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Question: Henry’s law constant of oxygen is \(1.4\times {{10}^{-3}}mol{{L}^{-1}}at{{m}^{-1}}\) at \(298K\). Ho...

Henry’s law constant of oxygen is 1.4×10−3molL−1atm−11.4\times {{10}^{-3}}mol{{L}^{-1}}at{{m}^{-1}} at 298K298K. How much oxygen is dissolved in 100mL100mL at 298K298K when the partial pressure of the oxygen is 0.5atm0.5atm ?
A) 1.4g1.4g
B) 3.2g3.2g
C) 22.4mg22.4mg
D) 2.24mg2.24mg

Explanation

Solution

Henry's law gives a measure of the solubility of the gases in liquid in terms of partial pressure. The amount of a gas present in a solution can be calculated by using the value of henry’s law constant and the partial pressure, where we first determine the solubility.
And then we determine the number of moles of that gas present in a specific amount of volume which is being asked in the question. After that we calculate the amount or the weight of the gas using the number of moles, just by multiplying it with the mass of that gas.

Complete answer:
In physical chemistry, Henry's law is a gas law that states that the amount of dissolved gas in a liquid is proportional to its partial pressure above the liquid. The proportionality factor is called Henry's law constant. The formula which we will use in order to determine the solubility of oxygen, is,
S=KHpS={{K}_{H}}p
Where SS is the solubility of the gas in that solution, KH{{K}_{H}} is the henry’s law constant and the pp is the partial pressure of the gas in the solution.
The solubility can be calculated by this equation as the value of Henry’s law constant and the value of partial pressure of the oxygen is given as 1.4×10−3molL−1atm−11.4\times {{10}^{-3}}mol{{L}^{-1}}at{{m}^{-1}} and 0.5atm0.5atm respectively.
After putting these values in the equation, the equation becomes
S=1.4×10−3molL−1atm−1×0.5atmS=1.4\times {{10}^{-3}}mol{{L}^{-1}}at{{m}^{-1}}\times 0.5atm
For a 100mL100mL the number of moles of oxygen present would be
n=1.4×10−3molL−1atm−1×0.5atm×1001000Ln=1.4\times {{10}^{-3}}mol{{L}^{-1}}at{{m}^{-1}}\times 0.5atm\times \dfrac{100}{1000}L
Now after calculating, the number of moles of oxygen came out to be n=7×10−5moln=7\times {{10}^{-5}}mol.
Now the weight or the amount of oxygen which is dissolved in the solution, in gram per mole would be,
W=7×10−5mol×32gW=7\times {{10}^{-5}}mol\times 32g
Where, WW is the weight of oxygen, and molecular mass of oxygen is 32g32g. So, after solving this equation we get, 2.24×10−3g2.24\times {{10}^{-3}}g which would be 2.24mg2.24mg in terms of milligram.

Hence the correct option would be option D.

Note: By the application of Henry’s law, we are able to determine the solubility of oxygen in the solution, just by using the given values of henry’s law constant and the partial pressure of oxygen.Then using this value of solubility, we find out the number of moles of oxygen present in 100L100L of solution. And then using this value we found out the amount of oxygen dissolved in the solution, just by multiplying the number of moles of oxygen with the mass of oxygen.