol$

Note:
Henry’s law is used in carbonated soft drinks. When the soft drink bottle is opened, some of the gas escapes giving a specific pop sound. This is due to the lower pressure above the liquid and carbon dioxide comes out as bubbles and produces effervescence. Henry's law is also applicable in respiration in the human body by easing the exchange of gases around alveoli.