Question

If ${N_2}$ gas is bubbled through water at $293\,K.$ calculate the solubility of ${N_2}$ gas? Assume that ${N_2}$ exerts a partial pressure of $0.987$ bar. Given that Henry’s law constant for ${N_2}$ at $293\,K$ is $76.48\,\dfrac{{k\,bar}}{{mole/litre}}$
$
  A)1.29 \times {10^{ - 5}}\dfrac{{mole}}{{litre}} \\
  B)1.29 \times {10^{ - 4}}\dfrac{{mole}}{{litre}}\, \\
  C)2.9 \times {10^{ - 3}}\dfrac{{mole}}{{litre}} \\
  D)2.9 \times {10^{ - 3}}\dfrac{{mole}}{{litre}} \\
 $

Answer 1

Hint: We can calculate the solubility of nitrogen gas using Henry’s law. From the values of henry’s law and pressure, we can calculate the solubility of the gas.
Formula used: We can calculate the solubility of a gas using the formula,
${P_{gas}} = k{\chi _{gas}}$
Here, ${P_{gas}}$ is the pressure of the gas
$k$ is Henry’s constant
${\chi _{gas}}$ is the mole fraction of the gas

Complete step by step answer:
We know that the solubility of a gas in a liquid is given with the help of Henry’s law.
Henry’s law states that the mole fraction of a gas that is dissolved in a liquid is directly proportional to the pressure of the gas.
The equation that is used to represent Henry’s law is written as,
${P_{gas}} = k{\chi _{gas}}$
From the given data, that is partial pressure of the gas is $0.987\,bar.$ The henry’s constant is $76.48\,\dfrac{{kbar}}{{mole/litre}}.$ we can calculate the solubility of the gas.

The formula that we use to calculate the solubility of the gas is,

\[
  {P_{gas}} = k{\chi _{gas}} \\
  {\chi _{gas}} = \dfrac{{{P_{gas}}}}{k} \\
 \]

The value of Henry’s constant in kbar is converted to bar by multiplying the value with 1000.
$
  bar = 76.48\dfrac{{k\,bar}}{{mole/litre}} \times \dfrac{{1000\,bar}}{{1\,kbar}} \\
  bar = 76480\,\,\dfrac{{bar}}{{mole/litre}} \\
 $
The value of henry’s constant in bar is $76480\,\,\dfrac{{bar}}{{mole/litre}}.$
We can substitute the value of partial pressure and Henry’s constant to get solubility.
$
  {\chi _{gas}} = \dfrac{k}{{{P_{gas}}}} \\
  {\chi _{gas}} = \dfrac{{0.987\,bar}}{{76480\,\dfrac{{bar}}{{mole/litre}}}} \\
  {\chi _{gas}} = 1.29 \times {10^{ - 5}}\dfrac{{mole}}{{litre}} \\
 $
The solubility of the gas is $1.29 \times {10^{ - 5}}\,\dfrac{{mole}}{{litre}}.$
Hence option (A) is correct.

Note:
There is no change in solubility of liquids and solids with pressure changes, whereas in gases, the solubility increases with increase in pressure. An example of solubility of gases with changes is pressure is carbonated beverages. All carbonated beverages are kept under pressure to raise the amount of carbon dioxide dissolved in the solution. When we open the bottle, the pressure present above the solution reduces and it leads to effervescences of the solution, and a few amounts of carbon dioxide bubbles.