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Henry’s law constant for \[C{O_2}\] in water is \[1.67 \times {10^8}\] pa at 298 K the quantity of \[C{O_2}\] in 500ml of soda water when packed under 2.5 atm pressure is:
(A) 0.082 mole
(B) 0.82 mole
(C) 0.41 mole
(D) 0.042 mole

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Last updated date: 20th Jun 2024
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Answer
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Hint: In order to answer the given question, we must first have an idea about what a Henry’s law is. Henry’s law is a type of gas law which states that the amount of gas dissolved in a liquid will be proportional to its partial pressure above the liquid. the formula for Henry’s law is given below:
\[p\propto C\]
\[p = {k_H}C\]

Complete step by step answer:
- Let us first understand about Henry’s law. Henry’s law is a type of gas law which states that the amount of gas dissolved in a liquid will be proportional to its partial pressure above the liquid. the formula for Henry’s law is given below:
\[p\alpha C\]
\[p = {k_H}C\]
- Now let us move onto the problem given
The Henry’s constant for a gas is given as
\[{k_H} = 1.67 \times {10^8}\]
The partial pressure of carbon dioxide is
\[{P_{C{O_2}}} = 2.5 atm = 2.5 \times 1.0132 \times {10^5}Pa\]
- From the Henry’s law
\[{P_{C{O_2}}} = {k_H}x\]
\[x = \dfrac{{{P_{C{O_2}}}}}{{{k_H}}}\]
\[x = \dfrac{{2.5 \times 1.01332 \times {{10}^5}}}{{1.67 \times {{10}^8}}} = 1.52 \times {10^{ - 3}}\]
As in the question, it is given that there is 500 ml of water. The amount of the soda will be neglected.
Therefore, the volume of water =500ml
Number of moles of water, i.e., \[{n_{{H_2}O}}\]=27.78 moles
- We can write the mole fraction as:
\[x = \dfrac{{{n_{C{O_2}}}}}{{{n_{{H_2}O}}}}\]
\[1.52 \times {10^{ - 3}} = \dfrac{{{n_{C{O_2}}}}}{{27.78}}\]
\[{n_{C{O_2}}} = 0.042\] moles.
The number of moles of the carbon dioxide is 0.042 moles.
So, the correct answer is “Option D”.

Note: We have to remember that Henry’s law has certain limitations.
- Henry’s law is not applicable when gases are kept under extremely high pressure.
- when the chemical reaction takes place between the gas and the solution, then Henry's law is not applicable.
- When the molecules are said to be in a state of equilibrium, then Henry's law will be applicable.