Question

The concentration of $C{O_2}$ in a soft disk that is bottled with a partial pressure of $C{O_2}$ as $4atm$ our the liquid at ${25^ \circ }C$ $\left( {{{\left( {{K_H}} \right)}_{{{25}^ \circ }C}} = 3.1 \times {{10}^{ - 2}}mol/litatm} \right)$
A.$1.24mol/lit$
B.$12.4mol/lit$
C.$0.124mol/lit$
D.$124mol/lit$

Answer 1

Hint: We know that Henry’s law states the relationship between solubility of the gas with partial pressure of the gas. We can calculate the concentration of carbon dioxide using the proportionality constant and the partial pressure of the gas. The product of the partial pressure and proportionality constant gives the concentration of the carbon dioxide.

Complete step by step solution:
Given data contains,
Partial pressure of carbon dioxide is $4atm$.
Proportional constant is $3.1 \times {10^{ - 2}}mol/litatm$.
We can explain Henry’s law as gas solubility present in the liquid is straightly proportional to the gas partial pressure present above the liquid.
For ionic/molecular solids, the solubility remains unaffected with respect to pressure.
For gases, the change in pressure would affect the solubility.
The solubility of a gas in liquid is straightly proportional to its partial pressure at any given temperature. At pressures of few atmospheres or less, the solubilities of gases obey Henry's law. The expression for Henry’s law is given as,
$C = kP$
Here, \[C\] represents concentration of the gaseous substance in solution
\[k\] represents proportionality constant
\[P\] represents partial pressure of the gaseous solute in contact with the solution.
We know that the concentration of carbon dioxide can be calculated using the formula,
$C = kP$
Let us substitute the values of proportionality constant and the partial pressure in the expression to calculate the concentration of carbon dioxide.
$C = kP$
$C = \left( {3.1 \times {{10}^{ - 2}}mol/litatm} \right)\left( {4atm} \right)$
$C = 0.124mol/lit$
We have calculated the concentration of the carbon dioxide as $0.124mol/lit$.
Therefore,option (C) is correct.

Note:
We can discuss some of the important applications of Henry’s law in the packing of soda cans and in deep-sea diving.
-Soda cans: We pack soda water bottles under higher pressures to raise the solubility of carbon dioxide gas. When soft drinks are opened some of the gas liberates giving a particular pop. This is because of the lower pressure above the liquid and carbon dioxide is liberated out in bubbles.
-Deep-sea diving: Helium is less soluble in nitrogen in our blood. In the deep sea, the surface of the water is less than the pressure. When the divers come faster towards the water surface, the pressure gets reduced and the dissolved nitrogen returns from blood and creates bubbles in veins. So, divers use oxygen diluted with helium.