Question

Calculate the concentration of $C{O_2}$ in a soft drink that is bottled with a partial pressure of $4atm$ over the liquid at $25^\circ C$ . The Henry’s law constant for $C{O_2}$ in water at $25^\circ C\,is\,3.1 \times {10^{ - 2}}atm/mole - litre$
A. $0.129mole/litre$
B. $129.03mole/litre$
C. $0.224mole/litre$
D. $224.03mole/litre$

Answer 1

Hint: Henry’s law explains the solubility of a gas in a liquid. It gives the relationship between solubility and pressure of a gas. Solubility helps us to understand the extent of dissolution of a solute or any component in the solution. It is generally used to study the nature of gases.

Complete step by step answer:
Solubility of a substance is the maximum amount of substance that can dissolve in a specific amount of solvent. This solubility depends on various factors like the nature of solute and solvent, temperature and pressure. Gases dissolve in many solvents. Water being a universal solvent, most of the gases get dissolved in it. Oxygen can dissolve only upto a small extent. Because of this dissolved oxygen, aquatic animals can survive in water. Solubility of gases is affected mainly by temperature and pressure.
As pressure increases the solubility of gases also increases. The relationship between pressure of a gas and its solubility in solvent was first given by Henry. Henry’s law states that at constant temperature, the solubility of a gas in a liquid is directly proportional to the pressure of the gas. Mathematically it can be expressed as-
$S\;\alpha \;P$
Where $S$ is the solubility and $P$ is the pressure of the gas.
$P = SK$ where $K$ is the Henry constant.
Now we have been given the pressure of $C{O_2}$ gas and its Henry’s constant. Substituting the values we get,
$S = {4}{{3.1 \times {{10}^{ - 2}}}} = 129.03lit/mole$

So, the correct answer is Option B.

Note: Solubility defines the amount of dissolution of any component in a solution. So here concentration means solubility.
Another most commonly used Henry’s law states that - the partial pressure of the gas in vapour phase is directly proportional to the mole fraction of the gas in solution.
Note: Solubility of gases increase with increase in pressure and decrease with increase in temperature. Henry’s law finds several applications in industry. For example, to increase the solubility of carbon-dioxide in aerated drinks, the bottles are sealed under high pressure