Question

How much oxygen is dissolved in 100mL water if partial pressure of oxygen is 0.5 atm and ${{K}_{H}}=1.4\times {{10}^{-3}}mol/L/atm$
[A] 22.4mg
[B] 22.4g
[C] 2.24g
[D] 2.24mg

Answer 1

Hint: To solve this, firstly find out the concentration of oxygen using the Henry’s law of partial pressure. Then use the formula of molarity to find out the number of moles of oxygen dissolved per litre of the solvent. Multiply the number of moles by the molecular mass of oxygen to get the final answer.

Complete step by step answer:
Here, we have oxygen which is a gas dissolved in water, a liquid so to find the amount of oxygen in water we can use Henry's law. Henry’s law states that-“The mass of a gas dissolved per unit volume of a solvent for a given temperature is directly proportional to its partial pressure of the gas at equilibrium.” Symbolically, we can write that-
     \[s={{K}_{H}}\times p\]
Where, ‘s’ is the concentration of the gas dissolved, ‘p’ is the partial pressure and ${{K}_{H}}$ is Henry's law constant.
From the question we know the partial pressure and the value of Henry’s law constant. Therefore, using that we can find out the concentration of oxygen.

We can write that-
$s={{K}_{H}}=1.4\times {{10}^{-3}}mol/L/atm\times 0.5atm=0.7\times {{10}^{-3}}mol/L$
Now we know the concentration as well as the volume so we can use the formula of molarity to find out the number of moles of oxygen in the given volume of water, where molarity is the concentration that we have calculated above.
As we know molarity is the number of moles of solute per litre of the solvent. So we can write that-
\[no.of\text{ moles of solute=molarity}\times volume\text{ of solvent(L)}\]
The volume of solvent is given to us as 100mL which is 0.1L.
Therefore, \[no.of\text{ moles of solute=0}\text{.7}\times \text{1}{{\text{0}}^{-3}}mol/L\times 0.1L=7\times {{10}^{-5}}mol\]

Now, we know the molecular mass of a molecule of oxygen is 32g/mol.
Therefore, mass of oxygen is $7\times {{10}^{-5}}mol\times 32g/mol=2.24\times {{10}^{-3}}g$
As we can see it matches none of the options in grams so let us convert it into milligram by multiplying it by 1000.
So, we will get 2.24 mg i.e. 2.24 mg of oxygen was dissolved in 100 mL of water.
So, the correct answer is “Option D”.

Note: We have used Henry’s law here to solve this problem but this law does not hold true under certain conditions. It is not applicable at very high pressure and very low temperature. It is also not applicable if the gas reacts chemically with the solvent or dissociates in it.